Thema: Fermatquotient B^(P-1) == 1 (mod P^2) Fermatquotienten mit extremen Erst-Prim-Basen Main table of content: http://www.fermatquotient.com/ Fach-Artikel-Hinweis: http://www.ams.org/mcom/2005-74-250/S0025-5718-04-01666-7/ 12.03.2010: Die Primzahl 44533417 hat 4 Fermatqotienten-Prim-Basen, die kleiner als sie selbst sind! 31.03.2010: Die Primzahl 94089029 hat ebenfalls 4 Fermatqotienten-Prim-Basen! 17.05.2010: Die Primzahl 112730201 hat ebenfalls 4 Fermatqotienten-Prim-Basen! 18.04.2011: Die Primzahl 211503199 bildet ebenfalls 4 Wieferich-Paare! 16.05.2011: The prime number 214084193 has likewise 4 Wieferich pairs! 12.06.2015: The prime number 465593413 has likewise 4 Wieferich pairs! 03.04.2016: Die Primzahl 511475143 bildet ebenfalls 4 Wieferich-Paare! 10.02.2017: Die Primzahl 555902117 hat ebenfalls 4 Fermatqotienten-Prim-Basen! 13.03.2017: The prime number 560003849 has likewise 4 Wieferich pairs! 22.06.2017: Die Primzahl 573506099 bildet ebenfalls 4 Wieferich-Paare! 27.09.2018: The prime number 631912823 has likewise 4 Wieferich pairs! 22.10.2019: Die Primzahl 741996397 bildet ebenfalls 4 Wieferich-Paare! 17.12.2019: The prime number 759500251 has likewise 4 Wieferich pairs! 27.12.2019: Die Primzahl 762585353 bildet ebenfalls 4 Wieferich-Paare! 21.07.2020: The prime number 824827673 has likewise 4 Wieferich pairs! 22.07.2020: Die Primzahl 825183503 bildet ebenfalls 4 Wieferich-Paare! 24.09.2020: The prime number 843609883 has likewise 4 Wieferich pairs! 01.01.2021: Die Primzahl 871905817 bildet ebenfalls 4 Wieferich-Paare! 20.02.2021: The prime number 885591739 has likewise 4 Wieferich pairs! (13.03.2023: Next update by 1.08E+09) Fermatquotienten mit relativ vielen Prim-Basen < Primzahl Gegenwärtig durchsucht bis zur Primzahl 1070229691 Anzahl (je erste 20) ; P: Primzahl^2 ; PB: Prim-Basen Quanity (20 piece each) ; P: (prime number)^2 ; PB: prime bases 1 P: 11 PB: 3 1 P: 43 PB: 19 1 P: 59 PB: 53 1 P: 71 PB: 11 1 P: 79 PB: 31 1 P: 97 PB: 53 1 P: 103 PB: 43 1 P: 137 PB: 19 1 P: 263 PB: 79 1 P: 331 PB: 71 1 P: 421 PB: 251 1 P: 433 PB: 349 1 P: 487 PB: 307 1 P: 523 PB: 241 1 P: 653 PB: 197 1 P: 659 PB: 503 1 P: 743 PB: 467 1 P: 859 PB: 643 1 P: 863 PB: 13 1 P: 919 PB: 457 2 P: 349 PB: 223, 317 2 P: 359 PB: 257, 331 2 P: 907 PB: 127, 761 2 P: 1483 PB: 421, 1061 2 P: 1697 PB: 461, 857 2 P: 1993 PB: 277, 1747 2 P: 2309 PB: 823, 1453 2 P: 2719 PB: 1487, 2269 2 P: 3617 PB: 1459, 3371 2 P: 9161 PB: 659, 7127 2 P: 9323 PB: 827, 3449 2 P: 9811 PB: 1637, 4871 2 P: 10369 PB: 3023, 4111 2 P: 10837 PB: 4523, 8863 2 P: 13883 PB: 9733, 10111 2 P: 17981 PB: 1171, 6911 2 P: 18539 PB: 1693, 9241 2 P: 19289 PB: 523, 8669 2 P: 21493 PB: 3253, 7561 2 P: 22147 PB: 5113, 21673 3 P: 13691 PB: 83, 8677, 11689 3 P: 35747 PB: 9151, 9689, 20849 3 P: 186601 PB: 33479, 46411, 120619 3 P: 355783 PB: 26723, 82561, 192383 3 P: 454501 PB: 76343, 106747, 272341 3 P: 489061 PB: 53201, 167173, 250027 3 P: 595571 PB: 166259, 183047, 423121 3 P: 723553 PB: 236021, 352837, 430873 3 P: 1334717 PB: 100411, 160697, 271169 3 P: 1983437 PB: 332743, 1293203, 1339813 3 P: 2232059 PB: 185137, 1212241, 1449307 3 P: 2313403 PB: 1048721, 1211191, 1982873 3 P: 2612999 PB: 860479, 1376719, 1813897 3 P: 3103757 PB: 650317, 743851, 2234797 3 P: 3218323 PB: 49999, 1363367, 3042763 3 P: 3519823 PB: 2386003, 2411797, 2921689 3 P: 3623203 PB: 79903, 1181017, 1355863 3 P: 4077473 PB: 514399, 2288359, 3672857 3 P: 4085167 PB: 1530709, 2072267, 3354187 3 P: 4418303 PB: 2112989, 3126239, 4330763 Weitere Primzahlen (Fermatquotienten) mit 3 Prim-Basen sind: 4560151, 5570791, 5753249, 5794211, 6289499, 7920883, 8170447, 8247583, 8446747, 8856131, 9015217, 9115277, 9540283, 9615937, 9629419, 9742969, 9847543, 10191029, 10580429, 10639507, 11049331, 11210669, 11380139, 11552977, 11562211, 11728841, 12037427, 12715909, 13123169, 13515077, 13786937, 13805501, 14190959, 14206799, 15417679, 16027367, 16976359, 17052097, 17623471, 17883233, 18200123, 18856913, 19133407, 19242481, 20657999, 20667299, 21089489, 21143261, 21379289, 21950333, 22443901, 22540499, 22615361, 24241859, 24529363, 25047283, 25086661, 25142041, 25418191, 26143669, 26905493, 28105723, 30031277, 30246487, 31428583, 32610503, 32721263, 32851963, 33189361, 33236711, 33680729, 35659549, 35683801, 36013507, 36043537, 36916721, 37264433, 39888623, 40810151, 41024507, 41455903, 41766391, 41880941, 42716293, 43590473, 44120333, 44865179, 44922281, 46176673, 46679669, 47436841, 48152597, 48460459, 48678131, 48750001, 48921493, 49220257, 49368019, 50884697, 51112169, 52012151, 52426141, 52684249, 52824383, 54035777, 54106807, 54248111, 54325163, 54871819, 54883273, 55584779, 55634531, 55705079, 55815769, 56518411, 57167587, 57914137, 58172159, 59224777, 59618837, 59667611, 60995257, 61003219, 61151483, 61161671, 61525241, 61942483, 63338411, 63531361, 64336399, 65440717, 65474401, 65982361, 66094687, 67781177, 68423357, 69139849, 69223321, 69297143, 70574731, 71466539, 72460147, 72569027, 72818587, 72898883, 73612751, 73857827, 75024427, 75700747, 76584509, 76989667, 77499407, 77696147, 77721239, 78310499, 78768709, 79217533, 80019679, 80051471, 80307589, 80746943, 81208447, 81386891, 81815791, 82263487, 82655413, 83197937, 83899741, 83916341, 85353007, 85441001, 85475389, 85895431, 86244929, 88634881, 90411619, 92253893, 94063447, 94142813, 95642033, 96854453, 96870031, 96932201, 97308157, 97873151, 98302289, 98709761, 99010687, 99432587, 99548443, 100252637, 100829497, 100947991, 102451633, 104573423, 105099437, 105467027, 106698607, 106762189, 107064457, 109345721, 110403061, 110455771, 112807417, 113486333, 113720267, 115113959, 115706417, 115849057, 116489137, 117913967, 117973267, 118272529, 118850449, 120039151, 120915979, 122242753, 122429449, 122993687, 124181537, 