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 // Copyright 2008 John Maddock
 //
 // Use, modification and distribution are subject to the
 // Boost Software License, Version 1.0.
 // (See accompanying file LICENSE_1_0.txt
 // or copy at http://www.boost.org/LICENSE_1_0.txt)
 
 #ifndef BOOST_MATH_SF_PRIME_HPP
 #define BOOST_MATH_SF_PRIME_HPP
 
 #include <boost/math/policies/error_handling.hpp>
 #include <boost/math/special_functions/math_fwd.hpp>
 #include <array>
 #include <cstdint>
 
 namespace boost{ namespace math{
 
    //
    // See https://github.com/boostorg/math/issues/923 for the reasons behind using struct's here:
    //
    template <bool>
    struct prime_data_imp
    {
       //
       // This is basically three big tables which together
       // occupy 19946 bytes, we use the smallest type which
       // will handle each value, and store the final set of 
       // values in a uint16_t with the values offset by 0xffff.
       // That gives us the first 10000 primes with the largest
       // being 104729:
       //
 #ifndef BOOST_MATH_HAVE_CONSTEXPR_TABLES
       static const unsigned b1 = 53;
       static const unsigned b2 = 6541;
       static const unsigned b3 = 10000;
       static const std::array<unsigned char, 54> a1;
       static const std::array<std::uint16_t, 6488> a2;
       static const std::array<std::uint16_t, 3458> a3;
 #else
       static constexpr unsigned b1 = 53;
       static constexpr unsigned b2 = 6541;
       static constexpr unsigned b3 = 10000;
       static constexpr std::array<unsigned char, 54> a1 = { {
          2u, 3u, 5u, 7u, 11u, 13u, 17u, 19u, 23u, 29u, 31u,
          37u, 41u, 43u, 47u, 53u, 59u, 61u, 67u, 71u, 73u,
          79u, 83u, 89u, 97u, 101u, 103u, 107u, 109u, 113u,
          127u, 131u, 137u, 139u, 149u, 151u, 157u, 163u,
          167u, 173u, 179u, 181u, 191u, 193u, 197u, 199u,
          211u, 223u, 227u, 229u, 233u, 239u, 241u, 251u
       }};
       static constexpr std::array<std::uint16_t, 6488> a2 = {{
          257u, 263u, 269u, 271u, 277u, 281u, 283u, 293u,
          307u, 311u, 313u, 317u, 331u, 337u, 347u, 349u, 353u,
          359u, 367u, 373u, 379u, 383u, 389u, 397u, 401u, 409u,
          419u, 421u, 431u, 433u, 439u, 443u, 449u, 457u, 461u,
          463u, 467u, 479u, 487u, 491u, 499u, 503u, 509u, 521u,
          523u, 541u, 547u, 557u, 563u, 569u, 571u, 577u, 587u,
          593u, 599u, 601u, 607u, 613u, 617u, 619u, 631u, 641u,
          643u, 647u, 653u, 659u, 661u, 673u, 677u, 683u, 691u,
          701u, 709u, 719u, 727u, 733u, 739u, 743u, 751u, 757u,
          761u, 769u, 773u, 787u, 797u, 809u, 811u, 821u, 823u,
          827u, 829u, 839u, 853u, 857u, 859u, 863u, 877u, 881u,
          883u, 887u, 907u, 911u, 919u, 929u, 937u, 941u, 947u,
          953u, 967u, 971u, 977u, 983u, 991u, 997u, 1009u, 1013u,
          1019u, 1021u, 1031u, 1033u, 1039u, 1049u, 1051u, 1061u, 1063u,
          1069u, 1087u, 1091u, 1093u, 1097u, 1103u, 1109u, 1117u, 1123u,
          1129u, 1151u, 1153u, 1163u, 1171u, 1181u, 1187u, 1193u, 1201u,
          1213u, 1217u, 1223u, 1229u, 1231u, 1237u, 1249u, 1259u, 1277u,
          1279u, 1283u, 1289u, 1291u, 1297u, 1301u, 1303u, 1307u, 1319u,
          1321u, 1327u, 1361u, 1367u, 1373u, 1381u, 1399u, 1409u, 1423u,
          1427u, 1429u, 1433u, 1439u, 1447u, 1451u, 1453u, 1459u, 1471u,
          1481u, 1483u, 1487u, 1489u, 1493u, 1499u, 1511u, 1523u, 1531u,
          1543u, 1549u, 1553u, 1559u, 1567u, 1571u, 1579u, 1583u, 1597u,
          1601u, 1607u, 1609u, 1613u, 1619u, 1621u, 1627u, 1637u, 1657u,
          1663u, 1667u, 1669u, 1693u, 1697u, 1699u, 1709u, 1721u, 1723u,
          1733u, 1741u, 1747u, 1753u, 1759u, 1777u, 1783u, 1787u, 1789u,
          1801u, 1811u, 1823u, 1831u, 1847u, 1861u, 1867u, 1871u, 1873u,
          1877u, 1879u, 1889u, 1901u, 1907u, 1913u, 1931u, 1933u, 1949u,
          1951u, 1973u, 1979u, 1987u, 1993u, 1997u, 1999u, 2003u, 2011u,
          2017u, 2027u, 2029u, 2039u, 2053u, 2063u, 2069u, 2081u, 2083u,
          2087u, 2089u, 2099u, 2111u, 2113u, 2129u, 2131u, 2137u, 2141u,
          2143u, 2153u, 2161u, 2179u, 2203u, 2207u, 2213u, 2221u, 2237u,
          2239u, 2243u, 2251u, 2267u, 2269u, 2273u, 2281u, 2287u, 2293u,
          2297u, 2309u, 2311u, 2333u, 2339u, 2341u, 2347u, 2351u, 2357u,
          2371u, 2377u, 2381u, 2383u, 2389u, 2393u, 2399u, 2411u, 2417u,
          2423u, 2437u, 2441u, 2447u, 2459u, 2467u, 2473u, 2477u, 2503u,
          2521u, 2531u, 2539u, 2543u, 2549u, 2551u, 2557u, 2579u, 2591u,
          2593u, 2609u, 2617u, 2621u, 2633u, 2647u, 2657u, 2659u, 2663u,
          2671u, 2677u, 2683u, 2687u, 2689u, 2693u, 2699u, 2707u, 2711u,
          2713u, 2719u, 2729u, 2731u, 2741u, 2749u, 2753u, 2767u, 2777u,
          2789u, 2791u, 2797u, 2801u, 2803u, 2819u, 2833u, 2837u, 2843u,
          2851u, 2857u, 2861u, 2879u, 2887u, 2897u, 2903u, 2909u, 2917u,
          2927u, 2939u, 2953u, 2957u, 2963u, 2969u, 2971u, 2999u, 3001u,
          3011u, 3019u, 3023u, 3037u, 3041u, 3049u, 3061u, 3067u, 3079u,
          3083u, 3089u, 3109u, 3119u, 3121u, 3137u, 3163u, 3167u, 3169u,
          3181u, 3187u, 3191u, 3203u, 3209u, 3217u, 3221u, 3229u, 3251u,
          3253u, 3257u, 3259u, 3271u, 3299u, 3301u, 3307u, 3313u, 3319u,
          3323u, 3329u, 3331u, 3343u, 3347u, 3359u, 3361u, 3371u, 3373u,
          3389u, 3391u, 3407u, 3413u, 3433u, 3449u, 3457u, 3461u, 3463u,
          3467u, 3469u, 3491u, 3499u, 3511u, 3517u, 3527u, 3529u, 3533u,
          3539u, 3541u, 3547u, 3557u, 3559u, 3571u, 3581u, 3583u, 3593u,
          3607u, 3613u, 3617u, 3623u, 3631u, 3637u, 3643u, 3659u, 3671u,
          3673u, 3677u, 3691u, 3697u, 3701u, 3709u, 3719u, 3727u, 3733u,
          3739u, 3761u, 3767u, 3769u, 3779u, 3793u, 3797u, 3803u, 3821u,
          3823u, 3833u, 3847u, 3851u, 3853u, 3863u, 3877u, 3881u, 3889u,
          3907u, 3911u, 3917u, 3919u, 3923u, 3929u, 3931u, 3943u, 3947u,
          3967u, 3989u, 4001u, 4003u, 4007u, 4013u, 4019u, 4021u, 4027u,
          4049u, 4051u, 4057u, 4073u, 4079u, 4091u, 4093u, 4099u, 4111u,
          4127u, 4129u, 4133u, 4139u, 4153u, 4157u, 4159u, 4177u, 4201u,
          4211u, 4217u, 4219u, 4229u, 4231u, 4241u, 4243u, 4253u, 4259u,
          4261u, 4271u, 4273u, 4283u, 4289u, 4297u, 4327u, 4337u, 4339u,
          4349u, 4357u, 4363u, 4373u, 4391u, 4397u, 4409u, 4421u, 4423u,
          4441u, 4447u, 4451u, 4457u, 4463u, 4481u, 4483u, 4493u, 4507u,
          4513u, 4517u, 4519u, 4523u, 4547u, 4549u, 4561u, 4567u, 4583u,
          4591u, 4597u, 4603u, 4621u, 4637u, 4639u, 4643u, 4649u, 4651u,
          4657u, 4663u, 4673u, 4679u, 4691u, 4703u, 4721u, 4723u, 4729u,
          4733u, 4751u, 4759u, 4783u, 4787u, 4789u, 4793u, 4799u, 4801u,
          4813u, 4817u, 4831u, 4861u, 4871u, 4877u, 4889u, 4903u, 4909u,
          4919u, 4931u, 4933u, 4937u, 4943u, 4951u, 4957u, 4967u, 4969u,
          4973u, 4987u, 4993u, 4999u, 5003u, 5009u, 5011u, 5021u, 5023u,
          5039u, 5051u, 5059u, 5077u, 5081u, 5087u, 5099u, 5101u, 5107u,
          5113u, 5119u, 5147u, 5153u, 5167u, 5171u, 5179u, 5189u, 5197u,
          5209u, 5227u, 5231u, 5233u, 5237u, 5261u, 5273u, 5279u, 5281u,
          5297u, 5303u, 5309u, 5323u, 5333u, 5347u, 5351u, 5381u, 5387u,
          5393u, 5399u, 5407u, 5413u, 5417u, 5419u, 5431u, 5437u, 5441u,
          5443u, 5449u, 5471u, 5477u, 5479u, 5483u, 5501u, 5503u, 5507u,
          5519u, 5521u, 5527u, 5531u, 5557u, 5563u, 5569u, 5573u, 5581u,
          5591u, 5623u, 5639u, 5641u, 5647u, 5651u, 5653u, 5657u, 5659u,
          5669u, 5683u, 5689u, 5693u, 5701u, 5711u, 5717u, 5737u, 5741u,
          5743u, 5749u, 5779u, 5783u, 5791u, 5801u, 5807u, 5813u, 5821u,
          5827u, 5839u, 5843u, 5849u, 5851u, 5857u, 5861u, 5867u, 5869u,
          5879u, 5881u, 5897u, 5903u, 5923u, 5927u, 5939u, 5953u, 5981u,
          5987u, 6007u, 6011u, 6029u, 6037u, 6043u, 6047u, 6053u, 6067u,
          6073u, 6079u, 6089u, 6091u, 6101u, 6113u, 6121u, 6131u, 6133u,
          6143u, 6151u, 6163u, 6173u, 6197u, 6199u, 6203u, 6211u, 6217u,
          6221u, 6229u, 6247u, 6257u, 6263u, 6269u, 6271u, 6277u, 6287u,
          6299u, 6301u, 6311u, 6317u, 6323u, 6329u, 6337u, 6343u, 6353u,
          6359u, 6361u, 6367u, 6373u, 6379u, 6389u, 6397u, 6421u, 6427u,
          6449u, 6451u, 6469u, 6473u, 6481u, 6491u, 6521u, 6529u, 6547u,
          6551u, 6553u, 6563u, 6569u, 6571u, 6577u, 6581u, 6599u, 6607u,
          6619u, 6637u, 6653u, 6659u, 6661u, 6673u, 6679u, 6689u, 6691u,
          6701u, 6703u, 6709u, 6719u, 6733u, 6737u, 6761u, 6763u, 6779u,
          6781u, 6791u, 6793u, 6803u, 6823u, 6827u, 6829u, 6833u, 6841u,
          6857u, 6863u, 6869u, 6871u, 6883u, 6899u, 6907u, 6911u, 6917u,
          6947u, 6949u, 6959u, 6961u, 6967u, 6971u, 6977u, 6983u, 6991u,
          6997u, 7001u, 7013u, 7019u, 7027u, 7039u, 7043u, 7057u, 7069u,
          7079u, 7103u, 7109u, 7121u, 7127u, 7129u, 7151u, 7159u, 7177u,
          7187u, 7193u, 7207u, 7211u, 7213u, 7219u, 7229u, 7237u, 7243u,
          7247u, 7253u, 7283u, 7297u, 7307u, 7309u, 7321u, 7331u, 7333u,
          7349u, 7351u, 7369u, 7393u, 7411u, 7417u, 7433u, 7451u, 7457u,
          7459u, 7477u, 7481u, 7487u, 7489u, 7499u, 7507u, 7517u, 7523u,
          7529u, 7537u, 7541u, 7547u, 7549u, 7559u, 7561u, 7573u, 7577u,
          7583u, 7589u, 7591u, 7603u, 7607u, 7621u, 7639u, 7643u, 7649u,
          7669u, 7673u, 7681u, 7687u, 7691u, 7699u, 7703u, 7717u, 7723u,
          7727u, 7741u, 7753u, 7757u, 7759u, 7789u, 7793u, 7817u, 7823u,
          7829u, 7841u, 7853u, 7867u, 7873u, 7877u, 7879u, 7883u, 7901u,
          7907u, 7919u, 7927u, 7933u, 7937u, 7949u, 7951u, 7963u, 7993u,
          8009u, 8011u, 8017u, 8039u, 8053u, 8059u, 8069u, 8081u, 8087u,
          8089u, 8093u, 8101u, 8111u, 8117u, 8123u, 8147u, 8161u, 8167u,
          8171u, 8179u, 8191u, 8209u, 8219u, 8221u, 8231u, 8233u, 8237u,
          8243u, 8263u, 8269u, 8273u, 8287u, 8291u, 8293u, 8297u, 8311u,
          8317u, 8329u, 8353u, 8363u, 8369u, 8377u, 8387u, 8389u, 8419u,
          8423u, 8429u, 8431u, 8443u, 8447u, 8461u, 8467u, 8501u, 8513u,
          8521u, 8527u, 8537u, 8539u, 8543u, 8563u, 8573u, 8581u, 8597u,
          8599u, 8609u, 8623u, 8627u, 8629u, 8641u, 8647u, 8663u, 8669u,
