BeginPackage["StrongPseudoprimeData`", "CNT`"]; 

(* BeginPackage["Pseudoprimes`", "CNT`"];  *)


StrongPseudoprimes::usage = "StrongPseudoprimes[bv_List,max] gives a list of all integers below max that are b-strong pseudoprimes for b in bv. max must be less than 10^16 and bv must include 2 and 3.";
 
LucasPseudoprimesAllTypes::usage ="LucasPseudoprimesAllTypes is a list of xxxx integers below 10^9 satisfying either the U- or V-primality conditions where the Lucas parameters P and Q are chosen by method A, method A*, or method A starting at -7 instead of 5.";


(* This file is based on  a list of 52593 integers: all the 
2-strong pseudoprimes and 3-strong pseudoprimes under 10^16.
Courtesy Daniel Bleichenbacher, Lucent Technologies. *)
    
Begin["`Private`"];

StrongPseudoprimes[{2,3}, max_] := 
Which[max <= 10^15, Select[
		StrongPseudoprimesRaw[1],#<max &],
		max <= 4 10^15, Join[
		StrongPseudoprimesRaw[1],Select[StrongPseudoprimesRaw[2],#<max &]],
			max <= 7 10^15,  Join[
		StrongPseudoprimesRaw[1],StrongPseudoprimesRaw[2],
        Select[StrongPseudoprimesRaw[3],#<max &]],
		True, Join[
		StrongPseudoprimesRaw[1],StrongPseudoprimesRaw[2],
			StrongPseudoprimesRaw[3], Select[StrongPseudoprimesRaw[4],#<max &]]] /; 
    max <= 10^16


StrongPseudoprimes[l_List, max_]:=
Select[StrongPseudoprimes[Drop[l,-1],max],
	StrongPseudoprimeQ[l[[-1]], #] &]   /; Length[l] >= 3 && 
	MemberQ[l,2] && MemberQ[l,3] &&!MemberQ[{{2,3,5},{2,3,5,7}, {2,3,5,7,11}},l]
		
StrongPseudoprimesRaw[1] = 
   {1373653, 1530787, 1987021, 2284453, 3116107, 5173601, 
    6787327, 11541307, 13694761, 15978007, 16070429, 
    16879501, 25326001, 27509653, 27664033, 28527049, 
    54029741, 61832377, 66096253, 74927161, 80375707, 
    101649241, 102690677, 104852881, 105919633, 106485121, 
    117987841, 143168581, 154287451, 161304001, 193949641, 
    206304961, 218642029, 223625851, 247318957, 252853921, 
    259765747, 275619961, 314184487, 326695141, 390612221, 
    393611653, 489994201, 540654409, 572228929, 579606301, 
    581618143, 682528687, 717653129, 745745461, 787085857, 
    846961321, 871157233, 927106561, 938376181, 960946321, 
    979363153, 981484561, 1028494429, 1157839381, 
    1168256953, 1236313501, 1463178817, 1481626513, 
    1518290707, 1521221473, 1538012449, 1638294661, 
    1854940231, 1856689453, 1860373241, 1909566073, 
    1921309633, 1991063449, 1995830761, 2057835781, 
    2117555641, 2217879901, 2284660351, 2311558021, 
    2323147201, 2412172153, 2431144801, 2626783921, 
    2693739751, 2736316301, 2781117721, 2837917633, 
    3028586471, 3056100623, 3215031751, 3299246833, 
    3344191241, 3407772817, 3513604657, 3697278427, 
    3708905341, 3863326897, 3867183937, 4060942381, 
    4079665633, 4117447441, 4275011401, 4277526901, 
    4297753027, 4440974833, 4572633451, 4710862501, 
    4735847353, 4844986513, 4916322919, 5209470001, 
    5254004881, 5277058561, 5417512777, 5523053647, 
    5608834741, 5664511351, 5755495201, 5764643587, 
    6015801097, 6770862367, 6825681757, 7181757397, 
    7294056727, 7451833009, 7937788909, 8214723001, 
    8382750241, 8762386393, 8767934587, 9839449621, 
    9974580661, 10263440017, 10757267947, 11362973707, 
    11573725351, 11723962867, 11990523751, 12088739521, 
    12439296869, 12630027463, 13204140643, 13260472501, 
    13359950017, 13379139271, 13451650351, 14386156093, 
    14489566081, 14834988481, 15114550951, 15443591617, 
    15579919981, 15915651727, 15937819453, 15985540033, 
    16149644101, 16571869921, 16648289101, 16789530577, 
    17148339001, 17204704661, 17475044329, 17849326081, 
    18459366157, 18829671451, 19370286343, 19683169273, 
