## PRP Records

### Probable Primes Top 10000

#### (291517 PRPs in the top)

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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 1-250 251-500 501-750 751-1000 1001-1250 1251-1500 1501-1750 1751-2000 2001-2250 2251-2500 2501-2750 2751-3000 3001-3250 3251-3500 3501-3750 3751-4000 4001-4250 4251-4500 4501-4750 4751-5000 5001-5250 5251-5500 5501-5750 5751-6000 6001-6250 6251-6500 6501-6750 6751-7000 7001-7250 7251-7500 7501-7750 7751-8000 8001-8250 8251-8500 8501-8750 8751-9000 9001-9250 9251-9500 9501-9750 9751-10000

 Rank Probable prime Digits (> 50000) Who ? When ? 1 (10^8177207-1)/9 8177207 Ryan Propper + Sergey Batalov 05/2021 2 (10^5794777-1)/9 5794777 Ryan Propper + Sergey Batalov 04/2021 3 (2^15135397+1)/3 4556209 Ryan Propper 06/2021 4 2^13380298-27 4027872 Jeff Gilchrist /Diepeveen-Reix-Underwood-Gilchrist 03/2021 5 (2^13372531+1)/3 4025533 Ryan Propper 09/2013 6 (2^13347311+1)/3 4017941 Ryan Propper 09/2013 7 (2^12720787-1)/1119429257/175573124547437977/8480999878421106991 3829294 Anonymous 10/2022 8 (2^12503723-2^6251862+1)/5 3763995 Ryan Propper + Sergey Batalov 07/2020 9 (2^10443557-1)/37289325994807 3143811 GIMPS-fre_games 07/2020 10 2^9092392+40291 2737083 Engracio Esmenda / Five or Bust 02/2011 11 (17^1990523-1)/16 2449236 Paul Bourdelais 08/2020 12 (35963^524288+1)/2 2388581 Ryan Propper 08/2022 13 (11^2264611+1)/12 2358349 Paul Bourdelais 07/2021 14 (5^3300593-1)/4 2307015 Anonymous 02/2022 15 (2^7313983-1)/305492080276193 2201714 Oliver Kruse 03/2018 16 (2^7080247-1)/156822217506727/11283326312536321/9632940548330339593 2131318 Gord Palameta 10/2017 17 (11^1868983-1)/10 1946345 Paul Bourdelais 06/2021 18 (3^3598867-1)/2 1717096 Ryan Propper 12/2021 19 (13^1503503-1)/12 1674817 Paul Bourdelais 04/2020 20 (10^1600787+1)/11 1600786 Paul Bourdelais 05/2020 21 (18^1270141-1)/17 1594372 Paul Bourdelais 12/2021 22 (14^1385203+1)/15 1587619 Paul Bourdelais 02/2022 23 (2^5243339-2^2621670+1)/5 1578402 Ryan Propper + Sergey Batalov 06/2020 24 (2^5240707-1)/75392810903 1577600 Tony Prest / Never Odd Or Even 07/2016 25 2^5146295+41693 1549190 Engracio Esmenda / Five or Bust 11/2009 26 (2^4834891-1)/1701881633/70659688575577 1455425 Gord Palameta 01/2017 27 (187503^262144+1)/2 1382288 Ryan Propper 08/2022 28 2^4583176+2131 1379674 Ben Maloney / Five or Bust 09/2009 29 F(6530879) 1364873 Ryan Propper 08/2022 30 (2^4533073+2^2266537+1)/5 1364591 Serge Batalov 03/2014 31 (13^1199467+1)/14 1336138 Paul Bourdelais 12/2015 32 (5^1888279-1)/4 1319850 Paul Bourdelais 04/2018 33 (5^1856147+1)/6 1297391 Paul Bourdelais 02/2019 34 (3^2704981-1)/2 1290604 Ryan Propper 12/2021 35 (20^984349-1)/19 1280667 Paul Bourdelais 09/2021 36 (2^4194304+1026473)/3 1262611 Tony Prest / Never Odd Or Even 07/2017 37 (2^4187251-1)/72234342371519 1260475 Tony Prest / Never Odd Or Even 05/2016 38 (14^1091401+1)/15 1250885 Paul Bourdelais 03/2014 39 (16^1025393+1)/17 1234695 Paul Bourdelais 08/2014 40 (2^4031399+1)/3 1213572 Tony Reix / Diepeveen-Underwood -Reix 02/2010 41 (3^2533963+1)/4 