## PRP Records

### Probable Primes Top 10000

#### (272243 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 (2^13372531+1)/3 4025533 Ryan Propper 09/2013 2 (2^13347311+1)/3 4017941 Ryan Propper 09/2013 3 (2^12503723-2^6251862+1)/5 3763995 Ryan Propper + Sergey Batalov 07/2020 4 (2^10443557-1)/37289325994807 3143811 GIMPS-fre_games 07/2020 5 2^9092392+40291 2737083 Engracio Esmenda / Five or Bust 02/2011 6 (17^1990523-1)/16 2449236 Paul Bourdelais 08/2020 7 (2^7313983-1)/305492080276193 2201714 Oliver Kruse 03/2018 8 (2^7080247-1)/156822217506727/11283326312536321/9632940548330339593 2131318 Gord Palameta 10/2017 9 (13^1503503-1)/12 1674817 Paul Bourdelais 04/2020 10 (10^1600787+1)/11 1600786 Paul Bourdelais 05/2020 11 (2^5243339-2^2621670+1)/5 1578402 Ryan Propper + Sergey Batalov 06/2020 12 (2^5240707-1)/75392810903 1577600 Tony Prest / Never Odd Or Even 07/2016 13 2^5146295+41693 1549190 Engracio Esmenda / Five or Bust 11/2009 14 (2^4834891-1)/1701881633/70659688575577 1455425 Gord Palameta 01/2017 15 2^4583176+2131 1379674 Ben Maloney / Five or Bust 09/2009 16 (2^4533073+2^2266537+1)/5 1364591 Serge Batalov 03/2014 17 (13^1199467+1)/14 1336138 Paul Bourdelais 12/2015 18 (5^1888279-1)/4 1319850 Paul Bourdelais 04/2018 19 (5^1856147+1)/6 1297391 Paul Bourdelais 02/2019 20 (2^4194304+1026473)/3 1262611 Tony Prest / Never Odd Or Even 07/2017 21 (2^4187251-1)/72234342371519 1260475 Tony Prest / Never Odd Or Even 05/2016 22 (14^1091401+1)/15 1250885 Paul Bourdelais 03/2014 23 (16^1025393+1)/17 1234695 Paul Bourdelais 08/2014 24 (2^4031399+1)/3 1213572 Tony Reix / Diepeveen-Underwood -Reix 02/2010 25 (3^2533963+1)/4 1209008 Paul Bourdelais 03/2020 26 2^3668660+1888801 1104377 Enzo Doria 03/2020 27 (106*23^800873-7)/11 1090573 Curtis Bright 05/2015 28 (7^1264699-1)/6 1068794 Paul Bourdelais 01/2014 29 (6^1365019-1)/5 1062191 Paul Bourdelais 12/2019 30 (3^2215303-1)/2 1056968 Paul Bourdelais 02/2019 31 (2^3464473-1)/604874508299177 1042896 Anand Nair 10/2014 32 (6^1313371+1)/7 1022001 Paul Bourdelais 01/2019 33 (2^3352132+9)/5 1009092 Tony Prest / Never Odd Or Even 06/2018 34 (2^3351958+191)/3/3/5/17/67/207061/11066359/1608561247/67472994221 1009003 Tony Prest / Never Odd Or Even 08/2019 35 (2^3351556+159)/5/7/7/2927/14552647/117615601/706874075837 1008886 Tony Prest / Never Odd Or Even 08/2019 36 (2^3350899+115)/3/3/11/409 1008717 Tony Prest / Never Odd Or Even 04/2020 37 (2^3350068+183)/953/15761231 1008461 Tony Prest / Never Odd Or Even 03/2020 38 (2^3349565+57)/23/263/77893 1008311 Tony Prest / Never Odd Or Even 03/2020 39 (2^3349080+137)/3/79/8060419099 1008162 Tony Prest / Never Odd Or Even 07/2020 40 (2^3348456+23)/3/41 1007984 Tony Prest / Never Odd Or Even 01/2019 41 (2^3348338+213)/7 1007950 Tony Prest / Never Odd Or Even 10/2018 42 (2^3347690+143)/3/7/167/585877 1007746 Tony Prest / Never Odd Or Even 06/2020 43 (2^3347613+103)/3/5/194809 1007726 Tony Prest / Never Odd Or Even 02/2020 44 (2^3346468+257)/3/7/13/71/10847 1007379 Tony Prest / Never Odd Or Even 05/2020 45 (2^3345946+187)/7/3122957 1007223 Tony Prest / Never Odd Or Even 03/2019 46 2^3345603+63 1007127 Tony Prest / Never Odd Or Even 05/2018 47 (2^3345474+255)/19/29/2557 1007082 Tony Prest / Never Odd Or Even 12/2019 48 (2^3345080+247)/31/3967 1006965 Tony Prest / Never Odd Or Even 03/2019 49 (2^3343888+209)/3/3/5/31/179 1006606 Tony Prest / Never Odd Or Even 11/2019 50 (2^3343774+115)/12239 1006573 Tony Prest / Never Odd Or Even 10/2018 51 (2^3343633+105)/137 1006532 Tony Prest / Never Odd Or Even 10/2018 52 (2^3343142+13)/587/212195573363/3775970066719 1006360 Tony Prest / Never Odd Or Even 05/2018 53 (2^3342880+215)/3/7/157/239/821 1006299 Tony Prest / Never Odd Or Even 04/2020 54 (2^3342588+95)/3/619/13174671553/22761066847 1006196 Tony Prest / Never Odd Or Even 08/2018 55 10^999999+593499 1000000 Peter Kaiser 02/2013 56 10^999999-172473 999999 Patrick De Geest 12/2016 57 (7^1178033+1)/8 995553 Paul Bourdelais 01/2019 58 2^3037438+1885789 914360 Enzo Doria 05/2019 59 2^3032354+74209 912830 Enzo Doria 01/2020 60 2^3018556+31 908676 Robert Price 09/2019 61 (3^1896463+1)/4 904843 Paul Bourdelais 01/2020 62 Tau(181^72558) 900969 Nik Lygeros / Olivier Rozier / LR team 07/2018 63 2^2976221+2041857 895932 Makoto Morimoto 09/2014 64 (2^2860553+1)/(3*1528891204123*11630352659013691) 861084 Gord Palameta 03/2019 65 2^2843446+1885789 855963 Enzo Doria 05/2019 66 (12^769543-1)/11 830476 Paul Bourdelais 12/2014 67 2^2740174+1884385 824875 Enzo Doria 01/2019 68 Tau(229^63498) 824146 Nik Lygeros / Olivier Rozier / LR team 07/2020 69 (9^860029+1)/10 820676 Paul Bourdelais 09/2020 70 2^2723045+60227 819719 Enzo Doria 01/2020 71 2^2711746+74179 816317 Enzo Doria 11/2019 72 (2^2687383+1)/(3*440088720954577) 808968 Gord Palameta 03/2019 73 (31^535571-1)/30 798729 Alexander Zhirkov 08/2019 74 (64*10^779465-1)/81 779465 Serge Batalov 09/2014 75 (64*10^762811-1)/9 762812 Serge Batalov 09/2014 76 2^2515946+60529 757376 Enzo Doria 10/2018 77 (15^639833-1)/14 752501 Paul Bourdelais 04/2019 78 2^2442546+74209 735280 Enzo Doria 03/2020 79 (10^718580+269)/9 718580 Serge Batalov 12/2014 80 (2^2327417-1)/23915387348002001 700606 Anand Nair 08/2014 81 F(3340367) 698096 Henri Lifchitz 03/2018 82 (2^2305781-2^1152891+1)/5 694109 Serge Batalov 01/2014 83 2^2291342+73519 689763 Enzo Doria 12/2018 84 (10^685224+89)/9 685224 Serge Batalov 12/2014 85 F(3244369) 678033 Henri Lifchitz 09/2017 86 2^2249255+28433 677094 Ben Maloney / Five or Bust 01/2009 87 (10^675470+269)/9 675470 Serge Batalov 12/2014 88 Tau(151^56086) 672156 Nik Lygeros / Olivier Rozier / LR team 10/2017 89 (9^703393+1)/10 671207 Paul Bourdelais 08/2015 90 (121^320483+1)/122 