124232263, 125101091, 125192261, 126740969, 127786787, 127848713, 129447293, 130055467, 130063393, 131662709, 131733313, 133012741, 133022473, 133273807, 134293097, 134523317, 136101899, 136255991, 137054843, 137110087, 137937377, 138569339, 138652931, 139046003, 139144331, 139367201, 139637413, 139790731, 140716699, 141326851, 141349529, 142229407, 143656181, 144206453, 144487549, 145783433, 145997141, 147518263, 147637727, 148454051, 148494539, 148688467, 151908313, 152148779, 154046647, 154324811, 155264741, 155552923, 155895137, 156524449, 156559159, 156880127, 157957633, 158797937, 160241219, 160759813, 161469079, 161598557, 161894399, 164158109, 164522143, 164808817, 169185407, 169377787, 169979669, 170041349, 170725943, 171257617, 171262711, 171699683, 172093553, 173544583, 173904763, 174764767, 176406883, 176819849, 176944939, 177728179, 177729467, 178354507, 178670449, 181007107, 181384579, 182251493, 182464013, 183004907, 183362423, 183988817, 184056409, 186283667, 187170707, 187291847, 188078857, 188156861, 189144097, 189485209, 191117497, 191121101, 191741831, 191929019, 192494279, 193128037, 193747549, 194341949, 194554903, 195625481, 195675101, 196228423, 196564033, 196699453, 197524013, 197969411, 197980571, 200983967, 203912701, 205678787, 205838177, 206700199, 207478519, 208578553, 208894201, 211774331, 211954753, 212105239, 212875529, 213468089, 214026551, 215646287, 216210173, 217687501, 218465887, 218520233, 218896817, 219164131, 220600111, 220833157, 221209829, 221269457, 222489809, 223733327, 223956353, 225061909, 227510489, 228055937, 229214903, 230255771, 230376511, 231740177, 231952873, 231993899, 233536757, 236039357, 236587937, 237319619, 237645007, 239120647, 240617291, 242076431, 242345717, 242365663, 243392203, 243497789, 244177639, 245227727, 245988157, 247044143, 248375747, 248416607, 248965471, 249247741, 249519871, 249696143, 249915817, 250303609, 250888031, 250938341, 252374867, 252827347, 253562131, 253797619, 255164401, 255275641, 255950879, 255978781, 257025121, 259583791, 260042093, 260959579, 261093097, 262191367, 263759081, 264585481, 265118311, 266083621, 266349091, 266500303, 266858093, 267217481, 267950497, 268572611, 268801177, 269169073, 269535817, 271031987, 273064159, 273342161, 273841439, 273936967, 274016293, 274191557, 275332661, 276715697, 276980101, 277826771, 279273517, 279348623, 279399553, 280215589, 280313339, 281415397, 283420211, 286249811, 286773283, 288050093, 288375413, 288675601, 288684421, 289525163, 289756333, 289855799, 290971027, 291218401, 292066703, 292984457, 293496799, 294088547, 294611167, 296922089, 298262879, 298773353, 298907779, 298927103, 299140417, 300872501, 302555311, 302632921, 303919601, 304083497, 304341137, 304856141, 308166413, 308501647, 309307051, 310937929, 311207581, 311742643, 312281521, 312799169, 313466561, 313513373, 313907221, 314201779, 316504183, 316598039, 316932131, 317392277, 317925599, 319129409, 320642741, 321330083, 323054107, 324007819, 326804143, 328219253, 329343943, 329626909, 329733737, 329783471, 329898713, 330974939, 331269817, 331621027, 331896127, 331979777, 332288513, 332359613, 332929549, 334317583, 336851393, 337688411, 338199023, 338740183, 338862079, 341551283, 348581879, 348614089, 349814711, 351569399, 352412183, 353009201, 353897473, 354296639, 354982039, 358364401, 358503287, 360946177, 363960841, 364358563, 366066133, 366978329, 367247381, 367907339, 370897561, 371084633, 371981837, 372631979, 372792803, 372935377, 373451171, 374536993, 378009241, 378720299, 378726541, 379738213, 383025569, 385490909, 386004559, 386332379, 387512423, 388358881, 389918689, 390159593, 390788737, 390875911, 390886973, 391515493, 393139217, 394690333, 396415573, 396694729, 397080529, 399223093, 399322883, 400860193, 401949511, 403535597, 403597993, 404247863, 404464349, 405210863, 405521651, 406089137, 407372429, 407635651, 407677819, 407883769, 408690923, 408830027, 408992047, 409181711, 409873001, 410301877, 410500219, 411197987, 411643409, 412364527, 412497577, 412548613, 414229723, 415356119, 415376551, 416666479, 416865151, 417481531, 421331873, 423091243, 424463203, 427699159, 429256213, 429557417, 431423371, 432570419, 433048949, 434296537, 435213679, 435441317, 436034659, 436491683, 437110339, 438081331, 438931769, 439041283, 440140223, 440219963, 441148943, 441875089, 442326719, 442869403, 444643471, 445163471, 445431983, 445651069, 447885337, 448375771, 448576957, 449002777, 450373127, 451453333, 453123767, 456095743, 456665701, 456933821, 458073229, 458282359, 458941313, 459604841, 460543093, 460775533, 461281589, 461393059, 461860523, 463617911, 464225789, 465174637, 466428059, 468587629, 469286137, 470132387, 476085887, 477177329, 477720547, 477748169, 478016359, 479045857, 479228677, 479902459, 480662309, 481293733, 482328251, 483218699, 483587959, 483896263, 486210997, 486288703, 486430283, 487548751, 487582519, 487678211, 487927261, 488058497, 488299033, 488799743, 489211243, 490166981, 490474781, 492172589, 494945917, 495319093, 497824421, 497919557, 498066601, 499630903, 500083321, 500349973, 500441147, 503849113, 504106787, 505899829, 506219543, 506394461, 507035993, 507450631, 508627729, 508942541, 509091631, 509656211, 510601631, 510613709, 512322823, 514437433, 518468081, 518491543, 520350139, 520756441, 521113961, 522857983, 522873083, 523484939, 523833251, 523977143, 525002593, 526204771, 526516799, 526696253, 527111201, 527849197, 527911589, 528048979, 528819827, 530422271, 530702273, 530706149, 530858261, 530938043, 532495307, 532866437, 533667479, 536423201, 536664077, 537920093, 538020611, 538468009, 539245493, 539750399, 541438223, 542746769, 544819003, 545331947, 546059803, 549010153, 550262707, 550289261, 550925917, 551334943, 552051683, 