1209008 Paul Bourdelais 03/2020 42 L(5466311) 1142392 Ryan Propper 08/2022 43 2^3690839-1868407 1111054 Enzo Doria 03/2021 44 2^3678448+384541 1107324 Enzo Doria 03/2022 45 2^3668660+1888801 1104377 Enzo Doria 03/2020 46 (106*23^800873-7)/11 1090573 Curtis Bright 05/2015 47 (7^1264699-1)/6 1068794 Paul Bourdelais 01/2014 48 (6^1365019-1)/5 1062191 Paul Bourdelais 12/2019 49 (3^2215303-1)/2 1056968 Paul Bourdelais 02/2019 50 10^1043372+7 1043373 Alfred Reich 12/2021 51 (2^3464473-1)/604874508299177 1042896 Anand Nair 10/2014 52 (6^1313371+1)/7 1022001 Paul Bourdelais 01/2019 53 (2^3352132+9)/5 1009092 Tony Prest / Never Odd Or Even 06/2018 54 (2^3351958+191)/3/3/5/17/67/207061/11066359/1608561247/67472994221 1009003 Tony Prest / Never Odd Or Even 08/2019 55 (2^3351556+159)/5/7/7/2927/14552647/117615601/706874075837 1008886 Tony Prest / Never Odd Or Even 08/2019 56 (2^3351346+113)/3/548533/39539021/94650838127 1008831 Tony Prest / Never Odd Or Even 11/2022 57 (2^3350899+115)/3/3/11/409 1008717 Tony Prest / Never Odd Or Even 04/2020 58 (2^3350068+183)/953/15761231 1008461 Tony Prest / Never Odd Or Even 03/2020 59 (2^3349565+57)/23/263/77893 1008311 Tony Prest / Never Odd Or Even 03/2020 60 (2^3349080+137)/3/79/8060419099 1008162 Tony Prest / Never Odd Or Even 07/2020 61 (2^3349027+183)/23/1277/11638321/5044848527 1008137 Tony Prest / Never Odd Or Even 09/2022 62 (2^3348456+23)/3/41 1007984 Tony Prest / Never Odd Or Even 01/2019 63 (2^3348338+213)/7 1007950 Tony Prest / Never Odd Or Even 10/2018 64 (2^3348184+123)/12491/322944263 1007892 Tony Prest / Never Odd Or Even 01/2021 65 (2^3348131+207)/5/11/41/43/12661193081/86868416749 1007862 Tony Prest / Never Odd Or Even 05/2021 66 (2^3348111+245)/9721/215412555797/19870494524087 1007854 Tony Prest / Never Odd Or Even 05/2021 67 (2^3347690+143)/3/7/167/585877 1007746 Tony Prest / Never Odd Or Even 06/2020 68 (2^3347613+103)/3/5/194809 1007726 Tony Prest / Never Odd Or Even 02/2020 69 (2^3347274+143)/3/3/3/234786457/3484003557569 1007608 Tony Prest / Never Odd Or Even 07/2022 70 (2^3346590+185)/3/31/83/2201765933/326210984543 1007400 Tony Prest / Never Odd Or Even 04/2021 71 (2^3346468+257)/3/7/13/71/10847 1007379 Tony Prest / Never Odd Or Even 05/2020 72 L(4819961) 1007313 Ryan Propper 07/2022 73 (2^3345946+187)/7/3122957 1007223 Tony Prest / Never Odd Or Even 03/2019 74 2^3345603+63 1007127 Tony Prest / Never Odd Or Even 05/2018 75 (2^3345474+255)/19/29/2557 1007082 Tony Prest / Never Odd Or Even 12/2019 76 (2^3345364+43)/53/79/109/2389/10889/16838309 1007035 Tony Prest / Never Odd Or Even 07/2022 77 (2^3345080+247)/31/3967 1006965 Tony Prest / Never Odd Or Even 03/2019 78 (2^3343888+209)/3/3/5/31/179 1006606 Tony Prest / Never Odd Or Even 11/2019 79 (2^3343774+115)/12239 1006573 Tony Prest / Never Odd Or Even 10/2018 80 (2^3343633+105)/137 1006532 Tony Prest / Never Odd Or Even 10/2018 81 (2^3343714+149)/3/11/17/6047/23869/3993469/171388950721 1006530 Tony Prest / Never Odd Or Even 01/2021 82 (2^3343629+183)/5/35107/2154259/28212829709 1006511 Tony Prest / Never Odd Or Even 05/2022 