    19887974881, 19950730381, 20402479987, 20881811341, 
    21147503653, 21276028621, 22050472501, 22106382481, 
    23306678557, 23510118061, 23624717761, 23701368913, 
    24107139253, 24392551501, 24422578867, 24988416967, 
    25005624001, 25366866661, 25575216391, 25877556253, 
    25998250969, 26636208701, 27031263841, 27686175193, 
    27716349961, 27812670211, 27840766309, 28369977301, 
    28448982721, 28844691487, 29028709709, 29041801993, 
    29118033181, 29201742593, 29210955643, 29294447873, 
    29373426253, 29431625653, 29922333841, 30172124251, 
    30443872681, 30446045761, 30481338889, 30750388021, 
    30876125113, 31029076801, 31126523401, 31503216821, 
    32387491207, 32511106651, 32710898557, 33717240721, 
    33835759453, 34508607337, 35414584453, 35992489031, 
    36599598181, 37131467521, 37589316601, 37638037027, 
    37643480873, 38062936957, 38437684489, 38785436071, 
    39024125797, 39350644453, 39546140761, 39656142241, 
    40044071713, 41169951829, 41752650241, 42304192981, 
    42383927401, 42550716781, 43174503763, 43480237033, 
    43522383061, 43536545821, 44368051087, 44453586241, 
    44732778751, 44778481441, 45155702353, 45484371451, 
    45806699431, 46249440269, 46493311411, 46914508321, 
    47113487011, 47775322057, 48354810571, 48732546721, 
    48958085233, 49417771651, 49432922029, 49570677001, 
    51020532067, 51045523829, 52035130951, 52139147581, 
    53395376761, 53700690781, 53735893129, 53754555097, 
    54689213377, 54712169821, 55556944453, 55877409253, 
    55909506421, 56209415767, 56690936821, 57200780881, 
    57412767413, 57698562127, 58064652253, 58416990259, 
    59281660531, 59587373077, 59974663057, 62175192661, 
    63288814753, 64099345441, 64244632957, 64496640913, 
    64563256801, 64871770261, 67233528253, 67403434561, 
    67462542181, 68045910643, 68130164881, 68956997281, 
    69308671141, 69810755197, 69845839381, 70155092233, 
    70675929869, 70836033421, 70926396661, 71197831981, 
    71361225343, 72325549531, 72471384541, 72504445291, 
    72725349421, 73796984161, 74190097801, 75285070351, 
    75350936251, 75522444337, 76830284977, 76923559261, 
    77475820141, 77744325121, 78613645351, 79493923517, 
    79696887661, 79792734421, 81193513801, 82318050361, 
    83222820253, 83828294551, 84787306537, 85500830227, 
    86888746621, 88331719141, 88473676747, 88974090367, 
    89191239481, 90671598247, 90991633633, 91035378253, 
    91109610649, 91609762861, 91811005901, 94247311507, 
    96038652943, 96133341781, 97317941197, 97427678041, 
    97771083301, 98071561561, 98515393021, 100270642393, 
    101537826241, 101720969437, 102105675253, 103724068681, 
    105929038561, 106044828847, 106592618467, 106691068061, 
    107333406181, 110449331137, 110627755057, 111535250143, 
    111737197441, 112323363773, 113034250297, 113554596313, 
    114247549027, 114889084129, 115744760041, 116104599451, 
    118670087467, 118670958253, 118719698527, 119255955241, 
    119401548001, 120007618741, 120020552713, 120032716801, 
    120160888093, 120939130271, 121002621841, 123165403681, 
    124766648371, 125291398207, 126223730461, 127045046701, 
    128093304751, 128112259843, 128166950929, 128282461501, 
    128634796153, 129231975421, 129480597511, 134287508041, 
    134369289601, 134408742913, 134670080641, 135388012033, 
    135586888951, 136136947201, 136657393141, 136720423927, 
    136734586321, 138894295567, 139499445457, 140065218901, 
    140743274857, 142186219181, 142434454681, 142672297633, 
    142873722181, 142940992861, 143193768587, 144540984001, 
    146309271109, 148600530541, 150401047441, 151099301809, 