554344601, 555517463, 557511659, 559379837, 559989887, 560622743, 562343081, 562421987, 563328317, 564362429, 564564079, 566170333, 566561803, 566745923, 569098687, 570640739, 572061851, 573419393, 573861839, 575097673, 575187337, 575421173, 575726093, 577171541, 578082137, 578906963, 579136301, 580646749, 581939893, 582377881, 582436511, 582752029, 583497797, 585167419, 586755667, 589266857, 589754743, 591770539, 592028557, 592796483, 593644907, 595642877, 597470833, 597814913, 599852423, 599930783, 600060289, 600301721, 601191233, 603141017, 606843791, 609113101, 613680143, 613767911, 615069863, 615473743, 616095119, 616356541, 617143601, 617455961, 618870053, 623694319, 624523843, 625835891, 627143579, 629467309, 629898527, 632681051, 633143647, 634692781, 636474551, 639865111, 639947773, 640632277, 640977497, 641084173, 641196821, 641271781, 641948831, 644443999, 644859877, 644862893, 647207783, 648194389, 649026227, 649144231, 650790929, 651827237, 652131731, 653046077, 653281931, 654261347, 654731681, 658574347, 659916749, 660968053, 662750579, 662797153, 662889001, 662911489, 663000913, 664337059, 664584163, 664898603, 665719673, 665917751, 667721867, 670311283, 670365119, 670380167, 670684043, 670773757, 671340203, 677702503, 677908919, 678393197, 679136657, 679478897, 681315071, 681416077, 683735953, 683755537, 683809703, 683825381, 685693439, 686524081, 688508033, 689473417, 690902941, 691036847, 691384613, 692462461, 692901169, 694684649, 695253829, 696934949, 698783867, 698920883, 699116773, 699752531, 702149939, 703203103, 704257649, 705234767, 706342829, 708392297, 710400421, 710542439, 710638549, 711621367, 712181473, 713886647, 715122971, 716831327, 716961391, 717111937, 718124161, 719042029, 720188701, 720274223, 721245901, 721298371, 721724629, 721764851, 723306517, 723710849, 724976327, 725028013, 725699719, 726245119, 728635307, 730203527, 730472597, 730754803, 731957011, 731959741, 733257331, 733458797, 733553507, 734381803, 735158117, 735699311, 738918319, 739709743, 739750993, 740335357, 742109671, 742383331, 744271447, 744737797, 744748889, 747014377, 747528043, 749217529, 749290807, 749485151, 749605093, 749916961, 751633457, 752664301, 755497751, 756322421, 756984499, 758011021, 758365739, 758494901, 758996437, 759354719, 762997517, 763407487, 765013297, 765042587, 766014721, 766852781, 767101499, 770235187, 771910219, 773663411, 775886291, 776221379, 776265731, 776509159, 779354441, 780867119, 782600563, 782669141, 784114411, 789820939, 790337117, 791495807, 791938669, 794612681, 795235183, 795789409, 796000549, 796922773, 797024219, 797481149, 798730169, 799770701, 799888697, 800209331, 800212667, 800544149, 801515971, 803527493, 803559037, 805238933, 806135171, 812100287, 812210561, 813764117, 813847087, 813925621, 818900443, 819077461, 819600307, 820695437, 821399521, 821925343, 822390769, 823061461, 824008223, 824862433, 825123913, 827690873, 827704379, 827747383, 828447601, 830052049, 832207153, 832911509, 834927559, 835294513, 836248807, 837259919, 838052251, 838298693, 838673711, 839132191, 840490579, 841674391, 843294203, 843598597, 843667141, 843966923, 846485911, 848709557, 849157513, 849349297, 849503587, 849658933, 852647197, 853019317, 853803233, 854683607, 854705771, 855523183, 856003171, 856803911, 860182723, 861028319, 862277531, 862634401, 864319459, 865049401, 865946923, 866002859, 866493319, 866655719, 866889601, 866949067, 867071851, 870566471, 871736449, 873168641, 873629707, 873861161, 875295067, 875489891, 875497097, 875778707, 876291589, 877756939, 878525621, 878748943, 878871407, 879833371, 879946499, 880976497, 883853819, 885828617, 887665169, 888113987, 888508531, 889289563, 890609527, 891373871, 891612797, 891851117, 892199339, 893371789, 893479529, 896083543, 896571469, 899600791, 900498271, 900923021, 901607761, 901759759, 902116531, 902174831, 902961637, 904770431, 905030773, 906763727, 908083541, 908131729, 908235817, 909295291, 914299339, 914693987, 915402679, 916494037, 916618481, 916933007, 917340467, 919451899, 920555267, 920656717, 920956849, 921449927, 924365329, 924582287, 925117111, 925854301, 926081753, 927463049, 929297183, 929463313, 931536919, 934004387, 934264729, 934313651, 936616991, 937915733, 938778931, 939653119, 939791417, 943056503, 943356199, 945173309, 946053611, 947241341, 948330967, 949832171, 951391871, 954010727, 954429683, 955616603, 955814329, 957463361, 957961649, 958127431, 958905427, 961553561, 963900181, 964787563, 966445003, 967450459, 970937593, 971444783, 972610181, 973977359, 977999959, 978045709, 978062131, 978697751, 978765967, 980441353, 981931021, 984345391, 989097709, 989913481, 990236939, 992066129, 993034901, 993638563, 993676087, 994100111, 994579307, 997351343, 998822537, 1002711001, 1003066679, 1007002691, 1007215723, 1010286509, 1012128629, 1012469243, 1012537067, 1013225713, 1013551369, 1014193853, 1014779257, 1016278129, 1017163421, 1017499499, 1018093201, 1019567261, 1020466511, 1020550403, 1020781001, 1021884559, 1023079163, 1023184579, 1024789093, 1025375419, 1025837383, 1025920921, 1029127703, 1030942879, 1030967467, 1031176739, 1031323133, 1033198379, 1033883569, 1033918217, 1035221129, 1035240769, 1035453143, 1037789147, 1038406513, 1039771079, 1040993669, 1043715059, 1045026139, 1046322539, 1046428987, 1046738053, 1048623773, 1050087109, 1051513819, 1051723163, 1051859933, 1052830307, 1052982683, 1055088539, 1056556733, 1056916811, 1056935371, 1058417047, 1060242619, 1060509631, 1060630387, 1061195959, 1061568943, 1061863723, 1063414147, 1064378971, 1064847401, 1066032691, 1066662041 4 P: 24329 PB: 1777, 3301, 4919, 13691 4 P: 2105669 PB: 248891, 654923, 1296877, 1865299 4 P: 9656869 PB: 788393, 1639607, 1786913, 7860337 4 P: 44533417 PB: 4901129, 4901969, 