## PRP Records

### Probable Primes Top 10000

#### (292102 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) !!!

See the Top discoverers
See the Latest PRPs
Search by form

 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 (67*10^1116676+23)/9 1116677 Ryan Propper + Sergey Batalov 01/2023 44 2^3690839-1868407 1111054 Enzo Doria 03/2021 45 2^3678448+384541 1107324 Enzo Doria 03/2022 46 2^3668660+1888801 1104377 Enzo Doria 03/2020 47 (106*23^800873-7)/11 1090573 Curtis Bright 05/2015 48 (7^1264699-1)/6 1068794 Paul Bourdelais 01/2014 49 (6^1365019-1)/5 1062191 Paul Bourdelais 12/2019 50 (3^2215303-1)/2 1056968 Paul Bourdelais 02/2019 51 10^1043372+7 1043373 Alfred Reich 12/2021 52 (2^3464473-1)/604874508299177 1042896 Anand Nair 10/2014 53 (6^1313371+1)/7 1022001 Paul Bourdelais 01/2019 54 (2^3352132+9)/5 1009092 Tony Prest / Never Odd Or Even 06/2018 55 (2^3351958+191)/3/3/5/17/67/207061/11066359/1608561247/67472994221 1009003 Tony Prest / Never Odd Or Even 08/2019 56 (2^3351556+159)/5/7/7/2927/14552647/117615601/706874075837 1008886 Tony Prest / Never Odd Or Even 08/2019 57 (2^3351346+113)/3/548533/39539021/94650838127 1008831 Tony Prest / Never Odd Or Even 11/2022 58 (2^3350899+115)/3/3/11/409 1008717 Tony Prest / Never Odd Or Even 04/2020 59 (2^3350068+183)/953/15761231 1008461 Tony Prest / Never Odd Or Even 03/2020 60 (2^3349565+57)/23/263/77893 1008311 Tony Prest / Never Odd Or Even 03/2020 61 (2^3349080+137)/3/79/8060419099 1008162 Tony Prest / Never Odd Or Even 07/2020 62 (2^3349027+183)/23/1277/11638321/5044848527 1008137 Tony Prest / Never Odd Or Even 09/2022 63 (2^3348456+23)/3/41 1007984 Tony Prest / Never Odd Or Even 01/2019 64 (2^3348338+213)/7 1007950 Tony Prest / Never Odd Or Even 10/2018 65 (2^3348184+123)/12491/322944263 1007892 Tony Prest / Never Odd Or Even 01/2021 66 (2^3348131+207)/5/11/41/43/12661193081/86868416749 1007862 Tony Prest / Never Odd Or Even 05/2021 67 (2^3348111+245)/9721/215412555797/19870494524087 1007854 Tony Prest / Never Odd Or Even 05/2021 68 (2^3347690+143)/3/7/167/585877 1007746 Tony Prest / Never Odd Or Even 06/2020 69 (2^3347613+103)/3/5/194809 1007726 Tony Prest / Never Odd Or Even 02/2020 70 (2^3347274+143)/3/3/3/234786457/3484003557569 1007608 Tony Prest / Never Odd Or Even 07/2022 71 (2^3346590+185)/3/31/83/2201765933/326210984543 1007400 Tony Prest / Never Odd Or Even 04/2021 72 (2^3346468+257)/3/7/13/71/10847 1007379 Tony Prest / Never Odd Or Even 05/2020 73 L(4819961) 1007313 Ryan Propper 07/2022 74 (2^3345946+187)/7/3122957 1007223 Tony Prest / Never Odd Or Even 03/2019 75 2^3345603+63 1007127 Tony Prest / Never Odd Or Even 05/2018 76 (2^3345474+255)/19/29/2557 1007082 Tony Prest / Never Odd Or Even 12/2019 77 (2^3345364+43)/53/79/109/2389/10889/16838309 1007035 Tony Prest / Never Odd Or Even 07/2022 78 (2^3345080+247)/31/3967 1006965 Tony Prest / Never Odd Or Even 03/2019 79 (2^3343888+209)/3/3/5/31/179 1006606 Tony Prest / Never Odd Or Even 11/2019 80 (2^3343774+115)/12239 1006573 Tony Prest / Never Odd Or Even 10/2018 81 (2^3343633+105)/137 1006532 Tony Prest / Never Odd Or Even 10/2018 82 (2^3343714+149)/3/11/17/6047/23869/3993469/171388950721 1006530 Tony Prest / Never Odd Or Even 01/2021 83 (2^3343629+183)/5/35107/2154259/28212829709 1006511 Tony Prest / Never Odd Or Even 05/2022 84 (2^3343142+13)/587/212195573363/3775970066719 1006360 Tony Prest / Never Odd Or Even 05/2018 85 (2^3342880+215)/3/7/157/239/821 1006299 Tony Prest / Never Odd Or Even 04/2020 86 (2^3342804+51)/13/13/43/2069/149173 1006272 Tony Prest / Never Odd Or Even 01/2023 87 (2^3342732+41)/3/7/28513800139379 1006248 Tony Prest / Never Odd Or Even 03/2023 88 (2^3342588+95)/3/619/13174671553/22761066847 1006196 Tony Prest / Never Odd Or Even 08/2018 89 (2^3322799+505)/3 1000262 Stefano Morozzi 08/2022 90 218767^37314+37314^218767 1000175 Gabor Levai 03/2023 91 2^3322077+659 1000045 Stefano Morozzi 04/2022 92 211185^54364+54364^211185 1000027 Gabor Levai 05/2022 96 10^999999+593499 1000000 Peter Kaiser 02/2013 93 10^999999+308267*10^292000+1 1000000 Sergey Batalov 09/2021 94 138159533888769035882147()973433052122012098003208^4096+1 1000000 Anonymous 11/2021 95 138159533888769035882147()973433052122012098115876^4096+1 1000000 Anonymous 11/2021 99 10^999999-172473 999999 Patrick De Geest 12/2016 97 10^999999-1087604*10^287000-1 999999 Ryan Propper + Sergey Batalov 09/2021 98 10^999999-1022306*10^287000-1 999999 Ryan Propper + Sergey Batalov 09/2021 100 (7^1178033+1)/8 995553 Paul Bourdelais 01/2019 101 10^995256+7 995257 Alfred Reich 11/2021 102 F(4740217) 990647 Ryan Propper 07/2022 103 2^3223639+74333 970413 Enzo Doria 10/2021 104 2^3118435+73793 938743 Enzo Doria 01/2021 105 2^3037438+1885789 914360 Enzo Doria 05/2019 106 2^3032354+74209 912830 Enzo Doria 01/2020 107 2^3018556+31 908676 Robert Price 09/2019 108 (3^1896463+1)/4 904843 Paul Bourdelais 01/2020 109 Tau(181^72558) 900969 Nik Lygeros / Olivier Rozier / LR team 07/2018 110 2^2976221+2041857 895932 Makoto Morimoto 09/2014 111 (35^568453-1)/34 877729 Paul Bourdelais 10/2021 112 L(4161629) 869730 Ryan Propper 07/2022 113 (2^2860553+1)/(3*1528891204123*11630352659013691) 861084 Gord Palameta 03/2019 114 2^2843446+1885789 855963 Enzo Doria 05/2019 115 3^1753088+2 836436 Paul Bourdelais 03/2022 116 (12^769543-1)/11 830476 Paul Bourdelais 12/2014 117 2^2740174+1884385 824875 Enzo Doria 01/2019 118 Tau(229^63498) 824146 Nik Lygeros / Olivier Rozier / LR team 07/2020 119 (9^860029+1)/10 820676 Paul Bourdelais 09/2020 120 2^2723045+60227 819719 Enzo Doria 01/2020 121 2^2711746+74179 816317 Enzo Doria 11/2019 122 (2^2687383+1)/(3*440088720954577) 808968 Gord Palameta 03/2019 123 (31^535571-1)/30 798729 Alexander Zhirkov 08/2019 124 (64*10^779465-1)/81 779465 Serge Batalov 09/2014 125 (64*10^762811-1)/9 762812 Serge Batalov 09/2014 126 2^2515946+60529 757376 Enzo Doria 10/2018 127 (15^639833-1)/14 752501 Paul Bourdelais 04/2019 128 2^2442546+74209 735280 Enzo Doria 03/2020 129 (10^718580+269)/9 718580 Serge Batalov 12/2014 130 (99^357779+1)/100 713995 Paul Bourdelais 02/2022 131 (81^370421+1)/82 706942 Paul Bourdelais 12/2021 132 (2^2327417-1)/23915387348002001 700606 Anand Nair 08/2014 133 F(3340367) 698096 Henri Lifchitz 03/2018 134 (2^2305781-2^1152891+1)/5 694109 Serge Batalov 01/2014 135 2^2291342+73519 689763 Enzo Doria 12/2018 136 (10^685224+89)/9 685224 Serge Batalov 12/2014 137 F(3244369) 678033 Henri Lifchitz 09/2017 138 2^2249255+28433 677094 Ben Maloney / Five or Bust 01/2009 139 (10^675470+269)/9 675470 Serge Batalov 12/2014 140 Tau(151^56086) 672156 Nik Lygeros / Olivier Rozier / LR team 10/2017 141 (9^703393+1)/10 671207 Paul Bourdelais 08/2015 142 (121^320483+1)/122 667496 Paul Bourdelais 08/2019 143 (10^666903-7)/3 666903 Rytis Slatkevicius 01/2023 144 2^2213586+71389 666356 Enzo Doria 04/2018 