          8677u, 8681u, 8689u, 8693u, 8699u, 8707u, 8713u, 8719u, 8731u,
          8737u, 8741u, 8747u, 8753u, 8761u, 8779u, 8783u, 8803u, 8807u,
          8819u, 8821u, 8831u, 8837u, 8839u, 8849u, 8861u, 8863u, 8867u,
          8887u, 8893u, 8923u, 8929u, 8933u, 8941u, 8951u, 8963u, 8969u,
          8971u, 8999u, 9001u, 9007u, 9011u, 9013u, 9029u, 9041u, 9043u,
          9049u, 9059u, 9067u, 9091u, 9103u, 9109u, 9127u, 9133u, 9137u,
          9151u, 9157u, 9161u, 9173u, 9181u, 9187u, 9199u, 9203u, 9209u,
          9221u, 9227u, 9239u, 9241u, 9257u, 9277u, 9281u, 9283u, 9293u,
          9311u, 9319u, 9323u, 9337u, 9341u, 9343u, 9349u, 9371u, 9377u,
          9391u, 9397u, 9403u, 9413u, 9419u, 9421u, 9431u, 9433u, 9437u,
          9439u, 9461u, 9463u, 9467u, 9473u, 9479u, 9491u, 9497u, 9511u,
          9521u, 9533u, 9539u, 9547u, 9551u, 9587u, 9601u, 9613u, 9619u,
          9623u, 9629u, 9631u, 9643u, 9649u, 9661u, 9677u, 9679u, 9689u,
          9697u, 9719u, 9721u, 9733u, 9739u, 9743u, 9749u, 9767u, 9769u,
          9781u, 9787u, 9791u, 9803u, 9811u, 9817u, 9829u, 9833u, 9839u,
          9851u, 9857u, 9859u, 9871u, 9883u, 9887u, 9901u, 9907u, 9923u,
          9929u, 9931u, 9941u, 9949u, 9967u, 9973u, 10007u, 10009u, 10037u,
          10039u, 10061u, 10067u, 10069u, 10079u, 10091u, 10093u, 10099u, 10103u,
          10111u, 10133u, 10139u, 10141u, 10151u, 10159u, 10163u, 10169u, 10177u,
          10181u, 10193u, 10211u, 10223u, 10243u, 10247u, 10253u, 10259u, 10267u,
          10271u, 10273u, 10289u, 10301u, 10303u, 10313u, 10321u, 10331u, 10333u,
          10337u, 10343u, 10357u, 10369u, 10391u, 10399u, 10427u, 10429u, 10433u,
          10453u, 10457u, 10459u, 10463u, 10477u, 10487u, 10499u, 10501u, 10513u,
          10529u, 10531u, 10559u, 10567u, 10589u, 10597u, 10601u, 10607u, 10613u,
          10627u, 10631u, 10639u, 10651u, 10657u, 10663u, 10667u, 10687u, 10691u,
          10709u, 10711u, 10723u, 10729u, 10733u, 10739u, 10753u, 10771u, 10781u,
          10789u, 10799u, 10831u, 10837u, 10847u, 10853u, 10859u, 10861u, 10867u,
          10883u, 10889u, 10891u, 10903u, 10909u, 10937u, 10939u, 10949u, 10957u,
          10973u, 10979u, 10987u, 10993u, 11003u, 11027u, 11047u, 11057u, 11059u,
          11069u, 11071u, 11083u, 11087u, 11093u, 11113u, 11117u, 11119u, 11131u,
          11149u, 11159u, 11161u, 11171u, 11173u, 11177u, 11197u, 11213u, 11239u,
          11243u, 11251u, 11257u, 11261u, 11273u, 11279u, 11287u, 11299u, 11311u,
          11317u, 11321u, 11329u, 11351u, 11353u, 11369u, 11383u, 11393u, 11399u,
          11411u, 11423u, 11437u, 11443u, 11447u, 11467u, 11471u, 11483u, 11489u,
          11491u, 11497u, 11503u, 11519u, 11527u, 11549u, 11551u, 11579u, 11587u,
          11593u, 11597u, 11617u, 11621u, 11633u, 11657u, 11677u, 11681u, 11689u,
          11699u, 11701u, 11717u, 11719u, 11731u, 11743u, 11777u, 11779u, 11783u,
          11789u, 11801u, 11807u, 11813u, 11821u, 11827u, 11831u, 11833u, 11839u,
          11863u, 11867u, 11887u, 11897u, 11903u, 11909u, 11923u, 11927u, 11933u,
          11939u, 11941u, 11953u, 11959u, 11969u, 11971u, 11981u, 11987u, 12007u,
          12011u, 12037u, 12041u, 12043u, 12049u, 12071u, 12073u, 12097u, 12101u,
          12107u, 12109u, 12113u, 12119u, 12143u, 12149u, 12157u, 12161u, 12163u,
          12197u, 12203u, 12211u, 12227u, 12239u, 12241u, 12251u, 12253u, 12263u,
          12269u, 12277u, 12281u, 12289u, 12301u, 12323u, 12329u, 12343u, 12347u,
          12373u, 12377u, 12379u, 12391u, 12401u, 12409u, 12413u, 12421u, 12433u,
          12437u, 12451u, 12457u, 12473u, 12479u, 12487u, 12491u, 12497u, 12503u,
          12511u, 12517u, 12527u, 12539u, 12541u, 12547u, 12553u, 12569u, 12577u,
          12583u, 12589u, 12601u, 12611u, 12613u, 12619u, 12637u, 12641u, 12647u,
          12653u, 12659u, 12671u, 12689u, 12697u, 12703u, 12713u, 12721u, 12739u,
          12743u, 12757u, 12763u, 12781u, 12791u, 12799u, 12809u, 12821u, 12823u,
          12829u, 12841u, 12853u, 12889u, 12893u, 12899u, 12907u, 12911u, 12917u,
          12919u, 12923u, 12941u, 12953u, 12959u, 12967u, 12973u, 12979u, 12983u,
          13001u, 13003u, 13007u, 13009u, 13033u, 13037u, 13043u, 13049u, 13063u,
          13093u, 13099u, 13103u, 13109u, 13121u, 13127u, 13147u, 13151u, 13159u,
          13163u, 13171u, 13177u, 13183u, 13187u, 13217u, 13219u, 13229u, 13241u,
          13249u, 13259u, 13267u, 13291u, 13297u, 13309u, 13313u, 13327u, 13331u,
          13337u, 13339u, 13367u, 13381u, 13397u, 13399u, 13411u, 13417u, 13421u,
          13441u, 13451u, 13457u, 13463u, 13469u, 13477u, 13487u, 13499u, 13513u,
          13523u, 13537u, 13553u, 13567u, 13577u, 13591u, 13597u, 13613u, 13619u,
          13627u, 13633u, 13649u, 13669u, 13679u, 13681u, 13687u, 13691u, 13693u,
          13697u, 13709u, 13711u, 13721u, 13723u, 13729u, 13751u, 13757u, 13759u,
          13763u, 13781u, 13789u, 13799u, 13807u, 13829u, 13831u, 13841u, 13859u,
          13873u, 13877u, 13879u, 13883u, 13901u, 13903u, 13907u, 13913u, 13921u,
          13931u, 13933u, 13963u, 13967u, 13997u, 13999u, 14009u, 14011u, 14029u,
          14033u, 14051u, 14057u, 14071u, 14081u, 14083u, 14087u, 14107u, 14143u,
          14149u, 14153u, 14159u, 14173u, 14177u, 14197u, 14207u, 14221u, 14243u,
          14249u, 14251u, 14281u, 14293u, 14303u, 14321u, 14323u, 14327u, 14341u,
          14347u, 14369u, 14387u, 14389u, 14401u, 14407u, 14411u, 14419u, 14423u,
          14431u, 14437u, 14447u, 14449u, 14461u, 14479u, 14489u, 14503u, 14519u,
          14533u, 14537u, 14543u, 14549u, 14551u, 14557u, 14561u, 14563u, 14591u,
          14593u, 14621u, 14627u, 14629u, 14633u, 14639u, 14653u, 14657u, 14669u,
          14683u, 14699u, 14713u, 14717u, 14723u, 14731u, 14737u, 14741u, 14747u,
          14753u, 14759u, 14767u, 14771u, 14779u, 14783u, 14797u, 14813u, 14821u,
          14827u, 14831u, 14843u, 14851u, 14867u, 14869u, 14879u, 14887u, 14891u,
          14897u, 14923u, 14929u, 14939u, 14947u, 14951u, 14957u, 14969u, 14983u,
          15013u, 15017u, 15031u, 15053u, 15061u, 15073u, 15077u, 15083u, 15091u,
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          53987u, 53993u, 54001u, 54011u, 54013u, 54037u, 54049u, 54059u, 54083u,
          54091u, 54101u, 54121u, 54133u, 54139u, 54151u, 54163u, 54167u, 54181u,
          54193u, 54217u, 54251u, 54269u, 54277u, 54287u, 54293u, 54311u, 54319u,
          54323u, 54331u, 54347u, 54361u, 54367u, 54371u, 54377u, 54401u, 54403u,
          54409u, 54413u, 54419u, 54421u, 54437u, 54443u, 54449u, 54469u, 54493u,
          54497u, 54499u, 54503u, 54517u, 54521u, 54539u, 54541u, 54547u, 54559u,
          54563u, 54577u, 54581u, 54583u, 54601u, 54617u, 54623u, 54629u, 54631u,
          54647u, 54667u, 54673u, 54679u, 54709u, 54713u, 54721u, 54727u, 54751u,
          54767u, 54773u, 54779u, 54787u, 54799u, 54829u, 54833u, 54851u, 54869u,
          54877u, 54881u, 54907u, 54917u, 54919u, 54941u, 54949u, 54959u, 54973u,
          54979u, 54983u, 55001u, 55009u, 55021u, 55049u, 55051u, 55057u, 55061u,
          55073u, 55079u, 55103u, 55109u, 55117u, 55127u, 55147u, 55163u, 55171u,
          55201u, 55207u, 55213u, 55217u, 55219u, 55229u, 55243u, 55249u, 55259u,
          55291u, 55313u, 55331u, 55333u, 55337u, 55339u, 55343u, 55351u, 55373u,
          55381u, 55399u, 55411u, 55439u, 55441u, 55457u, 55469u, 55487u, 55501u,
          55511u, 55529u, 55541u, 55547u, 55579u, 55589u, 55603u, 55609u, 55619u,
          55621u, 55631u, 55633u, 55639u, 55661u, 55663u, 55667u, 55673u, 55681u,
          55691u, 55697u, 55711u, 55717u, 55721u, 55733u, 55763u, 55787u, 55793u,
          55799u, 55807u, 55813u, 55817u, 55819u, 55823u, 55829u, 55837u, 55843u,
          55849u, 55871u, 55889u, 55897u, 55901u, 55903u, 55921u, 55927u, 55931u,
          55933u, 55949u, 55967u, 55987u, 55997u, 56003u, 56009u, 56039u, 56041u,
          56053u, 56081u, 56087u, 56093u, 56099u, 56101u, 56113u, 56123u, 56131u,
          56149u, 56167u, 56171u, 56179u, 56197u, 56207u, 56209u, 56237u, 56239u,
          56249u, 56263u, 56267u, 56269u, 56299u, 56311u, 56333u, 56359u, 56369u,
          56377u, 56383u, 56393u, 56401u, 56417u, 56431u, 56437u, 56443u, 56453u,
          56467u, 56473u, 56477u, 56479u, 56489u, 56501u, 56503u, 56509u, 56519u,
          56527u, 56531u, 56533u, 56543u, 56569u, 56591u, 56597u, 56599u, 56611u,
          56629u, 56633u, 56659u, 56663u, 56671u, 56681u, 56687u, 56701u, 56711u,
          56713u, 56731u, 56737u, 56747u, 56767u, 56773u, 56779u, 56783u, 56807u,
          56809u, 56813u, 56821u, 56827u, 56843u, 56857u, 56873u, 56891u, 56893u,
          56897u, 56909u, 56911u, 56921u, 56923u, 56929u, 56941u, 56951u, 56957u,
          56963u, 56983u, 56989u, 56993u, 56999u, 57037u, 57041u, 57047u, 57059u,
          57073u, 57077u, 57089u, 57097u, 57107u, 57119u, 57131u, 57139u, 57143u,
          57149u, 57163u, 57173u, 57179u, 57191u, 57193u, 57203u, 57221u, 57223u,
          57241u, 57251u, 57259u, 57269u, 57271u, 57283u, 57287u, 57301u, 57329u,
          57331u, 57347u, 57349u, 57367u, 57373u, 57383u, 57389u, 57397u, 57413u,
          57427u, 57457u, 57467u, 57487u, 57493u, 57503u, 57527u, 57529u, 57557u,
          57559u, 57571u, 57587u, 57593u, 57601u, 57637u, 57641u, 57649u, 57653u,
          57667u, 57679u, 57689u, 57697u, 57709u, 57713u, 57719u, 57727u, 57731u,
          57737u, 57751u, 57773u, 57781u, 57787u, 57791u, 57793u, 57803u, 57809u,
          57829u, 57839u, 57847u, 57853u, 57859u, 57881u, 57899u, 57901u, 57917u,
          57923u, 57943u, 57947u, 57973u, 57977u, 57991u, 58013u, 58027u, 58031u,
          58043u, 58049u, 58057u, 58061u, 58067u, 58073u, 58099u, 58109u, 58111u,
          58129u, 58147u, 58151u, 58153u, 58169u, 58171u, 58189u, 58193u, 58199u,
          58207u, 58211u, 58217u, 58229u, 58231u, 58237u, 58243u, 58271u, 58309u,
          58313u, 58321u, 58337u, 58363u, 58367u, 58369u, 58379u, 58391u, 58393u,
          58403u, 58411u, 58417u, 58427u, 58439u, 58441u, 58451u, 58453u, 58477u,
          58481u, 58511u, 58537u, 58543u, 58549u, 58567u, 58573u, 58579u, 58601u,
          58603u, 58613u, 58631u, 58657u, 58661u, 58679u, 58687u, 58693u, 58699u,