15772937, 35397001 4 P: 94089029 PB: 26972069, 44782937, 73134563, 82912807 4 P: 112730201 PB: 16676221, 38670271, 61993381, 105351137 4 P: 211503199 PB: 81558563, 98015507, 114416089, 128877641 4 P: 214084193 PB: 17548049, 101599279, 110406091, 162017143 4 P: 465593413 PB: 177631073, 261567619, 280244149, 429052639 4 P: 511475143 PB: 153232081, 184402489, 379914901, 474032297 4 P: 555902117 PB: 231969599, 359138501, 364339069, 386694557 4 P: 560003849 PB: 161650267, 179198449, 265518047, 502393349 4 P: 573506099 PB: 13657873, 155430809, 186147571, 300864607 4 P: 631912823 PB: 11093569, 92216221, 283457743, 545713211 4 P: 741996397 PB: 22301533, 44000197, 582895571, 613452187 4 P: 759500251 PB: 113777, 255352847, 340038317, 674276803 4 P: 762585353 PB: 77544163, 124579159, 236677697, 432709441 4 P: 824827673 PB: 41811919, 80235061, 166923173, 404344267 4 P: 825183503 PB: 26513177, 402314041, 405828769, 716145341 4 P: 843609883 PB: 24973367, 49289797, 402476099, 642437483 4 P: 871905817 PB: 358607419, 408086827, 484670093, 709433147 4 P: 885591739 PB: 41434373, 113275273, 352095587, 504703151 Weitere bekannte Primzahlen P mit Erst-Basis < 106 und mit 1 Prim-Basis < P sind: Anzahl ; P : Primzahl^2 ; PB: Prim-Basen Quanity ; P: (prime number)^2 ; PB: prime bases 1 P: 1093 PB: 2, (18979, 31481, 35447, 41263, 49633) 1 P: 1163 PB: 241, (9851, 10337, 26317, 63803, 71191) 1 P: 2777 PB: 59, (76631, 78229, 92311, 107581, 209213) 1 P: 3037 PB: 79, (29059, 33937, 65053, 77047, 89759) 1 P: 3511 PB: 2, (82183, 109441, 140167, 177383, 320039) 1 P: 4871 PB: 83, (5039, 41389, 48371, 59651, 101797) 1 P: 6451 PB: 31, (132287, 266159, 468581, 519307, 584603) 1 P: 15061 PB: 10993, (43283, 113417, 181927, 850247, 928307) 1 P: 20771 PB: 5, (62401, 147503, 479221, 506251, 546523) 1 P: 36713 PB: 36299, (37811, 214943, 313679, 412831, 775811) 1 P: 40487 PB: 5, (586871, 930737, 1198321, 1812227, 2527457) 1 P: 46021 PB: 17, (104851, 465643, 1676651, 1854731, 1973233) 1 P: 48947 PB: 17, (55889, 104537, 593839, 1084669, 1557797) 1 P: 77867 PB: 37, (2842643, 3941957, 4963603, 5917259, 6076309) 1 P: 86197 PB: 1801, (2238179, 2685373, 3803491, 4167607, 5433997) 1 P: 268573 PB: 67, (1416167, 5777113, 12264713, 12798547, 20292683) 1 P: 491531 PB: 7, (3927107, 6699599, 9554521, 12275647, 37247261) 1 P: 661049 PB: 383393, (1951603, 5739491, 14829809, 29271899, 35633867) 1 P: 1006003 PB: 3, (25671391, 31098449, 122106493, 139955303, 157323121) 1 P: 1012573 PB: 79, (6857453, 19863887, 56324069, 81870641, 95124187) 1 P: 1025273 PB: 41, (6025933, 15780299, 62726471, 95093311, 106658437) 1 P: 1050139 PB: 101, (17236369, 35801867, 44568761, 78261229, 130372919) 1 P: 1747591 PB: 13, (42623249, 91712209, 113437721, 152717153, 174058229) 1 P: 2481757 PB: 23, (19750699, 41567011, 69703979, 93249217, 118528693) 1 P: 2914393 PB: 97, (82677923, 192442031, 195781501, 272024723, 272556047) 1 P: 9377747 PB: 7748291, (545007049, 615320129, 1059716167, 1116593879, 1347620441) 1 P: 13703077 PB: 23, (302108893, 422705579, 826468789, 854828437, 1129878437) 1 P: 24490789 PB: 103, (233531447, 505722839, 1364781841, 1416499093, 1580378929) 1 P: 53471161 PB: 5, (2935562563, 3112162727, 4718355841, 5058189449, 5075148643) 1 P: 60312841 PB: 79, (3254495191, 4938141739, 5032567927, 5117730433, 5655325369) 1 P: 63061489 PB: 19, (264669157, 1595801533, 2096360803, 3637834439, 3723925817) 1 P: 138200401 PB: 41, (2809163893, 5273291269, 22458594217, 26681153203, 27745028471) 1 P: 139409857 PB: 5715719, (10439392709, 13898097491, 20037550457, 27741296179, 30680049677) 1 P: 315746063 PB: 83, (27975502799, 34797320447, 42884829133, 43206850039, 55366841293) 1 P: 1228488439 PB: 102109169, (34711966291, 40790414759, 98788675493, 116772462799, 124312064983) 1 P: 1645333507 PB: 5, (70163471359, 132514534511, 297916164361, 375696824873, 445550931433) 1 P: 6692367337 PB: 5, (341943421907, 404703009251, 489137456359, 537725725679, 998892348491) 1 P: 15546404183 PB: 23, (1208319499579, 1296514445971, 1622263147969, 1768903626233, 1862382537871) 1 P: 76407520781 PB: 37, (1615376096953, 1947144978263, 4755078378023, 5555474792761, 6272574182183) 1 P: 76704103313 PB: 97, (236917183271, 3419751673357, 3542586237977, 4405728325133, 10552275323981) 1 P: 188748146801 PB: 5, (20845208679083, 21152888888479, 21550723702241, 33555846775181, 39434865922241) 1 P: 478225523351 PB: 17, (2227246108447, 5079946164589, 10823769340031, 15771448668191, 24635400502469) 1 P: 2549536629329 PB: 23, (19925360452639, 54365062168699, 279100196041103, 480801805593553, 490496522015957) 1 P: 8206949094581 PB: 79, (105436981651843, 161160996306239, 542162754281641, 1054084283418239, 1497888643577993) 1 P: 13368932516573 PB: 43, (75933088226453, 193877128333111, 261327118301243, 327184192192069, 348821193068857) 1 P: 18088417183289 PB: 59, (1736413307266153, 3642332259680887, 3755017436004319, 6513830410176613, 8428052505136241) Weitere bekannte Primzahlen mit Erst-Prim-Basis < 1052 (<10126 mit P > 5E+07) und mit mindestens 2 Prim- Basen sind: Anzahl ; P: Primzahl^2 ; PB: Prim-Basen Quanity ; P: (prime number)^2 ; PB: prime bases 2 P: 19289 PB: 523, 8669 (43037, 336551, 985277, 997109, 1938301, 2137879, 2352947, 2382301, 2974651, 3092891) 2 P: 35059 PB: 179, 14591 (775823, 872863, 1401263, 1521781, 2278019, 2960231, 4029679, 4279619, 4600577, 5315809) 2 P: 60623 PB: 887, 34283 (81773, 241867, 2770991, 3148193, 3759221, 4959533, 5124593, 5657941, 5974097, 5987561) 2 P: 74047 PB: 239, 34213 (471073, 1866113, 2064373, 3769361, 5801171, 6814009, 8284453, 8336213, 9463759, 12750701) 2 P: 1125407 PB: 853, 716897 (10129429, 15221207, 17339159, 57460547, 78371639, 80376311, 90432679, 104170949, 167996239, 215975203) 2 P: 2806861 PB: 31, 1027799 (9360311, 36996461, 45202021, 284469877, 