667496 Paul Bourdelais 08/2019 91 2^2213586+71389 666356 Enzo Doria 04/2018 92 2^2205444+3 663905 Paul Bourdelais 08/2020 93 2^2187054+1886719 658369 Enzo Doria 11/2018 94 (6^840316-11)/5 653893 Paul Bourdelais 06/2020 95 (15^551927+1)/16 649116 Paul Bourdelais 07/2013 96 2^2153756+72181 648346 Enzo Doria 04/2018 97 (3^1353449-3^676725+1)/7 645759 Serge Batalov 03/2014 98 Tau(983^38932) 640784 Nik Lygeros / Olivier Rozier 02/2016 99 2^2119239+684443 637955 Enzo Doria 11/2018 100 (51*21^479149-1243)/4 633542 Curtis Bright 11/2015 101 2^2099459+71663 632001 Enzo Doria 07/2018 102 Tau(881^38992) 631568 Nik Lygeros / Olivier Rozier 01/2016 103 2^2097791+60563 631499 Enzo Doria 04/2018 104 2^2086750-3 628175 Paul Bourdelais 05/2020 105 2^2083766+73519 627277 Enzo Doria 01/2019 106 (20^472709-1)/19 615008 Paul Bourdelais 01/2015 107 PIPrime(613373) 613373 Adrian Bondrescu 05/2016 108 (19^476929+1)/20 609874 Paul Bourdelais 03/2015 109 2^2019811+1867211 608024 Enzo Doria 04/2018 110 F(2904353) 606974 Henri Lifchitz 07/2014 111 2^2014720+71893 606492 Enzo Doria 04/2018 112 (18^481147+1)/19 603970 Paul Bourdelais 07/2011 113 (15^505117-1)/14 594063 Paul Bourdelais 01/2015 114 (152^270217-1)/(152-1) 589570 Michael Stocker 06/2015 115 2^1950002+1867369 587010 Enzo Doria 02/2018 116 2^1940812+3 584243 Paul Bourdelais 06/2020 117 (3^1205459+1)/4 575150 Paul Bourdelais 08/2015 118 2^1882800+384541 566780 Enzo Doria 12/2017 119 (2^1882787-2^941394+1)/5 566775 Borys Jaworski 11/2012 120 2^1882474+71389 566682 Enzo Doria 04/2018 121 (6^727496-11)/5 566102 Paul Bourdelais 08/2019 122 2^1875552+3 564598 Paul Bourdelais 04/2020 123 3^1180181-2 563090 Jorge Coveiro 05/2020 124 2^1852265+1890425 557588 Enzo Doria 11/2017 125 8^615997-7^615997 556301 Jean-Louis Charton 07/2009 126 Tau(773^34960) 555339 Nik Lygeros / Olivier Rozier 09/2015 127 ((((((((((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 128 (2^1790743-1)/(146840927*158358984977*3835546416767873*20752172271489035681) 539014 Dario Alpern 06/2015 129 2^1787167+71963 537991 Enzo Doria 12/2018 130 (12^495953+1)/13 535223 Paul Bourdelais 11/2018 131 2^1773644+72511 533921 Enzo Doria 10/2018 132 (11559^131072+1)/2 532535 Serge Batalov 04/2018 133 2^1762004-3 530417 Paul Bourdelais 04/2020 134 (21^394579+1)/22 521719 Paul Bourdelais 10/2018 135 2^1730246+384439 520856 Enzo Doria 09/2017 136 (18^414269-1)/17 520020 Paul Bourdelais 12/2014 137 (20^393257+1)/21 511638 Paul Bourdelais 12/2014 138 (14^441697-1)/13 506241 Paul Bourdelais 12/2014 139 3^1059503-2^1059503 505512 Mike Oakes 04/2012 140 2^1670703+60293 502932 Enzo Doria 11/2017 141 (2^1669219-2^834610+1)/5 502485 Borys Jaworski 01/2011 142 2^1661176+336631 500064 Tony Prest / Never Odd Or Even 09/2019 143 2^1660973+368139 500003 Tony Prest / Never Odd Or Even 08/2020 144 2^1660964-382425 500000 