83 (2^3343142+13)/587/212195573363/3775970066719 1006360 Tony Prest / Never Odd Or Even 05/2018 84 (2^3342880+215)/3/7/157/239/821 1006299 Tony Prest / Never Odd Or Even 04/2020 85 (2^3342588+95)/3/619/13174671553/22761066847 1006196 Tony Prest / Never Odd Or Even 08/2018 86 (2^3322799+505)/3 1000262 Stefano Morozzi 08/2022 87 2^3322077+659 1000045 Stefano Morozzi 04/2022 88 211185^54364+54364^211185 1000027 Gabor Levai 05/2022 92 10^999999+593499 1000000 Peter Kaiser 02/2013 89 10^999999+308267*10^292000+1 1000000 Sergey Batalov 09/2021 90 138159533888769035882147()973433052122012098003208^4096+1 1000000 Anonymous 11/2021 91 138159533888769035882147()973433052122012098115876^4096+1 1000000 Anonymous 11/2021 95 10^999999-172473 999999 Patrick De Geest 12/2016 93 10^999999-1087604*10^287000-1 999999 Ryan Propper + Sergey Batalov 09/2021 94 10^999999-1022306*10^287000-1 999999 Ryan Propper + Sergey Batalov 09/2021 96 (7^1178033+1)/8 995553 Paul Bourdelais 01/2019 97 10^995256+7 995257 Alfred Reich 11/2021 98 F(4740217) 990647 Ryan Propper 07/2022 99 2^3223639+74333 970413 Enzo Doria 10/2021 100 2^3118435+73793 938743 Enzo Doria 01/2021 101 2^3037438+1885789 914360 Enzo Doria 05/2019 102 2^3032354+74209 912830 Enzo Doria 01/2020 103 2^3018556+31 908676 Robert Price 09/2019 104 (3^1896463+1)/4 904843 Paul Bourdelais 01/2020 105 Tau(181^72558) 900969 Nik Lygeros / Olivier Rozier / LR team 07/2018 106 2^2976221+2041857 895932 Makoto Morimoto 09/2014 107 (35^568453-1)/34 877729 Paul Bourdelais 10/2021 108 L(4161629) 869730 Ryan Propper 07/2022 109 (2^2860553+1)/(3*1528891204123*11630352659013691) 861084 Gord Palameta 03/2019 110 2^2843446+1885789 855963 Enzo Doria 05/2019 111 3^1753088+2 836436 Paul Bourdelais 03/2022 112 (12^769543-1)/11 830476 Paul Bourdelais 12/2014 113 2^2740174+1884385 824875 Enzo Doria 01/2019 114 Tau(229^63498) 824146 Nik Lygeros / Olivier Rozier / LR team 07/2020 115 (9^860029+1)/10 820676 Paul Bourdelais 09/2020 116 2^2723045+60227 819719 Enzo Doria 01/2020 117 2^2711746+74179 816317 Enzo Doria 11/2019 118 (2^2687383+1)/(3*440088720954577) 808968 Gord Palameta 03/2019 119 (31^535571-1)/30 798729 Alexander Zhirkov 08/2019 120 (64*10^779465-1)/81 779465 Serge Batalov 09/2014 121 (64*10^762811-1)/9 762812 Serge Batalov 09/2014 122 2^2515946+60529 757376 Enzo Doria 10/2018 123 (15^639833-1)/14 752501 Paul Bourdelais 04/2019 124 2^2442546+74209 735280 Enzo Doria 03/2020 125 (10^718580+269)/9 718580 Serge Batalov 12/2014 126 (99^357779+1)/100 713995 Paul Bourdelais 02/2022 127 (81^370421+1)/82 706942 Paul Bourdelais 12/2021 128 (2^2327417-1)/23915387348002001 700606 Anand Nair 08/2014 129 F(3340367) 698096 Henri Lifchitz 03/2018 130 (2^2305781-2^1152891+1)/5 694109 Serge Batalov 01/2014 131 2^2291342+73519 689763 Enzo Doria 12/2018 132 (10^685224+89)/9 685224 Serge Batalov 12/2014 133 F(3244369) 678033 Henri Lifchitz 09/2017 134 2^2249255+28433 677094 Ben Maloney / Five or Bust 01/2009 135 (10^675470+269)/9 675470 Serge Batalov 12/2014 136 Tau(151^56086) 672156 Nik Lygeros / Olivier Rozier / LR team 10/2017 