          58711u, 58727u, 58733u, 58741u, 58757u, 58763u, 58771u, 58787u, 58789u,
          58831u, 58889u, 58897u, 58901u, 58907u, 58909u, 58913u, 58921u, 58937u,
          58943u, 58963u, 58967u, 58979u, 58991u, 58997u, 59009u, 59011u, 59021u,
          59023u, 59029u, 59051u, 59053u, 59063u, 59069u, 59077u, 59083u, 59093u,
          59107u, 59113u, 59119u, 59123u, 59141u, 59149u, 59159u, 59167u, 59183u,
          59197u, 59207u, 59209u, 59219u, 59221u, 59233u, 59239u, 59243u, 59263u,
          59273u, 59281u, 59333u, 59341u, 59351u, 59357u, 59359u, 59369u, 59377u,
          59387u, 59393u, 59399u, 59407u, 59417u, 59419u, 59441u, 59443u, 59447u,
          59453u, 59467u, 59471u, 59473u, 59497u, 59509u, 59513u, 59539u, 59557u,
          59561u, 59567u, 59581u, 59611u, 59617u, 59621u, 59627u, 59629u, 59651u,
          59659u, 59663u, 59669u, 59671u, 59693u, 59699u, 59707u, 59723u, 59729u,
          59743u, 59747u, 59753u, 59771u, 59779u, 59791u, 59797u, 59809u, 59833u,
          59863u, 59879u, 59887u, 59921u, 59929u, 59951u, 59957u, 59971u, 59981u,
          59999u, 60013u, 60017u, 60029u, 60037u, 60041u, 60077u, 60083u, 60089u,
          60091u, 60101u, 60103u, 60107u, 60127u, 60133u, 60139u, 60149u, 60161u,
          60167u, 60169u, 60209u, 60217u, 60223u, 60251u, 60257u, 60259u, 60271u,
          60289u, 60293u, 60317u, 60331u, 60337u, 60343u, 60353u, 60373u, 60383u,
          60397u, 60413u, 60427u, 60443u, 60449u, 60457u, 60493u, 60497u, 60509u,
          60521u, 60527u, 60539u, 60589u, 60601u, 60607u, 60611u, 60617u, 60623u,
          60631u, 60637u, 60647u, 60649u, 60659u, 60661u, 60679u, 60689u, 60703u,
          60719u, 60727u, 60733u, 60737u, 60757u, 60761u, 60763u, 60773u, 60779u,
          60793u, 60811u, 60821u, 60859u, 60869u, 60887u, 60889u, 60899u, 60901u,
          60913u, 60917u, 60919u, 60923u, 60937u, 60943u, 60953u, 60961u, 61001u,
          61007u, 61027u, 61031u, 61043u, 61051u, 61057u, 61091u, 61099u, 61121u,
          61129u, 61141u, 61151u, 61153u, 61169u, 61211u, 61223u, 61231u, 61253u,
          61261u, 61283u, 61291u, 61297u, 61331u, 61333u, 61339u, 61343u, 61357u,
          61363u, 61379u, 61381u, 61403u, 61409u, 61417u, 61441u, 61463u, 61469u,
          61471u, 61483u, 61487u, 61493u, 61507u, 61511u, 61519u, 61543u, 61547u,
          61553u, 61559u, 61561u, 61583u, 61603u, 61609u, 61613u, 61627u, 61631u,
          61637u, 61643u, 61651u, 61657u, 61667u, 61673u, 61681u, 61687u, 61703u,
          61717u, 61723u, 61729u, 61751u, 61757u, 61781u, 61813u, 61819u, 61837u,
          61843u, 61861u, 61871u, 61879u, 61909u, 61927u, 61933u, 61949u, 61961u,
          61967u, 61979u, 61981u, 61987u, 61991u, 62003u, 62011u, 62017u, 62039u,
          62047u, 62053u, 62057u, 62071u, 62081u, 62099u, 62119u, 62129u, 62131u,
          62137u, 62141u, 62143u, 62171u, 62189u, 62191u, 62201u, 62207u, 62213u,
          62219u, 62233u, 62273u, 62297u, 62299u, 62303u, 62311u, 62323u, 62327u,
          62347u, 62351u, 62383u, 62401u, 62417u, 62423u, 62459u, 62467u, 62473u,
          62477u, 62483u, 62497u, 62501u, 62507u, 62533u, 62539u, 62549u, 62563u,
          62581u, 62591u, 62597u, 62603u, 62617u, 62627u, 62633u, 62639u, 62653u,
          62659u, 62683u, 62687u, 62701u, 62723u, 62731u, 62743u, 62753u, 62761u,
          62773u, 62791u, 62801u, 62819u, 62827u, 62851u, 62861u, 62869u, 62873u,
          62897u, 62903u, 62921u, 62927u, 62929u, 62939u, 62969u, 62971u, 62981u,
          62983u, 62987u, 62989u, 63029u, 63031u, 63059u, 63067u, 63073u, 63079u,
          63097u, 63103u, 63113u, 63127u, 63131u, 63149u, 63179u, 63197u, 63199u,
          63211u, 63241u, 63247u, 63277u, 63281u, 63299u, 63311u, 63313u, 63317u,
          63331u, 63337u, 63347u, 63353u, 63361u, 63367u, 63377u, 63389u, 63391u,
          63397u, 63409u, 63419u, 63421u, 63439u, 63443u, 63463u, 63467u, 63473u,
          63487u, 63493u, 63499u, 63521u, 63527u, 63533u, 63541u, 63559u, 63577u,
          63587u, 63589u, 63599u, 63601u, 63607u, 63611u, 63617u, 63629u, 63647u,
          63649u, 63659u, 63667u, 63671u, 63689u, 63691u, 63697u, 63703u, 63709u,
          63719u, 63727u, 63737u, 63743u, 63761u, 63773u, 63781u, 63793u, 63799u,
          63803u, 63809u, 63823u, 63839u, 63841u, 63853u, 63857u, 63863u, 63901u,
          63907u, 63913u, 63929u, 63949u, 63977u, 63997u, 64007u, 64013u, 64019u,
          64033u, 64037u, 64063u, 64067u, 64081u, 64091u, 64109u, 64123u, 64151u,
          64153u, 64157u, 64171u, 64187u, 64189u, 64217u, 64223u, 64231u, 64237u,
          64271u, 64279u, 64283u, 64301u, 64303u, 64319u, 64327u, 64333u, 64373u,
          64381u, 64399u, 64403u, 64433u, 64439u, 64451u, 64453u, 64483u, 64489u,
          64499u, 64513u, 64553u, 64567u, 64577u, 64579u, 64591u, 64601u, 64609u,
          64613u, 64621u, 64627u, 64633u, 64661u, 64663u, 64667u, 64679u, 64693u,
          64709u, 64717u, 64747u, 64763u, 64781u, 64783u, 64793u, 64811u, 64817u,
          64849u, 64853u, 64871u, 64877u, 64879u, 64891u, 64901u, 64919u, 64921u,
          64927u, 64937u, 64951u, 64969u, 64997u, 65003u, 65011u, 65027u, 65029u,
          65033u, 65053u, 65063u, 65071u, 65089u, 65099u, 65101u, 65111u, 65119u,
          65123u, 65129u, 65141u, 65147u, 65167u, 65171u, 65173u, 65179u, 65183u,
          65203u, 65213u, 65239u, 65257u, 65267u, 65269u, 65287u, 65293u, 65309u,
          65323u, 65327u, 65353u, 65357u, 65371u, 65381u, 65393u, 65407u, 65413u,
          65419u, 65423u, 65437u, 65447u, 65449u, 65479u, 65497u, 65519u, 65521u
       }};
       static constexpr std::array<std::uint16_t, 3458> a3 = {{
          2u, 4u, 8u, 16u, 22u, 28u, 44u,
          46u, 52u, 64u, 74u, 82u, 94u, 98u, 112u,
          116u, 122u, 142u, 152u, 164u, 166u, 172u, 178u,
          182u, 184u, 194u, 196u, 226u, 242u, 254u, 274u,
          292u, 296u, 302u, 304u, 308u, 316u, 332u, 346u,
          364u, 386u, 392u, 394u, 416u, 422u, 428u, 446u,
          448u, 458u, 494u, 502u, 506u, 512u, 532u, 536u,
          548u, 554u, 568u, 572u, 574u, 602u, 626u, 634u,
          638u, 644u, 656u, 686u, 704u, 736u, 758u, 766u,
          802u, 808u, 812u, 824u, 826u, 838u, 842u, 848u,
          868u, 878u, 896u, 914u, 922u, 928u, 932u, 956u,
          964u, 974u, 988u, 994u, 998u, 1006u, 1018u, 1034u,
          1036u, 1052u, 1058u, 1066u, 1082u, 1094u, 1108u, 1118u,
          1148u, 1162u, 1166u, 1178u, 1186u, 1198u, 1204u, 1214u,
          1216u, 1228u, 1256u, 1262u, 1274u, 1286u, 1306u, 1316u,
          1318u, 1328u, 1342u, 1348u, 1354u, 1384u, 1388u, 1396u,
          1408u, 1412u, 1414u, 1424u, 1438u, 1442u, 1468u, 1486u,
          1498u, 1508u, 1514u, 1522u, 1526u, 1538u, 1544u, 1568u,
          1586u, 1594u, 1604u, 1606u, 1618u, 1622u, 1634u, 1646u,
          1652u, 1654u, 1676u, 1678u, 1682u, 1684u, 1696u, 1712u,
          1726u, 1736u, 1738u, 1754u, 1772u, 1804u, 1808u, 1814u,
          1834u, 1856u, 1864u, 1874u, 1876u, 1886u, 1892u, 1894u,
          1898u, 1912u, 1918u, 1942u, 1946u, 1954u, 1958u, 1964u,
          1976u, 1988u, 1996u, 2002u, 2012u, 2024u, 2032u, 2042u,
          2044u, 2054u, 2066u, 2072u, 2084u, 2096u, 2116u, 2144u,
          2164u, 2174u, 2188u, 2198u, 2206u, 2216u, 2222u, 2224u,
          2228u, 2242u, 2248u, 2254u, 2266u, 2272u, 2284u, 2294u,
          2308u, 2318u, 2332u, 2348u, 2356u, 2366u, 2392u, 2396u,
          2398u, 2404u, 2408u, 2422u, 2426u, 2432u, 2444u, 2452u,
          2458u, 2488u, 2506u, 2518u, 2524u, 2536u, 2552u, 2564u,
          2576u, 2578u, 2606u, 2612u, 2626u, 2636u, 2672u, 2674u,
          2678u, 2684u, 2692u, 2704u, 2726u, 2744u, 2746u, 2776u,
          2794u, 2816u, 2836u, 2854u, 2864u, 2902u, 2908u, 2912u,
          2914u, 2938u, 2942u, 2948u, 2954u, 2956u, 2966u, 2972u,
          2986u, 2996u, 3004u, 3008u, 3032u, 3046u, 3062u, 3076u,
          3098u, 3104u, 3124u, 3134u, 3148u, 3152u, 3164u, 3176u,
          3178u, 3194u, 3202u, 3208u, 3214u, 3232u, 3236u, 3242u,
          3256u, 3278u, 3284u, 3286u, 3328u, 3344u, 3346u, 3356u,
          3362u, 3364u, 3368u, 3374u, 3382u, 3392u, 3412u, 3428u,
          3458u, 3466u, 3476u, 3484u, 3494u, 3496u, 3526u, 3532u,
          3538u, 3574u, 3584u, 3592u, 3608u, 3614u, 3616u, 3628u,
          3656u, 3658u, 3662u, 3668u, 3686u, 3698u, 3704u, 3712u,
          3722u, 3724u, 3728u, 3778u, 3782u, 3802u, 3806u, 3836u,
          3844u, 3848u, 3854u, 3866u, 3868u, 3892u, 3896u, 3904u,
          3922u, 3928u, 3932u, 3938u, 3946u, 3956u, 3958u, 3962u,
          3964u, 4004u, 4022u, 4058u, 4088u, 4118u, 4126u, 4142u,
          4156u, 4162u, 4174u, 4202u, 4204u, 4226u, 4228u, 4232u,
          4244u, 4274u, 4286u, 4292u, 4294u, 4298u, 4312u, 4322u,
          4324u, 4342u, 4364u, 4376u, 4394u, 4396u, 4406u, 4424u,
          4456u, 4462u, 4466u, 4468u, 4474u, 4484u, 4504u, 4516u,
          4526u, 4532u, 4544u, 4564u, 4576u, 4582u, 4586u, 4588u,
          4604u, 4606u, 4622u, 4628u, 4642u, 4646u, 4648u, 4664u,
          4666u, 4672u, 4688u, 4694u, 4702u, 4706u, 4714u, 4736u,
          4754u, 4762u, 4774u, 4778u, 4786u, 4792u, 4816u, 4838u,
          4844u, 4846u, 4858u, 4888u, 4894u, 4904u, 4916u, 4922u,
          4924u, 4946u, 4952u, 4954u, 4966u, 4972u, 4994u, 5002u,
          5014u, 5036u, 5038u, 5048u, 5054u, 5072u, 5084u, 5086u,
          5092u, 5104u, 5122u, 5128u, 5132u, 5152u, 5174u, 5182u,
          5194u, 5218u, 5234u, 5248u, 5258u, 5288u, 5306u, 5308u,
          5314u, 5318u, 5332u, 5342u, 5344u, 5356u, 5366u, 5378u,
          5384u, 5386u, 5402u, 5414u, 5416u, 5422u, 5434u, 5444u,
          5446u, 5456u, 5462u, 5464u, 5476u, 5488u, 5504u, 5524u,
          5534u, 5546u, 5554u, 5584u, 5594u, 5608u, 5612u, 5618u,
          5626u, 5632u, 5636u, 5656u, 5674u, 5698u, 5702u, 5714u,
          5722u, 5726u, 5728u, 5752u, 5758u, 5782u, 5792u, 5794u,
          5798u, 5804u, 5806u, 5812u, 5818u, 5824u, 5828u, 5852u,
          5854u, 5864u, 5876u, 5878u, 5884u, 5894u, 5902u, 5908u,
          5918u, 5936u, 5938u, 5944u, 5948u, 5968u, 5992u, 6002u,
          6014u, 6016u, 6028u, 6034u, 6058u, 6062u, 6098u, 6112u,
          6128u, 6136u, 6158u, 6164u, 6172u, 6176u, 6178u, 6184u,
          6206u, 6226u, 6242u, 6254u, 6272u, 6274u, 6286u, 6302u,
          6308u, 6314u, 6326u, 6332u, 6344u, 6346u, 6352u, 6364u,