Tony Prest / Never Odd Or Even 05/2020 145 (64*10^499210+53)/9 499211 Serge Batalov 03/2015 146 Tau(631^32370) 498503 Nik Lygeros / Olivier Rozier 05/2015 147 29^339887-28^339887 497051 Jean-Louis Charton 05/2019 148 (2^1629469-1)/644908484660139264379223 490496 Gord Palameta 11/2017 149 2^1617579+1889543 486940 Enzo Doria 09/2017 150 L(2316773) 484177 Serge Batalov 06/2017 151 2^1595483+184133 480289 Enzo Doria 07/2017 152 2^1594947+3 480127 Paul Bourdelais 07/2019 153 (94^241993-1)/93 477482 Paul Bourdelais 09/2020 154 2^1585195+1888373 477192 Enzo Doria 08/2017 155 2^1575391+71483 474240 Enzo Doria 04/2018 156 (2^1572882+5)/3 473485 Serge Batalov 08/2015 157 (6^608099-1)/5 473193 Paul Bourdelais 05/2010 158 2^1567006+1888099 471716 Enzo Doria 05/2017 159 2^1563067+1889813 470531 Enzo Doria 08/2017 160 2^1549797+60197 466536 Enzo Doria 02/2018 161 2^1549030+1887619 466305 Enzo Doria 05/2017 162 416^177481-415^177481 464840 Jean-Louis Charton 12/2016 163 2^1522569+71657 458339 Enzo Doria 04/2018 164 2^1518191+75353 457022 Ben Maloney / Five or Bust 01/2009 165 2^1506029+1890167 453360 Enzo Doria 02/2018 166 (34^294277+1)/35 450678 Paul Bourdelais 06/2018 167 2^1495434+1890439 450171 Enzo Doria 12/2017 168 2^1493170+784129 449489 Enzo Doria 08/2017 169 2^1489873+1888277 448497 Enzo Doria 06/2017 170 2^1484671+1888463 446931 Enzo Doria 06/2017 171 2^1482867+1886783 446388 Enzo Doria 04/2017 172 2^1482148+284011 446172 Enzo Doria 04/2017 173 2^1479356+1888291 445331 Enzo Doria 06/2017 174 2^1461244+784531 439879 Enzo Doria 10/2017 175 2^1443089+60227 434414 Enzo Doria 10/2017 176 (21^328129-1)/20 433858 Paul Bourdelais 06/2014 177 2^1434400+3 431798 Paul Bourdelais 06/2019 178 2^1432308+1888801 431168 Enzo Doria 10/2017 179 (2^1430131+1)/(3*356468732537*36519993971459) 430487 Gord Palameta 12/2018 180 2^1425483+1886813 429114 Enzo Doria 04/2017 181 (17^348259+1)/18 428514 Paul Bourdelais 05/2014 182 (10^427912+89)/9 427912 Serge Batalov 12/2014 183 2^1421089+1890167 427791 Enzo Doria 09/2017 184 (10^424861-7)/3 424861 Leonid Durman 01/2012 185 2^1404213+184217 422711 Enzo Doria 09/2017 186 2^1401872+1884385 422006 Enzo Doria 04/2017 187 2^1401257+6077 421821 Enzo Doria 09/2017 188 138^196873-137^196873 421285 Jean-Louis Charton 12/2009 189 2^1398269+131595 420921 Makoto Morimoto 10/2013 190 2^1397071+684443 420561 Enzo Doria 07/2017 191 953^141023-952^141023 420121 Jean-Louis Charton 10/2016 192 (3^877843-1)/2 418838 Paul Bourdelais 07/2010 193 2^1386321+60299 417325 Enzo Doria 02/2018 194 2^1386320+184531 417324 Enzo Doria 09/2017 195 2^1382074+1883587 416046 Enzo Doria 01/2017 196 2^1379907+1885223 415394 Enzo Doria 03/2017 197 2^1375574+1886719 414090 Enzo Doria 04/2017 198 2^1373111+1884833 413348 Enzo Doria 02/2017 199 2^1368632+1889731 412000 Enzo Doria 10/2017 200 (89*10^411590+1)/9 