307505977, 406507613, 446967163, 464723291, 554517239, 594105487) 2 P: 4242923 PB: 157, 417881 (202283041, 306071533, 467586211, 473331091, 541588909, 649697921, 654464543, 717194189, 1065791117, 1125968083) 2 P: 5681059 PB: 739, 1080229 (51895763, 150476617, 186873913, 337286701, 385869223, 436679549, 494444233, 546712937, 613324951, 803841167) 2 P: 8938997 PB: 521, 3945449 (134160811, 210544577, 376859629, 930874249, 1030165189, 1096212709, 1520825309, 1593549049, 2289251837, 2797897517) 2 P: 24350087 PB: 359, 22642177 (657652903, 1631841469, 2755092617, 3060262717, 4778350747, 6027095369, 6426353897, 7221786311, 7226446831, 7838117317) 2 P: 51554803 PB: 2707, 46266067 (164424269, 227789251, 697114241, 2437325311, 3101114503, 4215870913, 4244674253, 4480854589, 5567993047, 5726584433) 2 P: 70146647 PB: 1303, 55447729 (1093425181, 10547286391, 13433744111, 14966413663, 15307291781, 15869992561, 18876136781, 19877987113, 21417923353, 22167665629) 2 P: 95552731 PB: 6067, 9510791 (2527392731, 3517034099, 4080258551, 5005062277, 8846780377, 8952813787, 17391121691, 19240535101, 26050194281, 29305331533) 2 P: 96339169 PB: 7529, 71181493 (1630124053, 2414336663, 4104018587, 4700095019, 5139027571, 5673798439, 6353823011, 6956473621, 7643828851, 14652555779) 2 P: 105813941 PB: 2203, 82869481 (217409369, 1365059911, 7185147379, 8861588719, 13786631699, 16592476871, 18894157057, 24087586631, 25878902657, 29510250641) 2 P: 134318669 PB: 7069, 62222519 (1052426563, 1606526161, 3020556563, 6148790867, 8415946453, 8942029669, 9037229261, 12353434921, 17561874049, 17976891593) 2 P: 148838969 PB: 6781, 10156457 (7024645373, 11154281029, 12422169719, 13674005669, 22975617439, 28661847853, 29620705867, 31115454647, 35450656729, 35743962029) 2 P: 485998679 PB: 3847, 251817649 (19392291251, 25983542147, 49788030857, 51745761167, 55393194119, 57736334137, 70373914889, 74330268323, 120758440973, 140822905583) 2 P: 527474537 PB: 5087, 143031271 (14969254441, 21133837211, 32571645959, 43087760167, 47604000637, 48847406207, 50379048199, 51961161809, 53332581667, 57564310387) 2 P: 651087043 PB: 6983, 235959671 (39775182053, 107772713941, 115741008919, 129787304411, 147209510731, 150123124171, 165238493551, 189705243941, 194750941943, 230777441711) 2 P: 766237169 PB: 3203, 665521811 (7119081773, 30362889119, 35119042303, 40848249461, 59174100151, 81768331039, 106471133779, 112137502567, 125673332893, 127061870953) 2 P: 903240109 PB: 3229, 566049023 (59181846421, 95600957677, 102963418447, 107106456031, 109895029213, 113948711167, 115180310701, 117864987293, 120477798127, 217219602247) 2 P: 924662719 PB: 9227, 358272613 (5998460617, 19144560793, 101177588119, 178448336251, 187505453431, 215431063249, 225644164019, 248348847077, 306286245113, 354464939861) 2 P: 1025700953 PB: 6833, 487411871 (3240382819, 17492702933, 40682737603, 41896625207, 64674953831, 171031732897, 172994868509, 174996058519, 177662317837, 217635533729) 2 P: 1194789287 PB: 9161, 1193558893 (21394420651, 64328152879, 86083439077, 87275791783, 143062361389, 150946576349, 169035749023, 224499186031, 277005742513, 353604958477) 2 P: 1232531249 PB: 3079, 272014723 (71934716593, 106103856973, 118669710557, 160453575473, 185596387477, 186927153563, 187051805947, 187210329793, 191237002631, 208574344507) 2 P: 1419597889 PB: 2549, 1059785653 (4564567127, 96943077971, 132404044193, 163433531633, 174698990363, 196393301789, 260049477593, 294474330523, 304920665209, 329561058049) 2 P: 1448446723 PB: 7121, 719952553 (42506083457, 44115171883, 58551938843, 103897335631, 152161075817, 181051779847, 282604078651, 310958187461, 336713582479, 371296967933) 2 P: 1641918209 PB: 2063, 1320273629 (16789904587, 51672616519, 53850575627, 105210217243, 160227425381, 238811941237, 259916213723, 321183755929, 322761526531, 386966346719) 2 P: 2049931423 PB: 10009, 1054526021 (46333875493, 109685454077, 174607534741, 343359110789, 359971791181, 451685918591, 528828103567, 548622295531, 559633632139, 654869978407) 2 P: 2243046959 PB: 5231, 145089403 (46529657963, 55776424211, 277609210381, 279259336159, 304966503671, 358477114517, 505984544279, 518020478557, 520000148579, 520532694359) 2 P: 2280812437 PB: 3229, 1645531681 (19355300099, 57842737181, 99756262399, 154296755443, 182213373161, 333511165121, 370983786553, 395878770127, 412229507779, 432085962817) 2 P: 2428281227 PB: 9067, 698030429 (26931564091, 41978778833, 68841901907, 94269867283, 133205968199, 208430833241, 244279008781, 246132320377, 431548954607, 670857355583) 2 P: 2735825263 PB: 1423, 679415389 (11927934367, 32986498999, 179378071673, 249156322201, 249512677319, 347645109293, 349569075283, 352235626433, 483651484817, 618147517837) 2 P: 2738193011 PB: 7307, 1580850727 (74804375777, 86742363319, 125528802461, 156166393759, 445555479791, 540732982841, 542421965623, 608826031511, 615368261861, 665810656747) 2 P: 6847964467 PB: 6037, 2722083139 (49460767333, 260338749613, 269121292591, 404144501447, 444572650541, 629327452711, 636960378319, 687991039739, 912414338177, 1069929736297) 2 P: 8736065729 PB: 4657, 5247002339 (188767496677, 321866322247, 393253393259, 477787575037, 481672781479, 501253057727, 686625315907, 1686231517771, 1781209294853, 2186251084261) 2 P: 13593675839 PB: 2237, 776628283 (125525967487, 2689892932537, 2715525013819, 2983059291673, 3132024441269, 3505532497547, 3666310699847, 3699474990833, 4653163613453, 4792489822661) 2 P: 26774989673 PB: 5023, 5306446889 (305880839701, 3144789569791, 3510046323479, 3940532509343, 3947164483133, 4061421874481, 5028693419921, 5758196718641, 5789616550649, 5970944629157) 2 P: 33107163139 PB: 7523, 16840286759 (2352467967037, 2986979334431, 6576902090159, 8073829911041, 9122510049677, 9674807179979 10115043484109, 12612024602657, 