          6374u, 6382u, 6398u, 6406u, 6412u, 6428u, 6436u, 6448u,
          6452u, 6458u, 6464u, 6484u, 6496u, 6508u, 6512u, 6518u,
          6538u, 6542u, 6554u, 6556u, 6566u, 6568u, 6574u, 6604u,
          6626u, 6632u, 6634u, 6638u, 6676u, 6686u, 6688u, 6692u,
          6694u, 6716u, 6718u, 6734u, 6736u, 6742u, 6752u, 6772u,
          6778u, 6802u, 6806u, 6818u, 6832u, 6844u, 6848u, 6886u,
          6896u, 6926u, 6932u, 6934u, 6946u, 6958u, 6962u, 6968u,
          6998u, 7012u, 7016u, 7024u, 7042u, 7078u, 7082u, 7088u,
          7108u, 7112u, 7114u, 7126u, 7136u, 7138u, 7144u, 7154u,
          7166u, 7172u, 7184u, 7192u, 7198u, 7204u, 7228u, 7232u,
          7262u, 7282u, 7288u, 7324u, 7334u, 7336u, 7348u, 7354u,
          7358u, 7366u, 7372u, 7376u, 7388u, 7396u, 7402u, 7414u,
          7418u, 7424u, 7438u, 7442u, 7462u, 7474u, 7478u, 7484u,
          7502u, 7504u, 7508u, 7526u, 7528u, 7544u, 7556u, 7586u,
          7592u, 7598u, 7606u, 7646u, 7654u, 7702u, 7708u, 7724u,
          7742u, 7756u, 7768u, 7774u, 7792u, 7796u, 7816u, 7826u,
          7828u, 7834u, 7844u, 7852u, 7882u, 7886u, 7898u, 7918u,
          7924u, 7936u, 7942u, 7948u, 7982u, 7988u, 7994u, 8012u,
          8018u, 8026u, 8036u, 8048u, 8054u, 8062u, 8072u, 8074u,
          8078u, 8102u, 8108u, 8116u, 8138u, 8144u, 8146u, 8158u,
          8164u, 8174u, 8186u, 8192u, 8216u, 8222u, 8236u, 8248u,
          8284u, 8288u, 8312u, 8314u, 8324u, 8332u, 8342u, 8348u,
          8362u, 8372u, 8404u, 8408u, 8416u, 8426u, 8438u, 8464u,
          8482u, 8486u, 8492u, 8512u, 8516u, 8536u, 8542u, 8558u,
          8564u, 8566u, 8596u, 8608u, 8614u, 8624u, 8626u, 8632u,
          8642u, 8654u, 8662u, 8666u, 8668u, 8674u, 8684u, 8696u,
          8722u, 8744u, 8752u, 8758u, 8762u, 8776u, 8782u, 8788u,
          8818u, 8822u, 8828u, 8842u, 8846u, 8848u, 8876u, 8878u,
          8884u, 8906u, 8914u, 8918u, 8936u, 8954u, 8972u, 8974u,
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          29782u, 29792u, 29804u, 29834u, 29848u, 29858u, 29866u, 29878u,
          29884u, 29894u, 29906u, 29908u, 29926u, 29932u, 29936u, 29944u,
          29948u, 29972u, 29992u, 29996u, 30004u, 30014u, 30026u, 30034u,
          30046u, 30062u, 30068u, 30082u, 30086u, 30094u, 30098u, 30116u,
          30166u, 30172u, 30178u, 30182u, 30188u, 30196u, 30202u, 30212u,
          30238u, 30248u, 30254u, 30256u, 30266u, 30268u, 30278u, 30284u,
          30322u, 30334u, 30338u, 30346u, 30356u, 30376u, 30382u, 30388u,
          30394u, 30412u, 30422u, 30424u, 30436u, 30452u, 30454u, 30466u,
          30478u, 30482u, 30508u, 30518u, 30524u, 30544u, 30562u, 30602u,
          30614u, 30622u, 30632u, 30644u, 30646u, 30664u, 30676u, 30686u,
          30688u, 30698u, 30724u, 30728u, 30734u, 30746u, 30754u, 30758u,
          30788u, 30794u, 30796u, 30802u, 30818u, 30842u, 30866u, 30884u,
          30896u, 30908u, 30916u, 30922u, 30926u, 30934u, 30944u, 30952u,
          30958u, 30962u, 30982u, 30992u, 31018u, 31022u, 31046u, 31052u,
          31054u, 31066u, 31108u, 31126u, 31132u, 31136u, 31162u, 31168u,
          31196u, 31202u, 31204u, 31214u, 31222u, 31228u, 31234u, 31244u,
          31252u, 31262u, 31264u, 31286u, 31288u, 31292u, 31312u, 31316u,
          31322u, 31358u, 31372u, 31376u, 31396u, 31418u, 31424u, 31438u,
          31444u, 31454u, 31462u, 31466u, 31468u, 31472u, 31486u, 31504u,
          31538u, 31546u, 31568u, 31582u, 31592u, 31616u, 31622u, 31624u,
          31634u, 31636u, 31642u, 31652u, 31678u, 31696u, 31706u, 31724u,
          31748u, 31766u, 31768u, 31792u, 31832u, 31834u, 31838u, 31844u,
          31846u, 31852u, 31862u, 31888u, 31894u, 31906u, 31918u, 31924u,
          31928u, 31964u, 31966u, 31976u, 31988u, 32012u, 32014u, 32018u,
          32026u, 32036u, 32042u, 32044u, 32048u, 32072u, 32074u, 32078u,
          32114u, 32116u, 32138u, 32152u, 32176u, 32194u, 32236u, 32242u,
          32252u, 32254u, 32278u, 32294u, 32306u, 32308u, 32312u, 32314u,
          32324u, 32326u, 32336u, 32344u, 32348u, 32384u, 32392u, 32396u,
          32408u, 32426u, 32432u, 32438u, 32452u, 32474u, 32476u, 32482u,
          32506u, 32512u, 32522u, 32546u, 32566u, 32588u, 32594u, 32608u,
          32644u, 32672u, 32678u, 32686u, 32692u, 32716u, 32722u, 32734u,
          32762u, 32764u, 32782u, 32786u, 32788u, 32792u, 32812u, 32834u,
          32842u, 32852u, 32854u, 32872u, 32876u, 32884u, 32894u, 32908u,
          32918u, 32924u, 32932u, 32938u, 32944u, 32956u, 32972u, 32984u,
          32998u, 33008u, 33026u, 33028u, 33038u, 33062u, 33086u, 33092u,
          33104u, 33106u, 33128u, 33134u, 33154u, 33176u, 33178u, 33182u,
          33194u, 33196u, 33202u, 33238u, 33244u, 33266u, 33272u, 33274u,
          33302u, 33314u, 33332u, 33334u, 33338u, 33352u, 33358u, 33362u,
          33364u, 33374u, 33376u, 33392u, 33394u, 33404u, 33412u, 33418u,
          33428u, 33446u, 33458u, 33464u, 33478u, 33482u, 33488u, 33506u,
          33518u, 33544u, 33548u, 33554u, 33568u, 33574u, 33584u, 33596u,
          33598u, 33602u, 33604u, 33614u, 33638u, 33646u, 33656u, 33688u,
          33698u, 33706u, 33716u, 33722u, 33724u, 33742u, 33754u, 33782u,
          33812u, 33814u, 33832u, 33836u, 33842u, 33856u, 33862u, 33866u,
          33874u, 33896u, 33904u, 33934u, 33952u, 33962u, 33988u, 33992u,
          33994u, 34016u, 34024u, 34028u, 34036u, 34042u, 34046u, 34072u,
          34076u, 34088u, 34108u, 34126u, 34132u, 34144u, 34154u, 34172u,
          34174u, 34178u, 34184u, 34186u, 34198u, 34226u, 34232u, 34252u,
          34258u, 34274u, 34282u, 34288u, 34294u, 34298u, 34304u, 34324u,
          34336u, 34342u, 34346u, 34366u, 34372u, 34388u, 34394u, 34426u,
          34436u, 34454u, 34456u, 34468u, 34484u, 34508u, 34514u, 34522u,
          34534u, 34568u, 34574u, 34594u, 34616u, 34618u, 34634u, 34648u,
          34654u, 34658u, 34672u, 34678u, 34702u, 34732u, 34736u, 34744u,
          34756u, 34762u, 34778u, 34798u, 34808u, 34822u, 34826u, 34828u,
          34844u, 34856u, 34858u, 34868u, 34876u, 34882u, 34912u, 34924u,
          34934u, 34948u, 34958u, 34966u, 34976u, 34982u, 34984u, 34988u,
          35002u, 35012u, 35014u, 35024u, 35056u, 35074u, 35078u, 35086u,
          35114u, 35134u, 35138u, 35158u, 35164u, 35168u, 35198u, 35206u,
          35212u, 35234u, 35252u, 35264u, 35266u, 35276u, 35288u, 35294u,
          35312u, 35318u, 35372u, 35378u, 35392u, 35396u, 35402u, 35408u,
          35422u, 35446u, 35452u, 35464u, 35474u, 35486u, 35492u, 35516u,
          35528u, 35546u, 35554u, 35572u, 35576u, 35578u, 35582u, 35584u,
          35606u, 35614u, 35624u, 35626u, 35638u, 35648u, 35662u, 35668u,
          35672u, 35674u, 35686u, 35732u, 35738u, 35744u, 35746u, 35752u,
          35758u, 35788u, 35798u, 35806u, 35812u, 35824u, 35828u, 35842u,
          35848u, 35864u, 35876u, 35884u, 35894u, 35914u, 35932u, 35942u,
          35948u, 35954u, 35966u, 35968u, 35978u, 35992u, 35996u, 35998u,
          36002u, 36026u, 36038u, 36046u, 36064u, 36068u, 36076u, 36092u,
          36106u, 36118u, 36128u, 36146u, 36158u, 36166u, 36184u, 36188u,
          36202u, 36206u, 36212u, 36214u, 36236u, 36254u, 36262u, 36272u,
          36298u, 36302u, 36304u, 36328u, 36334u, 36338u, 36344u, 36356u,
          36382u, 36386u, 36394u, 36404u, 36422u, 36428u, 36442u, 36452u,
          36464u, 36466u, 36478u, 36484u, 36488u, 36496u, 36508u, 36524u,
          36526u, 36536u, 36542u, 36544u, 36566u, 36568u, 36572u, 36586u,
          36604u, 36614u, 36626u, 36646u, 36656u, 36662u, 36664u, 36668u,
          36682u, 36694u, 36698u, 36706u, 36716u, 36718u, 36724u, 36758u,
          36764u, 36766u, 36782u, 36794u, 36802u, 36824u, 36832u, 36862u,
          36872u, 36874u, 36898u, 36902u, 36916u, 36926u, 36946u, 36962u,
          36964u, 36968u, 36988u, 36998u, 37004u, 37012u, 37016u, 37024u,
          37028u, 37052u, 37058u, 37072u, 37076u, 37108u, 37112u, 37118u,
          37132u, 37138u, 37142u, 37144u, 37166u, 37226u, 37228u, 37234u,
          37258u, 37262u, 37276u, 37294u, 37306u, 37324u, 37336u, 37342u,
          37346u, 37376u, 37378u, 37394u, 37396u, 37418u, 37432u, 37448u,
          37466u, 37472u, 37508u, 37514u, 37532u, 37534u, 37544u, 37552u,
          37556u, 37558u, 37564u, 37588u, 37606u, 37636u, 37642u, 37648u,
          37682u, 37696u, 37702u, 37754u, 37756u, 37772u, 37784u, 37798u,
          37814u, 37822u, 37852u, 37856u, 37858u, 37864u, 37874u, 37886u,
          37888u, 37916u, 37922u, 37936u, 37948u, 37976u, 37994u, 38014u,
          38018u, 38026u, 38032u, 38038u, 38042u, 38048u, 38056u, 38078u,
          38084u, 38108u, 38116u, 38122u, 38134u, 38146u, 38152u, 38164u,
          38168u, 38188u, 38234u, 38252u, 38266u, 38276u, 38278u, 38302u,
          38306u, 38308u, 38332u, 38354u, 38368u, 38378u, 38384u, 38416u,
          38428u, 38432u, 38434u, 38444u, 38446u, 38456u, 38458u, 38462u,
          38468u, 38474u, 38486u, 38498u, 38512u, 38518u, 38524u, 38552u,
          38554u, 38572u, 38578u, 38584u, 38588u, 38612u, 38614u, 38626u,
          38638u, 38644u, 38648u, 38672u, 38696u, 38698u, 38704u, 38708u,
          38746u, 38752u, 38762u, 38774u, 38776u, 38788u, 38792u, 38812u,
          38834u, 38846u, 38848u, 38858u, 38864u, 38882u, 38924u, 38936u,
          38938u, 38944u, 38956u, 38978u, 38992u, 39002u, 39008u, 39014u,
          39016u, 39026u, 39044u, 39058u, 39062u, 39088u, 39104u, 39116u,
          39124u, 39142u, 39146u, 39148u, 39158u, 39166u, 39172u, 39176u,
          39182u, 39188u, 39194u
       }};
 #endif
    };
 
 #ifndef BOOST_MATH_HAVE_CONSTEXPR_TABLES
    template <bool b>
    const unsigned prime_data_imp<b>::b1;
    template <bool b>
    const unsigned prime_data_imp<b>::b2;
    template <bool b>
    const unsigned prime_data_imp<b>::b3;
 #else
    template <bool b>
    constexpr unsigned prime_data_imp<b>::b1;
    template <bool b>
    constexpr unsigned prime_data_imp<b>::b2;
    template <bool b>
    constexpr unsigned prime_data_imp<b>::b3;
 #endif
 
 #ifndef BOOST_MATH_HAVE_CONSTEXPR_TABLES
    template <bool b>
    const std::array<unsigned char, 54> prime_data_imp<b>::a1 = { {
          2u, 3u, 5u, 7u, 11u, 13u, 17u, 19u, 23u, 29u, 31u,