    151567921147, 151871211997, 153441518941, 155697519517, 
    156677923729, 157615339681, 157893105941, 159004666081, 
    159997800007, 161086014389, 161698820113, 163204128181, 
    163506354211, 165460595653, 166822841281, 167259489409, 
    167511984697, 167871590461, 168013453921, 168037388161, 
    169614390961, 169733554321, 169865699137, 169892970241, 
    169925718601, 170440557211, 170652642751, 172024232641, 
    172482035041, 173327250097, 173355306853, 174460968067, 
    175093079701, 175191945601, 175826956147, 176889653821, 
    177126574837, 178730896177, 178811421121, 179661750157, 
    183413388211, 183600055601, 184011185707, 185544298297, 
    186202683811, 186899072293, 186964596253, 187052662261, 
    187403492251, 187993323253, 188013914041, 188161582561, 
    189379341901, 191306981521, 191749833901, 192649998241, 
    193477919251, 194467446739, 194775768721, 195102778513, 
    195407278873, 196414988941, 199856194609, 202720026601, 
    204194969497, 204845795629, 204910260661, 205830306067, 
    207132041161, 207489679057, 207704284129, 209409003541, 
    210671885377, 211183380253, 213503633971, 214880132017, 
    216291665041, 216899043661, 217663272097, 218063627497, 
    218215348801, 218673063181, 220347528361, 220439475589, 
    220765940137, 222043264909, 222407969617, 223847502187, 
    224665456681, 224756824267, 226368183361, 230856866257, 
    231679672033, 233129684549, 234011113381, 234311749201, 
    234586128241, 235502725537, 236211406201, 236937279097, 
    237802699261, 239063545951, 239123078251, 239566120081, 
    240173032681, 240438464197, 244100277541, 244705581667, 
    244970876021, 245258365537, 245291853691, 246156139951, 
    246418172227, 246452380561, 246887390881, 247187217509, 
    247945488451, 248344385941, 250099658401, 251296189453, 
    251369212681, 252505670761, 253342076653, 254437547113, 
    254518763329, 254539341253, 257630981653, 258737953633, 
    260325499141, 261987152321, 265196971621, 266127188161, 
    267252099841, 267516487373, 269338548943, 271388845201, 
    272447722207, 275179630057, 275206295041, 275324666653, 
    275450028481, 275538119347, 275714519767, 277716000817, 
    278477097757, 281485174141, 283379139361, 283505629501, 
    283595922637, 284026441249, 284111157961, 284939504107, 
    285110050471, 288187385221, 288715819153, 289208644453, 
    290785439647, 291879706861, 293110152661, 295320648211, 
    295545735181, 297109208467, 297732153601, 299064109177, 
    299155487551, 299455474237, 299502010081, 302052174661, 
    303321964501, 303883012621, 304520079151, 307768373641, 
    310466878021, 312019585741, 312645548881, 312677530513, 
    312759427753, 314021369309, 314455378513, 315512767201, 
    315692559157, 315962312077, 316727954563, 317650877827, 
    322103070451, 325703187253, 326012836993, 327072537793, 
    329861629261, 331630652449, 332009410501, 336675266287, 
    338099746141, 341027579257, 342221459329, 342535473649, 
    344228434873, 346120528051, 349562959453, 350130266851, 
    352741412431, 353193975751, 354864744877, 355848714869, 
    356456510551, 358469284321, 361586581441, 362497014967, 
    362611193257, 362742704101, 362889406153, 363341894653, 
    363934839241, 364291060711, 365750089993, 368481433321, 
    368532871939, 372896866621, 378758150821, 380500866373, 
    381395190097, 383655122621, 388645867261, 388963341901, 
    391614491251, 393187167253, 393623401469, 394233108121, 
    396342331027, 396387488593, 396607137841, 396956737633, 
    397385563417, 398214876001, 401230163701, 404757120127, 
    405439595861, 405994847917, 406469950561, 406926034453, 