12839952745769, 14154039863317) 2 P: 105988925209 PB: 10111, 27228892879 (14275891827289, 19355462943361, 20065646144039, 25040941774787, 27191318752097, 29408961519983, 30632009871923, 31544246178817, 31612474146271, 34290185265593) 2 P: 243547988443 PB: 277, 182518719407 (11602576412627, 11604982066633, 11989096836077, 19633860704351, 28254131148511, 31816151242567, 34523197763753, 39125753186119, 46977572722963, 52232319710827) 2 P: 296588541479 PB: 2969, 262398477619 (5597254171387, 19271580450989, 35223833010577, 45840190733429, 51924843190177, 61819408724719, 62700547980073, 63917245601687, 65784491342051, 87724429265203) 2 P: 306871823327 PB: 9767, 300007611181 (13848824602441, 15758631230569, 36544646902471, 48077212964393, 54953048428679, 59817515961859, 83557275460559, 93762878917063, 113517842959909, 120435876580081) 2 P: 442958275769 PB: 3037, 201406395977 (90774100704167, 92392514132197, 160737093379529, 187046263015649, 229829276262977, 231271748493151, 252509022770717, 273305899590421, 306657877058669, 306964753626263) 3 P: 13691 PB: 83, 8677, 11689 (312401, 352637, 392299, 411727, 532607, 615479, 988297, 1338671, 1426111, 1642679) 3 P: 35747 PB: 9151, 9689, 20849 (1730779, 1798913, 1853857, 2240789, 2326507, 2347229, 4416541, 6784849, 8210399, 8649721) 3 P: 176406883 PB: 12379, 113731213, 162492457 (3877605001, 5820994759, 14049131557, 19676386139, 30649504241, 32526828613, 34275957337, 38388291229, 43406433053, 47950416133) 4 P: 24329 PB: 1777, 3301, 4919, 13691 (68737, 334637, 398219, 497411, 667859, 747463, 1305643, 2163281, 2163461, 2176337) 4 P: 312679516579 PB: 691, 64907851831, 77658868919, 235522640761 (31325849033971, 44836744895629, 45134248532909, 63249030424649, 79570438423159, 82116597241577, 88491847525703, 91547460390839, 93077866967821, 98861621683523) Statistik der Anzahl Prim-Basen < Primzahl P von bis ; Anzahl Primzahlen ; 1 Basis ; 2 Basen ; 3 Basen ; 4 Basen from until ; quanity of prime number ; 1 base ; 2 bases ; 3 bases ; 4 bases (Erwartungswert mit Poisson-Verteilung, Ist) ; (estimate with Poisson distribution, actual) 5 997 ; 166 ; (28.2, 21) ; (3.0, 3) ; (0.20, 0) ; (0.01, 0) 1009 9973 ; 1061 ; (126, 154) ; (8.6, 9) ; (0.4, 0) ; (0.01, 0) 10007 99991 ; 8363 ; (783, 776) ; (40.8, 42) ; (1.4, 2) ; (0.04, 1) 100003 999983 ; 68906 ; (5310, 5269) ; (223, 209) ; (6.3, 6) ; (0.13, 0) 1000003 9999991 ; 586081 ; (38339, 38567) ; (1348, 1312) ; (31.6, 29) ; (0.56, 2) 10000019 99999989 ; 5096876 ; (289605, 288677) ; (8752, 8574) ; (177, 173) ; (2.7, 2) 100000007 199999991 ; 5317482 ; (283319, 283037) ; (7986, 7809) ; (150, 143) ; (2.1, 1) 200000033 299999977 ; 5173388 ; (268112, 268775) ; (7339, 7366) ; (134, 130) ; (1.8, 2) 300000007 399999959 ; 5084001 ; (258902, 259615) ; (6956, 6970) ; (125, 100) ; (1.7, 0) 400000009 499999993 ; 5019541 ; (252364, 252178) ; (6689, 6660) ; (118, 119) ; (1.6, 1) 500000003 599999971 ; 4968836 ; (247302, 247152) ; (6486, 6426) ; (113, 109) ; (1.5, 4) 600000001 699999953 ; 4928228 ; (243252, 243039) ; (6324, 6310) ; (110, 94) ; (1.4, 1) 700000001 799999999 ; 4893248 ; (239824, 239907) ; (6188, 6384) ; (106, 101) ; (1.4, 3) 800000011 899999963 ; 4863036 ; (236886, 237404) ; (6073, 6008) ; (104, 105) ; (1.3, 5) 900000011 999999937 ; 4838319 ; (234407, 234740) ; (5975, 6036) ; (102, 87) ; (1.3, 0) 100000007 999999937 ; 45086079 ; (2264368, 2265847) ; (60017, 59969) ; (1062, 988) ; (14.1, 17) Fermatquotienten mit rekordgrosser Erst-Prim-Basis Gegenwärtig durchsucht bis zur Primzahl 1070229691 PB: Primbasis ; P: Primzahl^2 ; Basis/Primzahl PB: first prime base ; P: (prime number)^2 ; base/(prime number) PB: 5 P: 2 PB/P: 2.5 PB/P/ln(P): 3.61 PB: 17 P: 3 PB/P: 5.667 PB/P/ln(P): 5.158 PB: 19 P: 7^3 PB/P: 2.714 PB/P/ln(P): 1.3949 PB: 19 P: 13 PB/P: 1.462 PB/P/ln(P): 0.5698 PB: 131 P: 17 PB/P: 7.706 PB/P/ln(P): 2.7198 PB: 263 P: 23 PB/P: 11.435 PB/P/ln(P): 3.6469 PB: 691 P: 37^3 PB/P: 18.676 PB/P/ln(P): 5.172 PB: 1301 P: 67 PB/P: 19.418 PB/P/ln(P): 4.6182 PB: 3187 P: 89 PB/P: 35.809 PB/P/ln(P): 7.9777 PB: 3659 P: 139 PB/P: 26.324 PB/P/ln(P): 5.3347 PB: 4373 P: 163 PB/P: 26.828 PB/P/ln(P): 5.2669 PB: 5659 P: 269 PB/P: 21.037 PB/P/ln(P): 3.7602 PB: 6569 P: 379 PB/P: 17.332 PB/P/ln(P): 2.9191 PB: 10259 P: 439 PB/P: 23.369 PB/P/ln(P): 3.8407 PB: 15683 P: 491 PB/P: 31.941 PB/P/ln(P): 5.1547 PB: 19181 P: 691 PB/P: 27.758 PB/P/ln(P): 4.2456 PB: 29921 P: 701 PB/P: 42.683 PB/P/ln(P): 6.514 PB: 32503 P: 877 PB/P: 37.062 PB/P/ln(P): 5.4691 PB: 54563 P: 1009 PB/P: 54.076 PB/P/ln(P): 7.8182 PB: 57947 P: 1327 PB/P: 43.668 PB/P/ln(P): 6.0728 PB: 69833 P: 1427 PB/P: 48.937 PB/P/ln(P): 6.7375 PB: 98773 P: 1669 PB/P: 59.181 PB/P/ln(P): 7.9759 PB: 198397 P: 2687 PB/P: 73.836 PB/P/ln(P): 9.3508 PB: 407579 P: 4973 PB/P: 81.958 PB/P/ln(P): 9.6288 PB: 448733 P: 6367 PB/P: 70.478 PB/P/ln(P): 8.0465 PB: 465611 P: 7603 PB/P: 61.24 PB/P/ln(P): 6.853 PB: 533723 P: 9277 PB/P: 57.532 PB/P/ln(P): 6.2978 PB: 743123 P: 10531 PB/P: 70.565 PB/P/ln(P): 7.6187 PB: 855191 P: 11047 PB/P: 77.414 PB/P/ln(P): 8.3152 PB: 1373689 P: 12071 PB/P: 113.801 PB/P/ln(P): 12.1083 PB: 2278693 P: 18313 PB/P: 124.43 PB/P/ln(P): 12.6771 PB: 3187169 P: 29389 PB/P: 108.448 PB/P/ln(P): 10.5408 PB: 3396313 P: 34471 PB/P: 98.527 PB/P/ln(P): 9.4303 PB: 3929249 P: 42703 PB/P: 92.013 PB/P/ln(P): 8.63 PB: 5802337 P: 42961 PB/P: 135.061 PB/P/ln(P): 12.6603 PB: 7187051 P: 57731 PB/P: 124.492 PB/P/ln(P): 11.3551 PB: 8735449 P: 77773 PB/P: 112.32 PB/P/ln(P): 9.9737 PB: 10433377 P: 87299 PB/P: 119.513 PB/P/ln(P): 10.5047 PB: 10550777 P: 105517 PB/P: 99.991 PB/P/ln(P): 8.6448 PB: 12767593 P: 113957 PB/P: 112.039 PB/P/ln(P): 9.6224 PB: 16702663 P: 118369 PB/P: 141.107 PB/P/ln(P): 12.0794 PB: 17282311 P: 151303 PB/P: 114.223 PB/P/ln(P): 9.5768 PB: 20249773 P: 192631 PB/P: 105.122 PB/P/ln(P): 