          37u, 41u, 43u, 47u, 53u, 59u, 61u, 67u, 71u, 73u,
          79u, 83u, 89u, 97u, 101u, 103u, 107u, 109u, 113u,
          127u, 131u, 137u, 139u, 149u, 151u, 157u, 163u,
          167u, 173u, 179u, 181u, 191u, 193u, 197u, 199u,
          211u, 223u, 227u, 229u, 233u, 239u, 241u, 251u
       } };
    template <bool b>
    const std::array<std::uint16_t, 6488> prime_data_imp<b>::a2 = {{
          257u, 263u, 269u, 271u, 277u, 281u, 283u, 293u,
          307u, 311u, 313u, 317u, 331u, 337u, 347u, 349u, 353u,
          359u, 367u, 373u, 379u, 383u, 389u, 397u, 401u, 409u,
          419u, 421u, 431u, 433u, 439u, 443u, 449u, 457u, 461u,
          463u, 467u, 479u, 487u, 491u, 499u, 503u, 509u, 521u,
          523u, 541u, 547u, 557u, 563u, 569u, 571u, 577u, 587u,
          593u, 599u, 601u, 607u, 613u, 617u, 619u, 631u, 641u,
          643u, 647u, 653u, 659u, 661u, 673u, 677u, 683u, 691u,
          701u, 709u, 719u, 727u, 733u, 739u, 743u, 751u, 757u,
          761u, 769u, 773u, 787u, 797u, 809u, 811u, 821u, 823u,
          827u, 829u, 839u, 853u, 857u, 859u, 863u, 877u, 881u,
          883u, 887u, 907u, 911u, 919u, 929u, 937u, 941u, 947u,
          953u, 967u, 971u, 977u, 983u, 991u, 997u, 1009u, 1013u,
          1019u, 1021u, 1031u, 1033u, 1039u, 1049u, 1051u, 1061u, 1063u,
          1069u, 1087u, 1091u, 1093u, 1097u, 1103u, 1109u, 1117u, 1123u,
          1129u, 1151u, 1153u, 1163u, 1171u, 1181u, 1187u, 1193u, 1201u,
          1213u, 1217u, 1223u, 1229u, 1231u, 1237u, 1249u, 1259u, 1277u,
          1279u, 1283u, 1289u, 1291u, 1297u, 1301u, 1303u, 1307u, 1319u,
          1321u, 1327u, 1361u, 1367u, 1373u, 1381u, 1399u, 1409u, 1423u,
          1427u, 1429u, 1433u, 1439u, 1447u, 1451u, 1453u, 1459u, 1471u,
          1481u, 1483u, 1487u, 1489u, 1493u, 1499u, 1511u, 1523u, 1531u,
          1543u, 1549u, 1553u, 1559u, 1567u, 1571u, 1579u, 1583u, 1597u,
          1601u, 1607u, 1609u, 1613u, 1619u, 1621u, 1627u, 1637u, 1657u,
          1663u, 1667u, 1669u, 1693u, 1697u, 1699u, 1709u, 1721u, 1723u,
          1733u, 1741u, 1747u, 1753u, 1759u, 1777u, 1783u, 1787u, 1789u,
          1801u, 1811u, 1823u, 1831u, 1847u, 1861u, 1867u, 1871u, 1873u,
          1877u, 1879u, 1889u, 1901u, 1907u, 1913u, 1931u, 1933u, 1949u,
          1951u, 1973u, 1979u, 1987u, 1993u, 1997u, 1999u, 2003u, 2011u,
          2017u, 2027u, 2029u, 2039u, 2053u, 2063u, 2069u, 2081u, 2083u,
          2087u, 2089u, 2099u, 2111u, 2113u, 2129u, 2131u, 2137u, 2141u,
          2143u, 2153u, 2161u, 2179u, 2203u, 2207u, 2213u, 2221u, 2237u,
          2239u, 2243u, 2251u, 2267u, 2269u, 2273u, 2281u, 2287u, 2293u,
          2297u, 2309u, 2311u, 2333u, 2339u, 2341u, 2347u, 2351u, 2357u,
          2371u, 2377u, 2381u, 2383u, 2389u, 2393u, 2399u, 2411u, 2417u,
          2423u, 2437u, 2441u, 2447u, 2459u, 2467u, 2473u, 2477u, 2503u,
          2521u, 2531u, 2539u, 2543u, 2549u, 2551u, 2557u, 2579u, 2591u,
          2593u, 2609u, 2617u, 2621u, 2633u, 2647u, 2657u, 2659u, 2663u,
          2671u, 2677u, 2683u, 2687u, 2689u, 2693u, 2699u, 2707u, 2711u,
          2713u, 2719u, 2729u, 2731u, 2741u, 2749u, 2753u, 2767u, 2777u,
          2789u, 2791u, 2797u, 2801u, 2803u, 2819u, 2833u, 2837u, 2843u,
          2851u, 2857u, 2861u, 2879u, 2887u, 2897u, 2903u, 2909u, 2917u,
          2927u, 2939u, 2953u, 2957u, 2963u, 2969u, 2971u, 2999u, 3001u,
          3011u, 3019u, 3023u, 3037u, 3041u, 3049u, 3061u, 3067u, 3079u,
          3083u, 3089u, 3109u, 3119u, 3121u, 3137u, 3163u, 3167u, 3169u,
          3181u, 3187u, 3191u, 3203u, 3209u, 3217u, 3221u, 3229u, 3251u,
          3253u, 3257u, 3259u, 3271u, 3299u, 3301u, 3307u, 3313u, 3319u,
          3323u, 3329u, 3331u, 3343u, 3347u, 3359u, 3361u, 3371u, 3373u,
          3389u, 3391u, 3407u, 3413u, 3433u, 3449u, 3457u, 3461u, 3463u,
          3467u, 3469u, 3491u, 3499u, 3511u, 3517u, 3527u, 3529u, 3533u,
          3539u, 3541u, 3547u, 3557u, 3559u, 3571u, 3581u, 3583u, 3593u,
          3607u, 3613u, 3617u, 3623u, 3631u, 3637u, 3643u, 3659u, 3671u,
          3673u, 3677u, 3691u, 3697u, 3701u, 3709u, 3719u, 3727u, 3733u,
          3739u, 3761u, 3767u, 3769u, 3779u, 3793u, 3797u, 3803u, 3821u,
          3823u, 3833u, 3847u, 3851u, 3853u, 3863u, 3877u, 3881u, 3889u,
          3907u, 3911u, 3917u, 3919u, 3923u, 3929u, 3931u, 3943u, 3947u,
          3967u, 3989u, 4001u, 4003u, 4007u, 4013u, 4019u, 4021u, 4027u,
          4049u, 4051u, 4057u, 4073u, 4079u, 4091u, 4093u, 4099u, 4111u,
          4127u, 4129u, 4133u, 4139u, 4153u, 4157u, 4159u, 4177u, 4201u,
          4211u, 4217u, 4219u, 4229u, 4231u, 4241u, 4243u, 4253u, 4259u,
          4261u, 4271u, 4273u, 4283u, 4289u, 4297u, 4327u, 4337u, 4339u,
          4349u, 4357u, 4363u, 4373u, 4391u, 4397u, 4409u, 4421u, 4423u,
          4441u, 4447u, 4451u, 4457u, 4463u, 4481u, 4483u, 4493u, 4507u,
          4513u, 4517u, 4519u, 4523u, 4547u, 4549u, 4561u, 4567u, 4583u,
          4591u, 4597u, 4603u, 4621u, 4637u, 4639u, 4643u, 4649u, 4651u,
          4657u, 4663u, 4673u, 4679u, 4691u, 4703u, 4721u, 4723u, 4729u,
          4733u, 4751u, 4759u, 4783u, 4787u, 4789u, 4793u, 4799u, 4801u,
          4813u, 4817u, 4831u, 4861u, 4871u, 4877u, 4889u, 4903u, 4909u,
          4919u, 4931u, 4933u, 4937u, 4943u, 4951u, 4957u, 4967u, 4969u,
          4973u, 4987u, 4993u, 4999u, 5003u, 5009u, 5011u, 5021u, 5023u,
          5039u, 5051u, 5059u, 5077u, 5081u, 5087u, 5099u, 5101u, 5107u,
          5113u, 5119u, 5147u, 5153u, 5167u, 5171u, 5179u, 5189u, 5197u,
          5209u, 5227u, 5231u, 5233u, 5237u, 5261u, 5273u, 5279u, 5281u,
          5297u, 5303u, 5309u, 5323u, 5333u, 5347u, 5351u, 5381u, 5387u,
          5393u, 5399u, 5407u, 5413u, 5417u, 5419u, 5431u, 5437u, 5441u,
          5443u, 5449u, 5471u, 5477u, 5479u, 5483u, 5501u, 5503u, 5507u,
          5519u, 5521u, 5527u, 5531u, 5557u, 5563u, 5569u, 5573u, 5581u,
          5591u, 5623u, 5639u, 5641u, 5647u, 5651u, 5653u, 5657u, 5659u,
          5669u, 5683u, 5689u, 5693u, 5701u, 5711u, 5717u, 5737u, 5741u,
          5743u, 5749u, 5779u, 5783u, 5791u, 5801u, 5807u, 5813u, 5821u,
          5827u, 5839u, 5843u, 5849u, 5851u, 5857u, 5861u, 5867u, 5869u,
          5879u, 5881u, 5897u, 5903u, 5923u, 5927u, 5939u, 5953u, 5981u,
          5987u, 6007u, 6011u, 6029u, 6037u, 6043u, 6047u, 6053u, 6067u,
          6073u, 6079u, 6089u, 6091u, 6101u, 6113u, 6121u, 6131u, 6133u,
          6143u, 6151u, 6163u, 6173u, 6197u, 6199u, 6203u, 6211u, 6217u,
          6221u, 6229u, 6247u, 6257u, 6263u, 6269u, 6271u, 6277u, 6287u,
          6299u, 6301u, 6311u, 6317u, 6323u, 6329u, 6337u, 6343u, 6353u,
          6359u, 6361u, 6367u, 6373u, 6379u, 6389u, 6397u, 6421u, 6427u,
          6449u, 6451u, 6469u, 6473u, 6481u, 6491u, 6521u, 6529u, 6547u,
          6551u, 6553u, 6563u, 6569u, 6571u, 6577u, 6581u, 6599u, 6607u,
          6619u, 6637u, 6653u, 6659u, 6661u, 6673u, 6679u, 6689u, 6691u,
          6701u, 6703u, 6709u, 6719u, 6733u, 6737u, 6761u, 6763u, 6779u,
          6781u, 6791u, 6793u, 6803u, 6823u, 6827u, 6829u, 6833u, 6841u,
          6857u, 6863u, 6869u, 6871u, 6883u, 6899u, 6907u, 6911u, 6917u,
          6947u, 6949u, 6959u, 6961u, 6967u, 6971u, 6977u, 6983u, 6991u,
          6997u, 7001u, 7013u, 7019u, 7027u, 7039u, 7043u, 7057u, 7069u,
          7079u, 7103u, 7109u, 7121u, 7127u, 7129u, 7151u, 7159u, 7177u,
          7187u, 7193u, 7207u, 7211u, 7213u, 7219u, 7229u, 7237u, 7243u,
          7247u, 7253u, 7283u, 7297u, 7307u, 7309u, 7321u, 7331u, 7333u,
          7349u, 7351u, 7369u, 7393u, 7411u, 7417u, 7433u, 7451u, 7457u,
          7459u, 7477u, 7481u, 7487u, 7489u, 7499u, 7507u, 7517u, 7523u,
          7529u, 7537u, 7541u, 7547u, 7549u, 7559u, 7561u, 7573u, 7577u,
          7583u, 7589u, 7591u, 7603u, 7607u, 7621u, 7639u, 7643u, 7649u,
          7669u, 7673u, 7681u, 7687u, 7691u, 7699u, 7703u, 7717u, 7723u,
          7727u, 7741u, 7753u, 7757u, 7759u, 7789u, 7793u, 7817u, 7823u,
          7829u, 7841u, 7853u, 7867u, 7873u, 7877u, 7879u, 7883u, 7901u,
          7907u, 7919u, 7927u, 7933u, 7937u, 7949u, 7951u, 7963u, 7993u,
          8009u, 8011u, 8017u, 8039u, 8053u, 8059u, 8069u, 8081u, 8087u,
          8089u, 8093u, 8101u, 8111u, 8117u, 8123u, 8147u, 8161u, 8167u,
          8171u, 8179u, 8191u, 8209u, 8219u, 8221u, 8231u, 8233u, 8237u,
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          45869u, 45887u, 45893u, 45943u, 45949u, 45953u, 45959u, 45971u, 45979u,
          45989u, 46021u, 46027u, 46049u, 46051u, 46061u, 46073u, 46091u, 46093u,
          46099u, 46103u, 46133u, 46141u, 46147u, 46153u, 46171u, 46181u, 46183u,
          46187u, 46199u, 46219u, 46229u, 46237u, 46261u, 46271u, 46273u, 46279u,
          46301u, 46307u, 46309u, 46327u, 46337u, 46349u, 46351u, 46381u, 46399u,
          46411u, 46439u, 46441u, 46447u, 46451u, 46457u, 46471u, 46477u, 46489u,
          46499u, 46507u, 46511u, 46523u, 46549u, 46559u, 46567u, 46573u, 46589u,
          46591u, 46601u, 46619u, 46633u, 46639u, 46643u, 46649u, 46663u, 46679u,
          46681u, 46687u, 46691u, 46703u, 46723u, 46727u, 46747u, 46751u, 46757u,
          46769u, 46771u, 46807u, 46811u, 46817u, 46819u, 46829u, 46831u, 46853u,
          46861u, 46867u, 46877u, 46889u, 46901u, 46919u, 46933u, 46957u, 46993u,
          46997u, 47017u, 47041u, 47051u, 47057u, 47059u, 47087u, 47093u, 47111u,
          47119u, 47123u, 47129u, 47137u, 47143u, 47147u, 47149u, 47161u, 47189u,
          47207u, 47221u, 47237u, 47251u, 47269u, 47279u, 47287u, 47293u, 47297u,
          47303u, 47309u, 47317u, 47339u, 47351u, 47353u, 47363u, 47381u, 47387u,
          47389u, 47407u, 47417u, 47419u, 47431u, 47441u, 47459u, 47491u, 47497u,
          47501u, 47507u, 47513u, 47521u, 47527u, 47533u, 47543u, 47563u, 47569u,
          47581u, 47591u, 47599u, 47609u, 47623u, 47629u, 47639u, 47653u, 47657u,
          47659u, 47681u, 47699u, 47701u, 47711u, 47713u, 47717u, 47737u, 47741u,
          47743u, 47777u, 47779u, 47791u, 47797u, 47807u, 47809u, 47819u, 47837u,
          47843u, 47857u, 47869u, 47881u, 47903u, 47911u, 47917u, 47933u, 47939u,
          47947u, 47951u, 47963u, 47969u, 47977u, 47981u, 48017u, 48023u, 48029u,
          48049u, 48073u, 48079u, 48091u, 48109u, 48119u, 48121u, 48131u, 48157u,