    407979839041, 408147020569, 413006305897, 414487647001, 
    420295086553, 422090747821, 422227573633, 422429369617, 
    422957193121, 431229929521, 431441200009, 431619400057, 
    431761025767, 431776138393, 433102520077, 435018304033, 
    435761068681, 437667473161, 439777538227, 440097066011, 
    442079694253, 442950335521, 445657135529, 447287618161, 
    447862344697, 454386437569, 455334765029, 456105923047, 
    457453568161, 459814831561, 460269435361, 461792694061, 
    462761923861, 463566594877, 464566100833, 468428350349, 
    473505120463, 474006086413, 478267896913, 478324335061, 
    480117685477, 483799888027, 487702804843, 488137004581, 
    489693515557, 489995816309, 490883439061, 491206491751, 
    493314780817, 494442433171, 495746584453, 497336986513, 
    499433660461, 500212817677, 501086407781, 502460519653, 
    503013421633, 503544243361, 503691743521, 505130380987, 
    505139414011, 505259452297, 511490084137, 513378847081, 
    513465330457, 514599152497, 515216377441, 516478872457, 
    521646854653, 525473097661, 526659700141, 527057853229, 
    528929554561, 529099457833, 529916079421, 535351598167, 
    535566899401, 536949055777, 537396116401, 538007625121, 
    540245042443, 540535032461, 544561381729, 545445734653, 
    546348519181, 549866444221, 550000401193, 552386159821, 
    555066552097, 555889691701, 556452218827, 558973153051, 
    566017356451, 566066620153, 568874449501, 571672908901, 
    576043867981, 577255246921, 578545344721, 578804719897, 
    580096170721, 580280202001, 581400226009, 582408871201, 
    584181495577, 586186232941, 589328360167, 591020664389, 
    591090138721, 592050558553, 593851588177, 595117550101, 
    596144853937, 602248359169, 603264831751, 606420262369, 
    607103992681, 610443439453, 614396314153, 618220795033, 
    618731235361, 621441822301, 622674469957, 623130454339, 
    624954733021, 625748190271, 633135892033, 635619064033, 
    636059184931, 638377429717, 641498618881, 644971617751, 
    645800684497, 646987060861, 649180286947, 649447129633, 
    650687218081, 653720084461, 655120396153, 656853120991, 
    658118241901, 659937299407, 662299194577, 664632439453, 
    664688646343, 669084191257, 669094855201, 669344747653, 
    670066921261, 670529556841, 673542625537, 674137339849, 
    675467739253, 675997850881, 678707450821, 684096477751, 
    686764902641, 687093823153, 688529415421, 693284423977, 
    695017757167, 696834394453, 697263158401, 697485182521, 
    699908344327, 705105542233, 706202050871, 706387654351, 
    707161856941, 708414994561, 709276255381, 710100970541, 
    710865939169, 712293633559, 712614969307, 712619212861, 
    713961324001, 714683650141, 716766544033, 717335479321, 
    719793922121, 722478960391, 724301405213, 725570934661, 
    726765201277, 729421133761, 729423665209, 730984087681, 
    733224429367, 736775510329, 737647835653, 738931029301, 
    741483987301, 741881186287, 744049848481, 755871886423, 
    755921131687, 762625313137, 762655073251, 765964320409, 
    768424945753, 768450094081, 771210870139, 773128482367, 
    774840343681, 774954608581, 776516619121, 776723467147, 
    777325386241, 777862702207, 778342988809, 783366872671, 
    783488487601, 784605470221, 785507660101, 788996936701, 
    791682200107, 792139559221, 800294024161, 801484465633, 
    802180413847, 803710692937, 805426070221, 815988967201, 
    818768544241, 819949073833, 821831844961, 822861705247, 
    825236434837, 829546061653, 831321792001, 833833587121, 
    835804082467, 835935723811, 842638521121, 844419649681, 
    844454021797, 851402588401, 851717184667, 853196213761, 