8.6388 PB: 22650157 P: 205603 PB/P: 110.165 PB/P/ln(P): 9.005 PB: 25544539 P: 232091 PB/P: 110.063 PB/P/ln(P): 8.9084 PB: 35824357 P: 234869 PB/P: 152.529 PB/P/ln(P): 12.3338 PB: 37434521 P: 248099 PB/P: 150.885 PB/P/ln(P): 12.147 PB: 52899541 P: 336397 PB/P: 157.253 PB/P/ln(P): 12.3568 PB: 61864603 P: 387089 PB/P: 159.82 PB/P/ln(P): 12.4215 PB: 63979093 P: 457799 PB/P: 139.754 PB/P/ln(P): 10.7221 PB: 65270519 P: 466729 PB/P: 139.847 PB/P/ln(P): 10.7133 PB: 67221073 P: 482501 PB/P: 139.318 PB/P/ln(P): 10.6457 PB: 97817639 P: 483467 PB/P: 202.325 PB/P/ln(P): 15.458 PB: 99897997 P: 675097 PB/P: 147.976 PB/P/ln(P): 11.0244 PB: 102208501 P: 695503 PB/P: 146.956 PB/P/ln(P): 10.9242 PB: 134401583 P: 780697 PB/P: 172.156 PB/P/ln(P): 12.6884 PB: 172110641 P: 808597 PB/P: 212.851 PB/P/ln(P): 15.6473 PB: 172224587 P: 1099867 PB/P: 156.587 PB/P/ln(P): 11.2566 PB: 172936307 P: 1164811 PB/P: 148.467 PB/P/ln(P): 10.629 PB: 189969431 P: 1297171 PB/P: 146.449 PB/P/ln(P): 10.4044 PB: 216068857 P: 1357351 PB/P: 159.184 PB/P/ln(P): 11.2728 PB: 243518579 P: 1411637 PB/P: 172.508 PB/P/ln(P): 12.1825 PB: 260491381 P: 1543733 PB/P: 168.741 PB/P/ln(P): 11.8417 PB: 304262459 P: 1688681 PB/P: 180.178 PB/P/ln(P): 12.5652 PB: 326814533 P: 1878293 PB/P: 173.996 PB/P/ln(P): 12.0447 PB: 383277607 P: 1890211 PB/P: 202.77 PB/P/ln(P): 14.0304 PB: 399615703 P: 2193827 PB/P: 182.155 PB/P/ln(P): 12.4754 PB: 478465327 P: 2383907 PB/P: 200.706 PB/P/ln(P): 13.668 PB: 573655967 P: 2719001 PB/P: 210.98 PB/P/ln(P): 14.2403 PB: 601756457 P: 3341579 PB/P: 180.081 PB/P/ln(P): 11.9879 PB: 644365391 P: 3382229 PB/P: 190.515 PB/P/ln(P): 12.6722 PB: 799091687 P: 3789067 PB/P: 210.894 PB/P/ln(P): 13.9226 PB: 855262753 P: 4060339 PB/P: 210.638 PB/P/ln(P): 13.8425 PB: 975736721 P: 4227299 PB/P: 230.818 PB/P/ln(P): 15.1286 PB: 989218189 P: 4470209 PB/P: 221.291 PB/P/ln(P): 14.4513 PB: 1031754211 P: 4582153 PB/P: 225.168 PB/P/ln(P): 14.6807 PB: 1078829501 P: 4994477 PB/P: 216.004 PB/P/ln(P): 14.0046 PB: 1291671839 P: 5275771 PB/P: 244.831 PB/P/ln(P): 15.8173 PB: 1324421317 P: 6005309 PB/P: 220.542 PB/P/ln(P): 14.1299 PB: 1336975397 P: 6793483 PB/P: 196.803 PB/P/ln(P): 12.5101 PB: 1347463693 P: 6797017 PB/P: 198.243 PB/P/ln(P): 12.6013 PB: 1465505389 P: 7026241 PB/P: 208.576 PB/P/ln(P): 13.2302 PB: 1590556393 P: 7399703 PB/P: 214.949 PB/P/ln(P): 13.5898 PB: 1998927869 P: 8102407 PB/P: 246.708 PB/P/ln(P): 15.5087 PB: 2092723123 P: 8806081 PB/P: 237.645 PB/P/ln(P): 14.8612 PB: 2543800951 P: 10642277 PB/P: 239.028 PB/P/ln(P): 14.7727 PB: 2936062313 P: 11792681 PB/P: 248.973 PB/P/ln(P): 15.2904 PB: 3055358197 P: 12367819 PB/P: 247.041 PB/P/ln(P): 15.1275 PB: 3229999483 P: 13596733 PB/P: 237.557 PB/P/ln(P): 14.4628 PB: 3386113987 P: 15772961 PB/P: 214.678 PB/P/ln(P): 12.9529 PB: 3678480329 P: 16119541 PB/P: 228.2 PB/P/ln(P): 13.7507 PB: 3684100153 P: 17544251 PB/P: 209.989 PB/P/ln(P): 12.5891 PB: 4101896059 P: 18245023 PB/P: 224.823 PB/P/ln(P): 13.4468 PB: 6123289097 P: 18400853 PB/P: 332.772 PB/P/ln(P): 19.8932 (PB: 6039942803 P: 19737647 PB/P: 306.011 PB/P/ln(P): 18.2171) PB: 6354760933 P: 24658141 PB/P: 257.715 PB/P/ln(P): 15.1413 PB: 6944725937 P: 27420299 PB/P: 253.27 PB/P/ln(P): 14.7879 PB: 7022067839 P: 27588023 PB/P: 254.533 PB/P/ln(P): 14.8564 PB: 7050263653 P: 28278559 PB/P: 249.315 PB/P/ln(P): 14.5309 PB: 8977989287 P: 29334953 PB/P: 306.051 PB/P/ln(P): 17.7996 PB: 9626753497 P: 35765531 PB/P: 269.163 PB/P/ln(P): 15.4758 PB: 11205836029 P: 39666197 PB/P: 282.503 PB/P/ln(P): 16.1467 PB: 12075282181 P: 39845539 PB/P: 303.052 PB/P/ln(P): 17.3168 PB: 14832364403 P: 42956959 PB/P: 345.284 PB/P/ln(P): 19.6455 PB: 14977311959 P: 53821861 PB/P: 278.276 PB/P/ln(P): 15.6324 PB: 18778749973 P: 54620549 PB/P: 343.804 PB/P/ln(P): 19.2976 PB: 19275987287 P: 64676473 PB/P: 298.037 PB/P/ln(P): 16.5715 PB: 19654907803 P: 71093237 PB/P: 276.467 PB/P/ln(P): 15.2917 PB: 20506661807 P: 74550193 PB/P: 275.072 PB/P/ln(P): 15.1747 PB: 20798853613 P: 74684047 PB/P: 278.491 PB/P/ln(P): 15.3618 PB: 21482972759 P: 76735619 PB/P: 279.961 PB/P/ln(P): 15.4199 PB: 22484781379 P: 82509353 PB/P: 272.512 PB/P/ln(P): 14.9498 PB: 23122694369 P: 82612949 PB/P: 279.892 PB/P/ln(P): 15.3536 PB: 29483686501 P: 83936051 PB/P: 351.264 PB/P/ln(P): 19.252 PB: 39214303669 P: 103773443 PB/P: 377.884 PB/P/ln(P): 20.4729 PB: 39805350527 P: 121858483 PB/P: 326.652 PB/P/ln(P): 17.5446 PB: 42453444287 P: 134399953 PB/P: 315.874 PB/P/ln(P): 16.8769 PB: 50839176301 P: 141981347 PB/P: 358.069 PB/P/ln(P): 19.0755 PB: 56767791233 P: 159661273 PB/P: 355.551 PB/P/ln(P): 18.8236 (PB: 53909398349 P: 160402369 PB/P: 336.089 PB/P/ln(P): 17.7889) (PB: 54204973913 P: 163083029 PB/P: 332.377 PB/P/ln(P): 17.577) PB: 57535382831 P: 171488321 PB/P: 335.506 PB/P/ln(P): 17.6954 PB: 59776986149 P: 184945561 PB/P: 323.214 PB/P/ln(P): 16.9795 PB: 59896405577 P: 205631581 PB/P: 291.28 PB/P/ln(P): 15.2171 PB: 64363380659 P: 207956851 PB/P: 309.504 PB/P/ln(P): 16.1597 PB: 73564703321 P: 211076023 PB/P: 348.522 PB/P/ln(P): 18.1828 PB: 73967949301 P: 211282867 PB/P: 350.09 PB/P/ln(P): 18.2636 PB: 86075114747 P: 225765383 PB/P: 381.259 PB/P/ln(P): 19.8211 PB: 102068999581 P: 258538447 PB/P: 394.792 PB/P/ln(P): 20.3811 (PB: 97376522059 P: 269952959 PB/P: 360.717 PB/P/ln(P): 18.5805) (PB: 95923997423 P: 281208413 PB/P: 341.114 PB/P/ln(P): 17.5338) PB: 99754592869 P: 284999291 PB/P: 350.017 PB/P/ln(P): 17.9791 (PB: 96599874863 P: 289595351 PB/P: 333.568 PB/P/ln(P): 17.1201) PB: 107299854443 P: 303626507 PB/P: 353.394 PB/P/ln(P): 18.0937 PB: 111519207703 P: 324262507 PB/P: 343.916 PB/P/ln(P): 17.5494 PB: 116324061649 P: 333533689 PB/P: 348.763 PB/P/ln(P): 17.7711 (PB: 114148366483 P: 337520969 PB/P: 338.196 PB/P/ln(P): 17.2223) PB: 120881321537 P: 353287177 PB/P: 342.162 PB/P/ln(P): 17.3838 PB: 