          48163u, 48179u, 48187u, 48193u, 48197u, 48221u, 48239u, 48247u, 48259u,
          48271u, 48281u, 48299u, 48311u, 48313u, 48337u, 48341u, 48353u, 48371u,
          48383u, 48397u, 48407u, 48409u, 48413u, 48437u, 48449u, 48463u, 48473u,
          48479u, 48481u, 48487u, 48491u, 48497u, 48523u, 48527u, 48533u, 48539u,
          48541u, 48563u, 48571u, 48589u, 48593u, 48611u, 48619u, 48623u, 48647u,
          48649u, 48661u, 48673u, 48677u, 48679u, 48731u, 48733u, 48751u, 48757u,
          48761u, 48767u, 48779u, 48781u, 48787u, 48799u, 48809u, 48817u, 48821u,
          48823u, 48847u, 48857u, 48859u, 48869u, 48871u, 48883u, 48889u, 48907u,
          48947u, 48953u, 48973u, 48989u, 48991u, 49003u, 49009u, 49019u, 49031u,
          49033u, 49037u, 49043u, 49057u, 49069u, 49081u, 49103u, 49109u, 49117u,
          49121u, 49123u, 49139u, 49157u, 49169u, 49171u, 49177u, 49193u, 49199u,
          49201u, 49207u, 49211u, 49223u, 49253u, 49261u, 49277u, 49279u, 49297u,
          49307u, 49331u, 49333u, 49339u, 49363u, 49367u, 49369u, 49391u, 49393u,
          49409u, 49411u, 49417u, 49429u, 49433u, 49451u, 49459u, 49463u, 49477u,
          49481u, 49499u, 49523u, 49529u, 49531u, 49537u, 49547u, 49549u, 49559u,
          49597u, 49603u, 49613u, 49627u, 49633u, 49639u, 49663u, 49667u, 49669u,
          49681u, 49697u, 49711u, 49727u, 49739u, 49741u, 49747u, 49757u, 49783u,
          49787u, 49789u, 49801u, 49807u, 49811u, 49823u, 49831u, 49843u, 49853u,
          49871u, 49877u, 49891u, 49919u, 49921u, 49927u, 49937u, 49939u, 49943u,
          49957u, 49991u, 49993u, 49999u, 50021u, 50023u, 50033u, 50047u, 50051u,
          50053u, 50069u, 50077u, 50087u, 50093u, 50101u, 50111u, 50119u, 50123u,
          50129u, 50131u, 50147u, 50153u, 50159u, 50177u, 50207u, 50221u, 50227u,
          50231u, 50261u, 50263u, 50273u, 50287u, 50291u, 50311u, 50321u, 50329u,
          50333u, 50341u, 50359u, 50363u, 50377u, 50383u, 50387u, 50411u, 50417u,
          50423u, 50441u, 50459u, 50461u, 50497u, 50503u, 50513u, 50527u, 50539u,
          50543u, 50549u, 50551u, 50581u, 50587u, 50591u, 50593u, 50599u, 50627u,
          50647u, 50651u, 50671u, 50683u, 50707u, 50723u, 50741u, 50753u, 50767u,
          50773u, 50777u, 50789u, 50821u, 50833u, 50839u, 50849u, 50857u, 50867u,
          50873u, 50891u, 50893u, 50909u, 50923u, 50929u, 50951u, 50957u, 50969u,
          50971u, 50989u, 50993u, 51001u, 51031u, 51043u, 51047u, 51059u, 51061u,
          51071u, 51109u, 51131u, 51133u, 51137u, 51151u, 51157u, 51169u, 51193u,
          51197u, 51199u, 51203u, 51217u, 51229u, 51239u, 51241u, 51257u, 51263u,
          51283u, 51287u, 51307u, 51329u, 51341u, 51343u, 51347u, 51349u, 51361u,
          51383u, 51407u, 51413u, 51419u, 51421u, 51427u, 51431u, 51437u, 51439u,
          51449u, 51461u, 51473u, 51479u, 51481u, 51487u, 51503u, 51511u, 51517u,
          51521u, 51539u, 51551u, 51563u, 51577u, 51581u, 51593u, 51599u, 51607u,
          51613u, 51631u, 51637u, 51647u, 51659u, 51673u, 51679u, 51683u, 51691u,
          51713u, 51719u, 51721u, 51749u, 51767u, 51769u, 51787u, 51797u, 51803u,
          51817u, 51827u, 51829u, 51839u, 51853u, 51859u, 51869u, 51871u, 51893u,
          51899u, 51907u, 51913u, 51929u, 51941u, 51949u, 51971u, 51973u, 51977u,
          51991u, 52009u, 52021u, 52027u, 52051u, 52057u, 52067u, 52069u, 52081u,
          52103u, 52121u, 52127u, 52147u, 52153u, 52163u, 52177u, 52181u, 52183u,
          52189u, 52201u, 52223u, 52237u, 52249u, 52253u, 52259u, 52267u, 52289u,
          52291u, 52301u, 52313u, 52321u, 52361u, 52363u, 52369u, 52379u, 52387u,
          52391u, 52433u, 52453u, 52457u, 52489u, 52501u, 52511u, 52517u, 52529u,
          52541u, 52543u, 52553u, 52561u, 52567u, 52571u, 52579u, 52583u, 52609u,
          52627u, 52631u, 52639u, 52667u, 52673u, 52691u, 52697u, 52709u, 52711u,
          52721u, 52727u, 52733u, 52747u, 52757u, 52769u, 52783u, 52807u, 52813u,
          52817u, 52837u, 52859u, 52861u, 52879u, 52883u, 52889u, 52901u, 52903u,
          52919u, 52937u, 52951u, 52957u, 52963u, 52967u, 52973u, 52981u, 52999u,
          53003u, 53017u, 53047u, 53051u, 53069u, 53077u, 53087u, 53089u, 53093u,
          53101u, 53113u, 53117u, 53129u, 53147u, 53149u, 53161u, 53171u, 53173u,
          53189u, 53197u, 53201u, 53231u, 53233u, 53239u, 53267u, 53269u, 53279u,
          53281u, 53299u, 53309u, 53323u, 53327u, 53353u, 53359u, 53377u, 53381u,
          53401u, 53407u, 53411u, 53419u, 53437u, 53441u, 53453u, 53479u, 53503u,
          53507u, 53527u, 53549u, 53551u, 53569u, 53591u, 53593u, 53597u, 53609u,
          53611u, 53617u, 53623u, 53629u, 53633u, 53639u, 53653u, 53657u, 53681u,
          53693u, 53699u, 53717u, 53719u, 53731u, 53759u, 53773u, 53777u, 53783u,
          53791u, 53813u, 53819u, 53831u, 53849u, 53857u, 53861u, 53881u, 53887u,
          53891u, 53897u, 53899u, 53917u, 53923u, 53927u, 53939u, 53951u, 53959u,
          53987u, 53993u, 54001u, 54011u, 54013u, 54037u, 54049u, 54059u, 54083u,
          54091u, 54101u, 54121u, 54133u, 54139u, 54151u, 54163u, 54167u, 54181u,
          54193u, 54217u, 54251u, 54269u, 54277u, 54287u, 54293u, 54311u, 54319u,
          54323u, 54331u, 54347u, 54361u, 54367u, 54371u, 54377u, 54401u, 54403u,
          54409u, 54413u, 54419u, 54421u, 54437u, 54443u, 54449u, 54469u, 54493u,
          54497u, 54499u, 54503u, 54517u, 54521u, 54539u, 54541u, 54547u, 54559u,
          54563u, 54577u, 54581u, 54583u, 54601u, 54617u, 54623u, 54629u, 54631u,
          54647u, 54667u, 54673u, 54679u, 54709u, 54713u, 54721u, 54727u, 54751u,
          54767u, 54773u, 54779u, 54787u, 54799u, 54829u, 54833u, 54851u, 54869u,
          54877u, 54881u, 54907u, 54917u, 54919u, 54941u, 54949u, 54959u, 54973u,
          54979u, 54983u, 55001u, 55009u, 55021u, 55049u, 55051u, 55057u, 55061u,
          55073u, 55079u, 55103u, 55109u, 55117u, 55127u, 55147u, 55163u, 55171u,
          55201u, 55207u, 55213u, 55217u, 55219u, 55229u, 55243u, 55249u, 55259u,
          55291u, 55313u, 55331u, 55333u, 55337u, 55339u, 55343u, 55351u, 55373u,
          55381u, 55399u, 55411u, 55439u, 55441u, 55457u, 55469u, 55487u, 55501u,
          55511u, 55529u, 55541u, 55547u, 55579u, 55589u, 55603u, 55609u, 55619u,
          55621u, 55631u, 55633u, 55639u, 55661u, 55663u, 55667u, 55673u, 55681u,
          55691u, 55697u, 55711u, 55717u, 55721u, 55733u, 55763u, 55787u, 55793u,
          55799u, 55807u, 55813u, 55817u, 55819u, 55823u, 55829u, 55837u, 55843u,
          55849u, 55871u, 55889u, 55897u, 55901u, 55903u, 55921u, 55927u, 55931u,
          55933u, 55949u, 55967u, 55987u, 55997u, 56003u, 56009u, 56039u, 56041u,
          56053u, 56081u, 56087u, 56093u, 56099u, 56101u, 56113u, 56123u, 56131u,
          56149u, 56167u, 56171u, 56179u, 56197u, 56207u, 56209u, 56237u, 56239u,
          56249u, 56263u, 56267u, 56269u, 56299u, 56311u, 56333u, 56359u, 56369u,
          56377u, 56383u, 56393u, 56401u, 56417u, 56431u, 56437u, 56443u, 56453u,
          56467u, 56473u, 56477u, 56479u, 56489u, 56501u, 56503u, 56509u, 56519u,
          56527u, 56531u, 56533u, 56543u, 56569u, 56591u, 56597u, 56599u, 56611u,
          56629u, 56633u, 56659u, 56663u, 56671u, 56681u, 56687u, 56701u, 56711u,
          56713u, 56731u, 56737u, 56747u, 56767u, 56773u, 56779u, 56783u, 56807u,
          56809u, 56813u, 56821u, 56827u, 56843u, 56857u, 56873u, 56891u, 56893u,
          56897u, 56909u, 56911u, 56921u, 56923u, 56929u, 56941u, 56951u, 56957u,
          56963u, 56983u, 56989u, 56993u, 56999u, 57037u, 57041u, 57047u, 57059u,
          57073u, 57077u, 57089u, 57097u, 57107u, 57119u, 57131u, 57139u, 57143u,
          57149u, 57163u, 57173u, 57179u, 57191u, 57193u, 57203u, 57221u, 57223u,
          57241u, 57251u, 57259u, 57269u, 57271u, 57283u, 57287u, 57301u, 57329u,
          57331u, 57347u, 57349u, 57367u, 57373u, 57383u, 57389u, 57397u, 57413u,
          57427u, 57457u, 57467u, 57487u, 57493u, 57503u, 57527u, 57529u, 57557u,
          57559u, 57571u, 57587u, 57593u, 57601u, 57637u, 57641u, 57649u, 57653u,
          57667u, 57679u, 57689u, 57697u, 57709u, 57713u, 57719u, 57727u, 57731u,
          57737u, 57751u, 57773u, 57781u, 57787u, 57791u, 57793u, 57803u, 57809u,
          57829u, 57839u, 57847u, 57853u, 57859u, 57881u, 57899u, 57901u, 57917u,
          57923u, 57943u, 57947u, 57973u, 57977u, 57991u, 58013u, 58027u, 58031u,
          58043u, 58049u, 58057u, 58061u, 58067u, 58073u, 58099u, 58109u, 58111u,
          58129u, 58147u, 58151u, 58153u, 58169u, 58171u, 58189u, 58193u, 58199u,
          58207u, 58211u, 58217u, 58229u, 58231u, 58237u, 58243u, 58271u, 58309u,
          58313u, 58321u, 58337u, 58363u, 58367u, 58369u, 58379u, 58391u, 58393u,
          58403u, 58411u, 58417u, 58427u, 58439u, 58441u, 58451u, 58453u, 58477u,
          58481u, 58511u, 58537u, 58543u, 58549u, 58567u, 58573u, 58579u, 58601u,
          58603u, 58613u, 58631u, 58657u, 58661u, 58679u, 58687u, 58693u, 58699u,
          58711u, 58727u, 58733u, 58741u, 58757u, 58763u, 58771u, 58787u, 58789u,
          58831u, 58889u, 58897u, 58901u, 58907u, 58909u, 58913u, 58921u, 58937u,
          58943u, 58963u, 58967u, 58979u, 58991u, 58997u, 59009u, 59011u, 59021u,
          59023u, 59029u, 59051u, 59053u, 59063u, 59069u, 59077u, 59083u, 59093u,
          59107u, 59113u, 59119u, 59123u, 59141u, 59149u, 59159u, 59167u, 59183u,
          59197u, 59207u, 59209u, 59219u, 59221u, 59233u, 59239u, 59243u, 59263u,
          59273u, 59281u, 59333u, 59341u, 59351u, 59357u, 59359u, 59369u, 59377u,
          59387u, 59393u, 59399u, 59407u, 59417u, 59419u, 59441u, 59443u, 59447u,
          59453u, 59467u, 59471u, 59473u, 59497u, 59509u, 59513u, 59539u, 59557u,
          59561u, 59567u, 59581u, 59611u, 59617u, 59621u, 59627u, 59629u, 59651u,
          59659u, 59663u, 59669u, 59671u, 59693u, 59699u, 59707u, 59723u, 59729u,
          59743u, 59747u, 59753u, 59771u, 59779u, 59791u, 59797u, 59809u, 59833u,
          59863u, 59879u, 59887u, 59921u, 59929u, 59951u, 59957u, 59971u, 59981u,
          59999u, 60013u, 60017u, 60029u, 60037u, 60041u, 60077u, 60083u, 60089u,
          60091u, 60101u, 60103u, 60107u, 60127u, 60133u, 60139u, 60149u, 60161u,