    853711783207, 856030514653, 858597289327, 860140071793, 
    860873403781, 861584051161, 861692382253, 863370140641, 
    863586071317, 864376531201, 865837311389, 868289854321, 
    875088529801, 875604201037, 877246142977, 882049658249, 
    885281566681, 885740903191, 887327169121, 888216903241, 
    898842708409, 899882896681, 903421786681, 903621656953, 
    906437081089, 907203644569, 908201935681, 908354097289, 
    908597158561, 909703432061, 910320315449, 910631583793, 
    913359227041, 915426232033, 918678638767, 919555347461, 
    920747458877, 922422043201, 924633131731, 933148512217, 
    938800637347, 939625142653, 939821942809, 944105978971, 
    945788339953, 947372683753, 953198091301, 962010334297, 
    966299321527, 966410493049, 967857029107, 968555992801, 
    968936634821, 969734103001, 970650176641, 971273119213, 
    973922675041, 974456821001, 977136994081, 977501393977, 
    979184669653, 979319018341, 981290836501, 985016775601, 
    986924689453, 997031384161, 999236382301, 1002101725633, 
    1004006505001, 1005693130261, 1007729332849, 
    1008145330741, 1009094110501, 1009304352253, 
    1009781789941, 1011317175721, 1013963742457, 
    1014503715343, 1016962606441, 1018189472653, 
    1023100257121, 1024478493307, 1028577018169, 
    1032352860937, 1044731511253, 1052516956501, 
    1053597763681, 1059016451767, 1059881943121, 
    1060750744453, 1060920857599, 1064564468281, 
    1074568471021, 1088972527843, 1089609053653, 
    1093499469877, 1100477362141, 1101317770561, 
    1104775437169, 1105339579489, 1106487824557, 
    1106718256261, 1107936488881, 1108698788737, 
    1108746381601, 1110536445313, 1114442093161, 
    1114531700833, 1115955545821, 1118359654387, 
    1118675164753, 1121023561033, 1121610731251, 
    1122004669633, 1123382831581, 1124150856193, 
    1127681393617, 1128064333861, 1128105246337, 
    1128792948841, 1131046645009, 1133836295041, 
    1136371968811, 1138687632253, 1142675134453, 
    1144020045601, 1144039081249, 1148949062977, 
    1150447363201, 1151753231737, 1151982124021, 
    1152791681801, 1154159672581, 1158257600551, 
    1161179493769, 1162388969821, 1165050425137, 
    1165133944981, 1166917753633, 1170415575253, 
    1173354975253, 1174372863049, 1176455318347, 
    1177549989661, 1177806610657, 1179659369701, 
    1188059560451, 1192912308127, 1196678873251, 
    1197597106261, 1201841349367, 1203395684041, 
    1203962379481, 1205537391661, 1206912438817, 
    1210381992793, 1211958555757, 1217810486593, 
    1218861882397, 1219088082997, 1221365838191, 
    1225454692177, 1226534725441, 1235933933653, 
    1237424787289, 1238423846087, 1240088072653, 
    1241827324741, 1242025758433, 1242546067153, 
    1246591940833, 1249024105981, 1250901882187, 
    1253355248521, 1255537494091, 1259947883041, 
    1261394769601, 1261954454221, 1265782991761, 
    1266270405877, 1266356918287, 1267680187621, 
    1271789215441, 1274471613721, 1275258000061, 
    1277210203837, 1277674527631, 1278867359173, 
    1280466733597, 1280575706437, 1282492075801, 
    1288748726641, 1295730434701, 1297382964967, 
    1301723139601, 1302339572641, 1303276467781, 
    1310528518993, 1312654141633, 1313808932041, 
    1318632506647, 1324095131321, 1325623437433, 
    1328802855031, 1337247868963, 1340148888541, 
    1340182695433, 1343172069581, 1344535060061, 
    1346348942881, 1347430986721, 1350572284951, 
    1352431246321, 1355932740247, 1356702279661, 
    1362242655901, 1362559589821, 1363236634717, 
    1363802969401, 1364105061259, 1364779159453, 
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