137 (9^703393+1)/10 671207 Paul Bourdelais 08/2015 138 (121^320483+1)/122 667496 Paul Bourdelais 08/2019 139 2^2213586+71389 666356 Enzo Doria 04/2018 140 2^2205444+3 663905 Paul Bourdelais 08/2020 141 2^2191232+105 659627 Stefano Morozzi 10/2021 142 2^2187054+1886719 658369 Enzo Doria 11/2018 143 (6^840316-11)/5 653893 Paul Bourdelais 06/2020 144 (15^551927+1)/16 649116 Paul Bourdelais 07/2013 145 2^2153756+72181 648346 Enzo Doria 04/2018 146 (3^1353449-3^676725+1)/7 645759 Serge Batalov 03/2014 147 Tau(983^38932) 640784 Nik Lygeros / Olivier Rozier 02/2016 148 2^2119239+684443 637955 Enzo Doria 11/2018 149 2^2117699+89 637491 Stefano Morozzi 10/2021 150 2^2107382+105 634385 Stefano Morozzi 10/2021 151 (51*21^479149-1243)/4 633542 Curtis Bright 11/2015 152 2^2099459+71663 632001 Enzo Doria 07/2018 153 Tau(881^38992) 631568 Nik Lygeros / Olivier Rozier 01/2016 154 2^2097791+60563 631499 Enzo Doria 04/2018 155 2^2086750-3 628175 Paul Bourdelais 05/2020 156 2^2083766+73519 627277 Enzo Doria 01/2019 157 (20^472709-1)/19 615008 Paul Bourdelais 01/2015 158 PIPrime(613373) 613373 Adrian Bondrescu 05/2016 159 11^586020-2 610277 Paul Bourdelais 11/2021 160 (19^476929+1)/20 609874 Paul Bourdelais 03/2015 161 2^2019811+1867211 608024 Enzo Doria 04/2018 162 F(2904353) 606974 Henri Lifchitz 07/2014 163 2^2014720+71893 606492 Enzo Doria 04/2018 164 L(2894561) 604928 Ryan Propper 06/2022 165 (18^481147+1)/19 603970 Paul Bourdelais 07/2011 166 200^262144+119^262144 603202 Kellen Shenton 08/2022 167 (15^505117-1)/14 594063 Paul Bourdelais 01/2015 168 (152^270217-1)/(152-1) 589570 Michael Stocker 06/2015 169 Phi(177147,94259) 587458 Anonymous 09/2022 170 2^1950002+1867369 587010 Enzo Doria 02/2018 171 2^1940812+3 584243 Paul Bourdelais 06/2020 172 2^1923104+153 578912 Stefano Morozzi 07/2021 173 (3^1205459+1)/4 575150 Paul Bourdelais 08/2015 174 2^1882800+384541 566780 Enzo Doria 12/2017 175 (2^1882787-2^941394+1)/5 566775 Borys Jaworski 11/2012 176 2^1882474+71389 566682 Enzo Doria 04/2018 177 (6^727496-11)/5 566102 Paul Bourdelais 08/2019 178 2^1875552+3 564598 Paul Bourdelais 04/2020 179 3^1180181-2 563090 Jorge Coveiro 05/2020 180 2^1852265+1890425 557588 Enzo Doria 11/2017 181 5^797390-2 557352 Paul Bourdelais 03/2021 182 8^615997-7^615997 556301 Jean-Louis Charton 07/2009 183 Tau(773^34960) 555339 Nik Lygeros / Olivier Rozier 09/2015 184 ((((((((((1361^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+66768)^3+300840)^3+1623568 555154 Serge Batalov 08/2013 185 (42^337081-1)/41 547165 Paul Bourdelais 09/2021 186 (2^1790743-1)/(146840927*158358984977*3835546416767873*20752172271489035681) 539014 Dario Alpern 06/2015 187 10^538640-3 538640 Paul Bourdelais 01/2021 188 2^1787167+71963 537991 Enzo Doria 12/2018 189 (12^495953+1)/13 535223 Paul Bourdelais 11/2018 190 2^1773644+72511 533921 Enzo Doria 10/2018 191 (92^271639-1)/91 533440 Paul Bourdelais 02/2022 192 (11559^131072+1)/2 532535 Serge Batalov 04/2018 193 (85^275881-1)/84 532289 Paul Bourdelais 02/2022 194 2^1762004-3 530417 Paul Bourdelais 04/2020 195 (73^280697+1)/74 523028 