          60167u, 60169u, 60209u, 60217u, 60223u, 60251u, 60257u, 60259u, 60271u,
          60289u, 60293u, 60317u, 60331u, 60337u, 60343u, 60353u, 60373u, 60383u,
          60397u, 60413u, 60427u, 60443u, 60449u, 60457u, 60493u, 60497u, 60509u,
          60521u, 60527u, 60539u, 60589u, 60601u, 60607u, 60611u, 60617u, 60623u,
          60631u, 60637u, 60647u, 60649u, 60659u, 60661u, 60679u, 60689u, 60703u,
          60719u, 60727u, 60733u, 60737u, 60757u, 60761u, 60763u, 60773u, 60779u,
          60793u, 60811u, 60821u, 60859u, 60869u, 60887u, 60889u, 60899u, 60901u,
          60913u, 60917u, 60919u, 60923u, 60937u, 60943u, 60953u, 60961u, 61001u,
          61007u, 61027u, 61031u, 61043u, 61051u, 61057u, 61091u, 61099u, 61121u,
          61129u, 61141u, 61151u, 61153u, 61169u, 61211u, 61223u, 61231u, 61253u,
          61261u, 61283u, 61291u, 61297u, 61331u, 61333u, 61339u, 61343u, 61357u,
          61363u, 61379u, 61381u, 61403u, 61409u, 61417u, 61441u, 61463u, 61469u,
          61471u, 61483u, 61487u, 61493u, 61507u, 61511u, 61519u, 61543u, 61547u,
          61553u, 61559u, 61561u, 61583u, 61603u, 61609u, 61613u, 61627u, 61631u,
          61637u, 61643u, 61651u, 61657u, 61667u, 61673u, 61681u, 61687u, 61703u,
          61717u, 61723u, 61729u, 61751u, 61757u, 61781u, 61813u, 61819u, 61837u,
          61843u, 61861u, 61871u, 61879u, 61909u, 61927u, 61933u, 61949u, 61961u,
          61967u, 61979u, 61981u, 61987u, 61991u, 62003u, 62011u, 62017u, 62039u,
          62047u, 62053u, 62057u, 62071u, 62081u, 62099u, 62119u, 62129u, 62131u,
          62137u, 62141u, 62143u, 62171u, 62189u, 62191u, 62201u, 62207u, 62213u,
          62219u, 62233u, 62273u, 62297u, 62299u, 62303u, 62311u, 62323u, 62327u,
          62347u, 62351u, 62383u, 62401u, 62417u, 62423u, 62459u, 62467u, 62473u,
          62477u, 62483u, 62497u, 62501u, 62507u, 62533u, 62539u, 62549u, 62563u,
          62581u, 62591u, 62597u, 62603u, 62617u, 62627u, 62633u, 62639u, 62653u,
          62659u, 62683u, 62687u, 62701u, 62723u, 62731u, 62743u, 62753u, 62761u,
          62773u, 62791u, 62801u, 62819u, 62827u, 62851u, 62861u, 62869u, 62873u,
          62897u, 62903u, 62921u, 62927u, 62929u, 62939u, 62969u, 62971u, 62981u,
          62983u, 62987u, 62989u, 63029u, 63031u, 63059u, 63067u, 63073u, 63079u,
          63097u, 63103u, 63113u, 63127u, 63131u, 63149u, 63179u, 63197u, 63199u,
          63211u, 63241u, 63247u, 63277u, 63281u, 63299u, 63311u, 63313u, 63317u,
          63331u, 63337u, 63347u, 63353u, 63361u, 63367u, 63377u, 63389u, 63391u,
          63397u, 63409u, 63419u, 63421u, 63439u, 63443u, 63463u, 63467u, 63473u,
          63487u, 63493u, 63499u, 63521u, 63527u, 63533u, 63541u, 63559u, 63577u,
          63587u, 63589u, 63599u, 63601u, 63607u, 63611u, 63617u, 63629u, 63647u,
          63649u, 63659u, 63667u, 63671u, 63689u, 63691u, 63697u, 63703u, 63709u,
          63719u, 63727u, 63737u, 63743u, 63761u, 63773u, 63781u, 63793u, 63799u,
          63803u, 63809u, 63823u, 63839u, 63841u, 63853u, 63857u, 63863u, 63901u,
          63907u, 63913u, 63929u, 63949u, 63977u, 63997u, 64007u, 64013u, 64019u,
          64033u, 64037u, 64063u, 64067u, 64081u, 64091u, 64109u, 64123u, 64151u,
          64153u, 64157u, 64171u, 64187u, 64189u, 64217u, 64223u, 64231u, 64237u,
          64271u, 64279u, 64283u, 64301u, 64303u, 64319u, 64327u, 64333u, 64373u,
          64381u, 64399u, 64403u, 64433u, 64439u, 64451u, 64453u, 64483u, 64489u,
          64499u, 64513u, 64553u, 64567u, 64577u, 64579u, 64591u, 64601u, 64609u,
          64613u, 64621u, 64627u, 64633u, 64661u, 64663u, 64667u, 64679u, 64693u,
          64709u, 64717u, 64747u, 64763u, 64781u, 64783u, 64793u, 64811u, 64817u,
          64849u, 64853u, 64871u, 64877u, 64879u, 64891u, 64901u, 64919u, 64921u,
          64927u, 64937u, 64951u, 64969u, 64997u, 65003u, 65011u, 65027u, 65029u,
          65033u, 65053u, 65063u, 65071u, 65089u, 65099u, 65101u, 65111u, 65119u,
          65123u, 65129u, 65141u, 65147u, 65167u, 65171u, 65173u, 65179u, 65183u,
          65203u, 65213u, 65239u, 65257u, 65267u, 65269u, 65287u, 65293u, 65309u,
          65323u, 65327u, 65353u, 65357u, 65371u, 65381u, 65393u, 65407u, 65413u,
          65419u, 65423u, 65437u, 65447u, 65449u, 65479u, 65497u, 65519u, 65521u
       }};
       template <bool b>
       const std::array<std::uint16_t, 3458> prime_data_imp<b>::a3 = {{
          2u, 4u, 8u, 16u, 22u, 28u, 44u,
          46u, 52u, 64u, 74u, 82u, 94u, 98u, 112u,
          116u, 122u, 142u, 152u, 164u, 166u, 172u, 178u,
          182u, 184u, 194u, 196u, 226u, 242u, 254u, 274u,
          292u, 296u, 302u, 304u, 308u, 316u, 332u, 346u,
          364u, 386u, 392u, 394u, 416u, 422u, 428u, 446u,
          448u, 458u, 494u, 502u, 506u, 512u, 532u, 536u,
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          21416u, 21424u, 21434u, 21446u, 21458u, 21476u, 21478u, 21502u,
          21506u, 21514u, 21536u, 21548u, 21568u, 21572u, 21584u, 21586u,
          21598u, 21614u, 21616u, 21644u, 21646u, 21652u, 21676u, 21686u,
          21688u, 21716u, 21718u, 21722u, 21742u, 21746u, 21758u, 21764u,
          21778u, 21782u, 21788u, 21802u, 21824u, 21848u, 21868u, 21872u,
          21886u, 21892u, 21898u, 21908u, 21938u, 21946u, 21956u, 21974u,
          21976u, 21982u, 21988u, 22004u, 22006u, 22012u, 22018u, 22022u,
          22024u, 22048u, 22052u, 22054u, 22078u, 22088u, 22094u, 22096u,
          22106u, 22108u, 22114u, 22136u, 22144u, 22148u, 22156u, 22162u,
          22166u, 22184u, 22186u, 22204u, 22208u, 22216u, 22232u, 22258u,
          22262u, 22268u, 22276u, 22298u, 22318u, 22334u, 22342u, 22346u,
          22352u, 22376u, 22382u, 22396u, 22408u, 22424u, 22426u, 22438u,
          22442u, 22456u, 22466u, 22468u, 22472u, 22484u, 22502u, 22534u,
          22544u, 22558u, 22582u, 22594u, 22634u, 22642u, 22676u, 22688u,
          22702u, 22706u, 22724u, 22726u, 22754u, 22766u, 22786u, 22792u,
          22802u, 22804u, 22844u, 22862u, 22876u, 22888u, 22892u, 22928u,
          22934u, 22936u, 22958u, 22964u, 22978u, 22988u, 23012u, 23054u,
          23056u, 23072u, 23074u, 23108u, 23116u, 23122u, 23126u, 23128u,
          23132u, 23146u, 23186u, 23194u, 23206u, 23212u, 23236u, 23254u,
          23258u, 23264u, 23266u, 23272u, 23276u, 23278u, 23282u, 23284u,
          23308u, 23318u, 23326u, 23332u, 23338u, 23348u, 23362u, 23368u,
          23384u, 23402u, 23416u, 23434u, 23458u, 23462u, 23468u, 23474u,
          23482u, 23486u, 23506u, 23516u, 23522u, 23534u, 23536u, 23548u,
          23552u, 23566u, 23572u, 23578u, 23584u, 23588u, 23602u, 23618u,
          23654u, 23668u, 23674u, 23678u, 23692u, 23696u, 23702u, 23726u,
          23734u, 23738u, 23758u, 23768u, 23782u, 23794u, 23828u, 23836u,
          23846u, 23852u, 23858u, 23864u, 23878u, 23882u, 23896u, 23908u,
          23914u, 23924u, 23942u, 23956u, 23966u, 23978u, 23984u, 23986u,
          23992u, 23998u, 24026u, 24028u, 24032u, 24056u, 24062u, 24064u,
          24068u, 24076u, 24092u, 24098u, 24118u, 24122u, 24124u, 24134u,
          24136u, 24146u, 24154u, 24218u, 24224u, 24232u, 24244u, 24248u,
          24262u, 24274u, 24284u, 24286u, 24298u, 24304u, 24314u, 24332u,
          24356u, 24362u, 24364u, 24374u, 24382u, 24388u, 24404u, 24424u,
          24428u, 24442u, 24448u, 24454u, 24466u, 24472u, 24476u, 24482u,
          24484u, 24488u, 24496u, 24518u, 24524u, 24532u, 24536u, 24538u,
          24554u, 24572u, 24586u, 24592u, 24614u, 24628u, 24638u, 24652u,
          24656u, 24662u, 24664u, 24668u, 24682u, 24692u, 24704u, 24712u,
          24728u, 24736u, 24746u, 24754u, 24778u, 24818u, 24824u, 24836u,
          24838u, 24844u, 24862u, 24866u, 24868u, 24872u, 24902u, 24904u,
          24934u, 24938u, 24946u, 24964u, 24976u, 24988u, 24992u, 24994u,
          24998u, 25012u, 25048u, 25064u, 25082u, 25084u, 25096u, 25106u,
          25112u, 25124u, 25142u, 25144u, 25162u, 25168u, 25174u, 25196u,
          25214u, 25252u, 25258u, 25268u, 25286u, 25288u, 25298u, 25306u,
          25312u, 25328u, 25352u, 25366u, 25372u, 25376u, 25382u, 25396u,
          25412u, 25436u, 25442u, 25454u, 25462u, 25474u, 25484u, 25498u,
          25544u, 25546u, 25562u, 25564u, 25586u, 25592u, 25594u, 25604u,
          25606u, 25616u, 25618u, 25624u, 25628u, 25648u, 25658u, 25664u,
          25694u, 25702u, 25708u, 25714u, 25718u, 25748u, 25756u, 25762u,
          25768u, 25774u, 25796u, 25832u, 25834u, 25838u, 25846u, 25852u,
          25858u, 25862u, 25876u, 25888u, 25898u, 25918u, 25922u, 25924u,
          25928u, 25958u, 25964u, 25978u, 25994u, 26006u, 26036u, 26038u,
          26042u, 26048u, 26056u, 26086u, 26096u, 26104u, 26138u, 26156u,
          26168u, 26176u, 26198u, 26218u, 26222u, 26236u, 26246u, 26266u,
          26272u, 26276u, 26278u, 26288u, 26302u, 26306u, 26332u, 26338u,
          26374u, 26386u, 26404u, 26408u, 26416u, 26422u, 26426u, 26432u,
          26434u, 26462u, 26468u, 26474u, 26498u, 26506u, 26516u, 26542u,
          26548u, 26572u, 26576u, 26584u, 26608u, 26618u, 26638u, 26642u,
          26644u, 26654u, 26668u, 26684u, 26686u, 26692u, 26698u, 26702u,
          26708u, 26716u, 26734u, 26762u, 26776u, 26782u, 26798u, 26812u,
          26818u, 26822u, 26828u, 26834u, 26842u, 26846u, 26848u, 26852u,
          26864u, 26866u, 26878u, 26884u, 26896u, 26924u, 26926u, 26932u,
          26944u, 26954u, 26968u, 26972u, 27016u, 27022u, 27032u, 27034u,
          27046u, 27058u, 27088u, 27092u, 27104u, 27106u, 27112u, 27122u,
          27134u, 27136u, 27146u, 27148u, 27158u, 27164u, 27172u, 27182u,
          27188u, 27202u, 27218u, 27226u, 27232u, 27244u, 27254u, 27256u,
          27266u, 27274u, 27286u, 27296u, 27314u, 27322u, 27326u, 27328u,
          27332u, 27358u, 27364u, 27386u, 27392u, 27406u, 27416u, 27422u,
          27424u, 27452u, 27458u, 27466u, 27512u, 27518u, 27524u, 27542u,
          27548u, 27554u, 27562u, 27568u, 27578u, 27596u, 27598u, 27604u,
          27616u, 27634u, 27644u, 27652u, 27664u, 27694u, 27704u, 27706u,
          27716u, 27718u, 27722u, 27728u, 27746u, 27748u, 27752u, 27772u,
          27784u, 27788u, 27794u, 27802u, 27836u, 27842u, 27848u, 27872u,
          27884u, 27892u, 27928u, 27944u, 27946u, 27952u, 27956u, 27958u,