122098894223 P: 367996697 PB/P: 331.793 PB/P/ln(P): 16.8222 PB: 126949873723 P: 370099721 PB/P: 343.015 PB/P/ln(P): 17.3861 PB: 134878886671 P: 387469553 PB/P: 348.102 PB/P/ln(P): 17.603 PB: 148454423753 P: 389328211 PB/P: 381.309 PB/P/ln(P): 19.2776 PB: 151949083597 P: 416875439 PB/P: 364.495 PB/P/ln(P): 18.3641 PB: 152274889439 P: 430516487 PB/P: 353.703 PB/P/ln(P): 17.7914 PB: 152572550957 P: 446806099 PB/P: 341.474 PB/P/ln(P): 17.1443 PB: 206833775459 P: 448904497 PB/P: 460.752 PB/P/ln(P): 23.1274 (PB: 167199056653 P: 468483503 PB/P: 356.894 PB/P/ln(P): 17.876) (PB: 181946022437 P: 519585967 PB/P: 350.175 PB/P/ln(P): 17.449) (PB: 201347003573 P: 560960437 PB/P: 358.933 PB/P/ln(P): 17.8173) PB: 231005198519 P: 572708953 PB/P: 403.355 PB/P/ln(P): 20.0019 (PB: 217798983937 P: 576832759 PB/P: 377.577 PB/P/ln(P): 18.7169) (PB: 226855019179 P: 614635331 PB/P: 369.089 PB/P/ln(P): 18.2387) PB: 246595932169 P: 647403871 PB/P: 380.9 PB/P/ln(P): 18.7742 PB: 274941749879 P: 692764867 PB/P: 396.876 PB/P/ln(P): 19.4966 (PB: 261359916221 P: 732346577 PB/P: 356.88 PB/P/ln(P): 17.484) (PB: 266140462607 P: 738208817 PB/P: 360.522 PB/P/ln(P): 17.6556) (PB: 262634376721 P: 749343967 PB/P: 350.486 PB/P/ln(P): 17.1515) (PB: 269096593037 P: 757971013 PB/P: 355.022 PB/P/ln(P): 17.3638) PB: 277717701421 P: 829405079 PB/P: 334.84 PB/P/ln(P): 16.3048 PB: 331763046047 P: 832353493 PB/P: 398.584 PB/P/ln(P): 19.4055 (PB: 305424222497 P: 841176239 PB/P: 363.092 PB/P/ln(P): 17.6684) (PB: 315443836399 P: 870984997 PB/P: 362.169 PB/P/ln(P): 17.5937) (PB: 315001660153 P: 873055649 PB/P: 360.804 PB/P/ln(P): 17.5254) (PB: 309899220229 P: 882944129 PB/P: 350.984 PB/P/ln(P): 17.0391) (PB: 331388241071 P: 884938801 PB/P: 374.476 PB/P/ln(P): 18.1775) PB: 367783427507 P: 888242437 PB/P: 414.057 PB/P/ln(P): 20.0952 (PB: 322082884069 P: 893987327 PB/P: 360.277 PB/P/ln(P): 17.4797) (PB: 340671192637 P: 905273093 PB/P: 376.319 PB/P/ln(P): 18.2469) PB: 375364265531 P: 940639561 PB/P: 399.052 PB/P/ln(P): 19.3133 PB: 393108599183 P: 942045733 PB/P: 417.292 PB/P/ln(P): 20.1946 (PB: 334509477977 P: 945560911 PB/P: 353.768 PB/P/ln(P): 17.1173) (PB: 351026832029 P: 974018209 PB/P: 360.39 PB/P/ln(P): 17.4127) (PB: 348666488113 P: 986505349 PB/P: 353.436 PB/P/ln(P): 17.0662) PB: 395063707939 P: 1019361059 PB/P: 387.56 PB/P/ln(P): 18.6844 Weitere Primzahlen (Fermatquotienten) mit einer Erst-Prim-Basis PB/P/ln(P) > 12 sind: 912497, 2739437, 2771933, 2997157, 3392281, 3791717, 4075871, 4223537, 4565623, 4848601, 5201291, 5407117, 5506471, 6385781, 6523841, 7184159, 7716899, 7904423, 8228879, 8478061, 9066319, 9142561, 9420211, 9480571, 9808451, 10136083, 10432921, 11370449, 11390161, 11856139, 11865037, 12934007, 13005053, 13041103, 13172311, 13936499, 13964147, 14150407, 14374861, 14500177, 14535457, 14728093, 14770339, 14883587, 15091303, 15099817, 16333649, 16355987, 17799653, 18370787, 18394529, 18522013, 19556413, 19723189, 20368811, 20395891, 20417029, 20771683, 21326639, 21675761, 22031771, 22399669, 22455893, 22744213, 23284799, 23661559, 25085779, 26267341, 26495551, 26515141, 26982103, 27306869, 27469031, 27944533, 28065733, 28196537, 29203991, 29316263, 29410921, 29955677, 29987849, 30571061, 30690029, 30727219, 30936727, 31680041, 31822229, 32670637, 32726191, 32835809, 32861011, 32957803, 33437917, 33504157, 33529183, 34102379, 34225507, 34231019, 34454477, 34563251, 34573691, 34679819, 34744553, 35067563, 35134219, 36078463, 36126301, 36530269, 36651743, 36696851, 36781351, 36963697, 38256067, 39589339, 40013803, 40679383, 40964141, 41240027, 41813641, 42421283, 42570911, 42727051, 43295137, 43792933, 43903439, 44008751, 44106631, 44145641, 44168437, 44282191, 44431129, 44644349, 44966167, 45155497, 45245831, 45320299, 45362263, 45427513, 45456421, 45496361, 45724787, 45971941, 45977563, 46234861, 46370227, 46541629, 46634267, 46905979, 46943821, 47511371, 47671061, 47777537, 47920969, 48710731, 48904543, 49365931, 49501651, 49946999, 49972801, 50281843, 50308669, 50312221, 50439757, 51079397, 51317291, 51410453, 51837323, 51962087, 52080047, 52127711, 52150937, 52396891, 52476947, 52548439, 52724279, 53015563, 53351267, 53404523, 53622143, 53692159, 54411361, 54747523, 55435273, 55943869, 56013647, 56194349, 56412053, 56984117, 57387997, 58171063, 58265351, 58865617, 58897841, 59310443, 59567117, 59820317, 60383461, 60664081, 61026019, 61131011, 61218161, 61877869, 62419787, 62556661, 62604209, 62682509, 62703943, 63099607, 63437261, 63583031, 63749753, 64221419, 64221893, 64292441, 64395589, 64721611, 65458873, 65909413, 65999291, 66143059, 66337717, 66345787, 66468401, 66841241, 66932981, 66950857, 67367687, 67407037, 67637231, 68228357, 68597189, 68624623, 68673383, 68868791, 68900837, 69024209, 69131897, 69318703, 69753031, 70495343, 70968463, 71521249, 71932711, 72431923, 72714413, 72985621, 73139951, 73887127, 74001211, 74625349, 74648227, 74809951, 75200143, 75290623, 76174729, 76436303, 76527811, 77024669, 77623877, 78386843, 78537721, 80221909, 80405653, 81623741, 81777109, 81990941, 82187111, 82356383, 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1054129663, 1054318823, 1054948117, 1055857321, 1056284149, 1056294773, 1057182109, 1057520741, 1057810321, 1058616473, 1058832157, 1058888531, 1058985847, 1059029701, 1059046061, 1059114821, 1059460931, 1059579823, 1060087243, 1061244991, 1061920199, 1061996321, 1062130247, 1062175799, 1062203837, 1062428921, 1062901289, 1063328093, 1063387411, 1063891693, 1064138653, 1064391667, 1064705039, 1064957501, 1065311801, 1065430321, 1066198387, 1066800667, 1066904483, 1066970123, 1067066327, 1067072581, 1067201111, 1067487719, 1067971631, 1068111767, 1069262057, 1069397657, 1069439801, 1070026739, 1070042983, 1070185793, 1070219081 13.03.2023 Richard Fischer