Paul Bourdelais 02/2022 196 (21^394579+1)/22 521719 Paul Bourdelais 10/2018 197 2^1730246+384439 520856 Enzo Doria 09/2017 198 (55^299087+1)/56 520519 Paul Bourdelais 02/2022 199 (18^414269-1)/17 520020 Paul Bourdelais 12/2014 200 20^396120-3 515365 Paul Bourdelais 01/2021 201 (62^286483+1)/63 513488 Paul Bourdelais 02/2022 202 (20^393257+1)/21 511638 Paul Bourdelais 12/2014 203 10^509546+3 509547 Paul Bourdelais 01/2021 204 (72^273149-1)/71 507327 Paul Bourdelais 02/2022 205 107890^49423+49423^107890 506429 Miklos Levai 02/2022 206 (14^441697-1)/13 506241 Paul Bourdelais 12/2014 207 3^1059503-2^1059503 505512 Mike Oakes 04/2012 208 101542^92885+92885^101542 504465 Gabor Levai 04/2022 209 105098^61113+61113^105098 503014 Miklos Levai 09/2022 210 2^1670703+60293 502932 Enzo Doria 11/2017 211 (2^1669219-2^834610+1)/5 502485 Borys Jaworski 01/2011 212 101311^90816+90816^101311 502317 Gabor Levai 12/2021 213 101643^87368+87368^101643 502254 Gabor Levai 11/2022 214 101863^84922+84922^101863 502085 Gabor Levai 10/2022 215 100207^99856+99856^100207 500973 Gabor Levai 11/2021 216 101839^83028+83028^101839 500969 Gabor Levai 11/2022 217 100263^98600+98600^100263 500702 Gabor Levai 09/2021 218 101761^82168+82168^101761 500126 Gabor Levai 03/2022 219 2^1661176+336631 500064 Tony Prest / Never Odd Or Even 09/2019 220 101070^88579+88579^101070 500027 Gabor Levai 01/2022 221 (85^259159-1)/84 500025 Paul Bourdelais 11/2021 222 2^1660973+368139 500003 Tony Prest / Never Odd Or Even 08/2020 223 2^1660964-382425 500000 Tony Prest / Never Odd Or Even 05/2020 224 (87^257689-1)/86 499791 Paul Bourdelais 01/2021 225 (64*10^499210+53)/9 499211 Serge Batalov 03/2015 226 Tau(631^32370) 498503 Nik Lygeros / Olivier Rozier 05/2015 227 29^339887-28^339887 497051 Jean-Louis Charton 05/2019 228 (2^1629469-1)/644908484660139264379223 490496 Gord Palameta 11/2017 229 10^487291+7 487292 Alfred Reich 06/2021 230 2^1617579+1889543 486940 Enzo Doria 09/2017 231 L(2316773) 484177 Serge Batalov 06/2017 232 (57^275669-1)/56 484039 Paul Bourdelais 04/2021 233 10^480684-3 480684 Paul Bourdelais 01/2021 234 2^1595483+184133 480289 Enzo Doria 07/2017 235 2^1594947+3 480127 Paul Bourdelais 07/2019 236 (94^241993-1)/93 477482 Paul Bourdelais 09/2020 237 2^1585195+1888373 477192 Enzo Doria 08/2017 238 (33^313553+1)/34 476134 Paul Bourdelais 02/2021 239 3^994536+16 474515 Robert Price 10/2020 240 2^1575391+71483 474240 Enzo Doria 04/2018 241 (2^1572882+5)/3 473485 Serge Batalov 08/2015 242 (6^608099-1)/5 473193 Paul Bourdelais 05/2010 243 3^989124+16 471933 Robert Price 10/2020 244 2^1567006+1888099 471716 Enzo Doria 05/2017 245 2^1563067+1889813 470531 Enzo Doria 08/2017 246 2^1549797+60197 466536 Enzo Doria 02/2018 247 2^1549030+1887619 466305 Enzo Doria 05/2017 248 416^177481-415^177481 464840 Jean-Louis Charton 12/2016 249 (78^245183-1)/77 463908 Paul Bourdelais 02/2021 250 2^1522569+71657 458339 Enzo Doria 04/2018

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: November, 28 2022 11:49 (Time in France)

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