411591 Serge Batalov 09/2014 201 F(1968721) 411439 Henri Lifchitz 11/2009 202 2^1366066+683749 411227 Enzo Doria 02/2017 203 2^1355790+1888939 408134 Enzo Doria 07/2017 204 2^1355635+1884203 408087 Enzo Doria 01/2017 205 (2^1347781-2^673891+1)/5 405722 Borys Jaworski 10/2008 206 2^1347744-3 405712 Paul Bourdelais 07/2019 207 Tau(863^24630) 397727 Nik Lygeros / Olivier Rozier 01/2016 208 2^1319770+1884949 397291 Enzo Doria 06/2017 209 2^1313062+1888849 395272 Enzo Doria 08/2017 210 (1073516^81920+1)/(1073516^16384+1) 395236 Serge Batalov 01/2017 211 (1059995^81920+1)/(1059995^16384+1) 394875 Serge Batalov 01/2017 212 2^1311618+783529 394837 Enzo Doria 01/2017 213 2^1308000+1883521 393748 Enzo Doria 02/2017 214 (1009565^81920+1)/(1009565^16384+1) 393487 Serge Batalov 01/2017 215 (995042^81920+1)/(995042^16384+1) 393075 Serge Batalov 01/2017 216 (988945^81920+1)/(988945^16384+1) 392900 Serge Batalov 01/2017 217 (988823^81920+1)/(988823^16384+1) 392897 Serge Batalov 01/2017 218 (2^1304983-1)/52199321 392832 Tony Prest / Never Odd Or Even 03/2014 219 (978970^81920+1)/(978970^16384+1) 392612 Serge Batalov 01/2017 220 2^1303102+1866409 392273 Enzo Doria 09/2017 221 2^1302818+283429 392188 Enzo Doria 01/2017 222 (934422^81920+1)/(934422^16384+1) 391286 Serge Batalov 01/2017 223 2^1299181+1886867 391093 Enzo Doria 04/2017 224 (37^249341-1)/36 391016 Paul Bourdelais 08/2020 225 2^1298304+1882891 390829 Enzo Doria 01/2017 226 (874207^81920+1)/(874207^16384+1) 389390 Serge Batalov 01/2017 227 15^328574+328574^15 386434 Serge Batalov 05/2014 228 2^1280078+1885099 385342 Enzo Doria 08/2017 229 2^1274941+1880717 383796 Enzo Doria 10/2016 230 2^1272632+383431 383101 Enzo Doria 01/2017 231 2^1271346+1889839 382714 Enzo Doria 08/2017 232 (10^380976-7)/3 380976 Leonid Durman 01/2012 233 2^1257787+1447761 378632 Makoto Morimoto 10/2013 234 (2^1257787+32270)/(2*233*281*2207*3011) 378620 Makoto Morimoto 12/2016 235 (77^200657-1)/76 378536 Paul Bourdelais 08/2020 236 F(1803059) 376817 Henri Lifchitz 06/2009 237 (97^187393-1)/96 372306 Paul Bourdelais 09/2020 238 2^1234709+883127 371685 Enzo Doria 12/2016 239 2^1231466+283819 370709 Enzo Doria 07/2017 240 2^1220335+1881263 367358 Enzo Doria 11/2016 241 2^1216694+1884769 366262 Enzo Doria 02/2017 242 2^1215889-3 366020 Paul Bourdelais 06/2019 243 2^1215296+1885441 365841 Enzo Doria 03/2017 244 2^1214307+1888115 365543 Enzo Doria 05/2017 245 2^1213815+3 365395 Paul Bourdelais 06/2019 246 2^1207345+1882577 363448 Enzo Doria 12/2016 247 2^1207073+883727 363366 Enzo Doria 03/2017 248 3^761457-2 363308 Ryan Propper 07/2015 249 (2^1200887+344126)/2 361503 Stefano Morozzi 10/2020 250 (2^1200856+305790)/2 361494 Stefano Morozzi 10/2020

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 25 2020 07:52 (Time in France)

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