          27962u, 27968u, 27988u, 27994u, 28018u, 28022u, 28024u, 28028u,
          28046u, 28066u, 28072u, 28094u, 28102u, 28148u, 28166u, 28168u,
          28184u, 28204u, 28226u, 28228u, 28252u, 28274u, 28276u, 28292u,
          28316u, 28336u, 28352u, 28354u, 28358u, 28366u, 28376u, 28378u,
          28388u, 28402u, 28406u, 28414u, 28432u, 28436u, 28444u, 28448u,
          28462u, 28472u, 28474u, 28498u, 28514u, 28522u, 28528u, 28544u,
          28564u, 28574u, 28576u, 28582u, 28586u, 28616u, 28618u, 28634u,
          28666u, 28672u, 28684u, 28694u, 28718u, 28726u, 28738u, 28756u,
          28772u, 28774u, 28786u, 28792u, 28796u, 28808u, 28814u, 28816u,
          28844u, 28862u, 28864u, 28886u, 28892u, 28898u, 28904u, 28906u,
          28912u, 28928u, 28942u, 28948u, 28978u, 28994u, 28996u, 29006u,
          29008u, 29012u, 29024u, 29026u, 29038u, 29048u, 29062u, 29068u,
          29078u, 29086u, 29114u, 29116u, 29152u, 29158u, 29174u, 29188u,
          29192u, 29212u, 29236u, 29242u, 29246u, 29254u, 29258u, 29276u,
          29284u, 29288u, 29302u, 29306u, 29312u, 29314u, 29338u, 29354u,
          29368u, 29372u, 29398u, 29414u, 29416u, 29426u, 29458u, 29464u,
          29468u, 29474u, 29486u, 29492u, 29528u, 29536u, 29548u, 29552u,
          29554u, 29558u, 29566u, 29572u, 29576u, 29596u, 29608u, 29618u,
          29642u, 29654u, 29656u, 29668u, 29678u, 29684u, 29696u, 29698u,
          29704u, 29722u, 29726u, 29732u, 29738u, 29744u, 29752u, 29776u,
          29782u, 29792u, 29804u, 29834u, 29848u, 29858u, 29866u, 29878u,
          29884u, 29894u, 29906u, 29908u, 29926u, 29932u, 29936u, 29944u,
          29948u, 29972u, 29992u, 29996u, 30004u, 30014u, 30026u, 30034u,
          30046u, 30062u, 30068u, 30082u, 30086u, 30094u, 30098u, 30116u,
          30166u, 30172u, 30178u, 30182u, 30188u, 30196u, 30202u, 30212u,
          30238u, 30248u, 30254u, 30256u, 30266u, 30268u, 30278u, 30284u,
          30322u, 30334u, 30338u, 30346u, 30356u, 30376u, 30382u, 30388u,
          30394u, 30412u, 30422u, 30424u, 30436u, 30452u, 30454u, 30466u,
          30478u, 30482u, 30508u, 30518u, 30524u, 30544u, 30562u, 30602u,
          30614u, 30622u, 30632u, 30644u, 30646u, 30664u, 30676u, 30686u,
          30688u, 30698u, 30724u, 30728u, 30734u, 30746u, 30754u, 30758u,
          30788u, 30794u, 30796u, 30802u, 30818u, 30842u, 30866u, 30884u,
          30896u, 30908u, 30916u, 30922u, 30926u, 30934u, 30944u, 30952u,
          30958u, 30962u, 30982u, 30992u, 31018u, 31022u, 31046u, 31052u,
          31054u, 31066u, 31108u, 31126u, 31132u, 31136u, 31162u, 31168u,
          31196u, 31202u, 31204u, 31214u, 31222u, 31228u, 31234u, 31244u,
          31252u, 31262u, 31264u, 31286u, 31288u, 31292u, 31312u, 31316u,
          31322u, 31358u, 31372u, 31376u, 31396u, 31418u, 31424u, 31438u,
          31444u, 31454u, 31462u, 31466u, 31468u, 31472u, 31486u, 31504u,
          31538u, 31546u, 31568u, 31582u, 31592u, 31616u, 31622u, 31624u,
          31634u, 31636u, 31642u, 31652u, 31678u, 31696u, 31706u, 31724u,
          31748u, 31766u, 31768u, 31792u, 31832u, 31834u, 31838u, 31844u,
          31846u, 31852u, 31862u, 31888u, 31894u, 31906u, 31918u, 31924u,
          31928u, 31964u, 31966u, 31976u, 31988u, 32012u, 32014u, 32018u,
          32026u, 32036u, 32042u, 32044u, 32048u, 32072u, 32074u, 32078u,
          32114u, 32116u, 32138u, 32152u, 32176u, 32194u, 32236u, 32242u,
          32252u, 32254u, 32278u, 32294u, 32306u, 32308u, 32312u, 32314u,
          32324u, 32326u, 32336u, 32344u, 32348u, 32384u, 32392u, 32396u,
          32408u, 32426u, 32432u, 32438u, 32452u, 32474u, 32476u, 32482u,
          32506u, 32512u, 32522u, 32546u, 32566u, 32588u, 32594u, 32608u,
          32644u, 32672u, 32678u, 32686u, 32692u, 32716u, 32722u, 32734u,
          32762u, 32764u, 32782u, 32786u, 32788u, 32792u, 32812u, 32834u,
          32842u, 32852u, 32854u, 32872u, 32876u, 32884u, 32894u, 32908u,
          32918u, 32924u, 32932u, 32938u, 32944u, 32956u, 32972u, 32984u,
          32998u, 33008u, 33026u, 33028u, 33038u, 33062u, 33086u, 33092u,
          33104u, 33106u, 33128u, 33134u, 33154u, 33176u, 33178u, 33182u,
          33194u, 33196u, 33202u, 33238u, 33244u, 33266u, 33272u, 33274u,
          33302u, 33314u, 33332u, 33334u, 33338u, 33352u, 33358u, 33362u,
          33364u, 33374u, 33376u, 33392u, 33394u, 33404u, 33412u, 33418u,
          33428u, 33446u, 33458u, 33464u, 33478u, 33482u, 33488u, 33506u,
          33518u, 33544u, 33548u, 33554u, 33568u, 33574u, 33584u, 33596u,
          33598u, 33602u, 33604u, 33614u, 33638u, 33646u, 33656u, 33688u,
          33698u, 33706u, 33716u, 33722u, 33724u, 33742u, 33754u, 33782u,
          33812u, 33814u, 33832u, 33836u, 33842u, 33856u, 33862u, 33866u,
          33874u, 33896u, 33904u, 33934u, 33952u, 33962u, 33988u, 33992u,
          33994u, 34016u, 34024u, 34028u, 34036u, 34042u, 34046u, 34072u,
          34076u, 34088u, 34108u, 34126u, 34132u, 34144u, 34154u, 34172u,
          34174u, 34178u, 34184u, 34186u, 34198u, 34226u, 34232u, 34252u,
          34258u, 34274u, 34282u, 34288u, 34294u, 34298u, 34304u, 34324u,
          34336u, 34342u, 34346u, 34366u, 34372u, 34388u, 34394u, 34426u,
          34436u, 34454u, 34456u, 34468u, 34484u, 34508u, 34514u, 34522u,
          34534u, 34568u, 34574u, 34594u, 34616u, 34618u, 34634u, 34648u,
          34654u, 34658u, 34672u, 34678u, 34702u, 34732u, 34736u, 34744u,
          34756u, 34762u, 34778u, 34798u, 34808u, 34822u, 34826u, 34828u,
          34844u, 34856u, 34858u, 34868u, 34876u, 34882u, 34912u, 34924u,
          34934u, 34948u, 34958u, 34966u, 34976u, 34982u, 34984u, 34988u,
          35002u, 35012u, 35014u, 35024u, 35056u, 35074u, 35078u, 35086u,
          35114u, 35134u, 35138u, 35158u, 35164u, 35168u, 35198u, 35206u,
          35212u, 35234u, 35252u, 35264u, 35266u, 35276u, 35288u, 35294u,
          35312u, 35318u, 35372u, 35378u, 35392u, 35396u, 35402u, 35408u,
          35422u, 35446u, 35452u, 35464u, 35474u, 35486u, 35492u, 35516u,
          35528u, 35546u, 35554u, 35572u, 35576u, 35578u, 35582u, 35584u,
          35606u, 35614u, 35624u, 35626u, 35638u, 35648u, 35662u, 35668u,
          35672u, 35674u, 35686u, 35732u, 35738u, 35744u, 35746u, 35752u,
          35758u, 35788u, 35798u, 35806u, 35812u, 35824u, 35828u, 35842u,
          35848u, 35864u, 35876u, 35884u, 35894u, 35914u, 35932u, 35942u,
          35948u, 35954u, 35966u, 35968u, 35978u, 35992u, 35996u, 35998u,
          36002u, 36026u, 36038u, 36046u, 36064u, 36068u, 36076u, 36092u,
          36106u, 36118u, 36128u, 36146u, 36158u, 36166u, 36184u, 36188u,
          36202u, 36206u, 36212u, 36214u, 36236u, 36254u, 36262u, 36272u,
          36298u, 36302u, 36304u, 36328u, 36334u, 36338u, 36344u, 36356u,
          36382u, 36386u, 36394u, 36404u, 36422u, 36428u, 36442u, 36452u,
          36464u, 36466u, 36478u, 36484u, 36488u, 36496u, 36508u, 36524u,
          36526u, 36536u, 36542u, 36544u, 36566u, 36568u, 36572u, 36586u,
          36604u, 36614u, 36626u, 36646u, 36656u, 36662u, 36664u, 36668u,
          36682u, 36694u, 36698u, 36706u, 36716u, 36718u, 36724u, 36758u,
          36764u, 36766u, 36782u, 36794u, 36802u, 36824u, 36832u, 36862u,
          36872u, 36874u, 36898u, 36902u, 36916u, 36926u, 36946u, 36962u,
          36964u, 36968u, 36988u, 36998u, 37004u, 37012u, 37016u, 37024u,
          37028u, 37052u, 37058u, 37072u, 37076u, 37108u, 37112u, 37118u,
          37132u, 37138u, 37142u, 37144u, 37166u, 37226u, 37228u, 37234u,
          37258u, 37262u, 37276u, 37294u, 37306u, 37324u, 37336u, 37342u,
          37346u, 37376u, 37378u, 37394u, 37396u, 37418u, 37432u, 37448u,
          37466u, 37472u, 37508u, 37514u, 37532u, 37534u, 37544u, 37552u,
          37556u, 37558u, 37564u, 37588u, 37606u, 37636u, 37642u, 37648u,
          37682u, 37696u, 37702u, 37754u, 37756u, 37772u, 37784u, 37798u,
          37814u, 37822u, 37852u, 37856u, 37858u, 37864u, 37874u, 37886u,
          37888u, 37916u, 37922u, 37936u, 37948u, 37976u, 37994u, 38014u,
          38018u, 38026u, 38032u, 38038u, 38042u, 38048u, 38056u, 38078u,
          38084u, 38108u, 38116u, 38122u, 38134u, 38146u, 38152u, 38164u,
          38168u, 38188u, 38234u, 38252u, 38266u, 38276u, 38278u, 38302u,
          38306u, 38308u, 38332u, 38354u, 38368u, 38378u, 38384u, 38416u,
          38428u, 38432u, 38434u, 38444u, 38446u, 38456u, 38458u, 38462u,
          38468u, 38474u, 38486u, 38498u, 38512u, 38518u, 38524u, 38552u,
          38554u, 38572u, 38578u, 38584u, 38588u, 38612u, 38614u, 38626u,
          38638u, 38644u, 38648u, 38672u, 38696u, 38698u, 38704u, 38708u,
          38746u, 38752u, 38762u, 38774u, 38776u, 38788u, 38792u, 38812u,
          38834u, 38846u, 38848u, 38858u, 38864u, 38882u, 38924u, 38936u,
          38938u, 38944u, 38956u, 38978u, 38992u, 39002u, 39008u, 39014u,
          39016u, 39026u, 39044u, 39058u, 39062u, 39088u, 39104u, 39116u,
          39124u, 39142u, 39146u, 39148u, 39158u, 39166u, 39172u, 39176u,
          39182u, 39188u, 39194u
       }};
 #else
 template <bool b>
 constexpr std::array<unsigned char, 54> prime_data_imp<b>::a1;
 template <bool b>
 constexpr std::array<std::uint16_t, 6488> prime_data_imp<b>::a2;
 template <bool b>
 constexpr std::array<std::uint16_t, 3458> prime_data_imp<b>::a3;
 #endif
 
    using prime_data = prime_data_imp<true>;
 
    template <class Policy>
    BOOST_MATH_CONSTEXPR_TABLE_FUNCTION std::uint32_t prime(unsigned n, const Policy& pol)
    {
 
       if(n <= prime_data::b1)
          return prime_data::a1[n];
       if(n <= prime_data::b2)
          return prime_data::a2[n - prime_data::b1 - 1];
       if(n >= prime_data::b3)
       {
          return boost::math::policies::raise_domain_error<std::uint32_t>(
             "boost::math::prime<%1%>", "Argument n out of range: got %1%", n, pol);
       }
       return static_cast<std::uint32_t>(prime_data::a3[n - prime_data::b2 - 1]) + 0xFFFFu;
    }
 
    inline BOOST_MATH_CONSTEXPR_TABLE_FUNCTION std::uint32_t prime(unsigned n)
    {
       return boost::math::prime(n, boost::math::policies::policy<>());
    }
 
    static const unsigned max_prime = 9999;
 
 }} // namespace boost and math
 
 #endif // BOOST_MATH_SF_PRIME_HPP