145 2^2205444+3 663905 Paul Bourdelais 08/2020 146 2^2191232+105 659627 Stefano Morozzi 10/2021 147 2^2187054+1886719 658369 Enzo Doria 11/2018 148 (6^840316-11)/5 653893 Paul Bourdelais 06/2020 149 (15^551927+1)/16 649116 Paul Bourdelais 07/2013 150 2^2153756+72181 648346 Enzo Doria 04/2018 151 (3^1353449-3^676725+1)/7 645759 Serge Batalov 03/2014 152 Tau(983^38932) 640784 Nik Lygeros / Olivier Rozier 02/2016 153 2^2119239+684443 637955 Enzo Doria 11/2018 154 2^2117699+89 637491 Stefano Morozzi 10/2021 155 (5*10^636570+31)/9 636570 Rytis Slatkevicius 02/2023 156 2^2107382+105 634385 Stefano Morozzi 10/2021 157 (51*21^479149-1243)/4 633542 Curtis Bright 11/2015 158 2^2099459+71663 632001 Enzo Doria 07/2018 159 (10^631715+53)/9 631715 Rytis Slatkevicius 01/2023 160 Tau(881^38992) 631568 Nik Lygeros / Olivier Rozier 01/2016 161 2^2097791+60563 631499 Enzo Doria 04/2018 162 2^2086750-3 628175 Paul Bourdelais 05/2020 163 2^2083766+73519 627277 Enzo Doria 01/2019 164 (20^472709-1)/19 615008 Paul Bourdelais 01/2015 165 PIPrime(613373) 613373 Adrian Bondrescu 05/2016 166 11^586020-2 610277 Paul Bourdelais 11/2021 167 (19^476929+1)/20 609874 Paul Bourdelais 03/2015 168 2^2019811+1867211 608024 Enzo Doria 04/2018 169 F(2904353) 606974 Henri Lifchitz 07/2014 170 2^2014720+71893 606492 Enzo Doria 04/2018 171 L(2894561) 604928 Ryan Propper 06/2022 172 (18^481147+1)/19 603970 Paul Bourdelais 07/2011 173 200^262144+119^262144 603202 Kellen Shenton 08/2022 174 (15^505117-1)/14 594063 Paul Bourdelais 01/2015 175 (152^270217-1)/(152-1) 589570 Michael Stocker 06/2015 176 Phi(177147,94259) 587458 Anonymous 09/2022 177 2^1950002+1867369 587010 Enzo Doria 02/2018 178 2^1940812+3 584243 Paul Bourdelais 06/2020 179 2^1923104+153 578912 Stefano Morozzi 07/2021 180 (3^1205459+1)/4 575150 Paul Bourdelais 08/2015 181 2^1882800+384541 566780 Enzo Doria 12/2017 182 (2^1882787-2^941394+1)/5 566775 Borys Jaworski 11/2012 183 2^1882474+71389 566682 Enzo Doria 04/2018 184 (6^727496-11)/5 566102 Paul Bourdelais 08/2019 185 2^1875552+3 564598 Paul Bourdelais 04/2020 186 (10^563535-7)/3 563535 Rytis Slatkevicius 02/2023 187 3^1180181-2 563090 Jorge Coveiro 05/2020 188 2^1852265+1890425 557588 Enzo Doria 11/2017 189 5^797390-2 557352 Paul Bourdelais 03/2021 190 8^615997-7^615997 556301 Jean-Louis Charton 07/2009 191 Tau(773^34960) 555339 Nik Lygeros / Olivier Rozier 09/2015 192 ((((((((((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 193 (42^337081-1)/41 547165 Paul Bourdelais 09/2021 194 (2^1790743-1)/(146840927*158358984977*3835546416767873*20752172271489035681) 539014 Dario Alpern 06/2015 195 10^538640-3 538640 Paul Bourdelais 01/2021 196 (10^538508+53)/9 538508 Rytis Slatkevicius 01/2023 197 2^1787167+71963 537991 Enzo Doria 12/2018 198 (12^495953+1)/13 535223 Paul Bourdelais 11/2018 199 2^1773644+72511 533921 Enzo Doria 10/2018 200 (92^271639-1)/91 533440 Paul Bourdelais 02/2022 201 (11559^131072+1)/2 532535 Serge Batalov 04/2018 202 (85^275881-1)/84 532289 Paul Bourdelais 02/2022 203 2^1762004-3 530417 Paul Bourdelais 04/2020 204 (73^280697+1)/74 523028 Paul Bourdelais 02/2022 205 (21^394579+1)/22 521719 Paul Bourdelais 10/2018 206 2^1730246+384439 520856 Enzo Doria 09/2017 207 (55^299087+1)/56 520519 Paul Bourdelais 02/2022 208 (18^414269-1)/17 520020 Paul Bourdelais 12/2014 209 20^396120-3 515365 Paul Bourdelais 01/2021 210 (62^286483+1)/63 513488 Paul Bourdelais 02/2022 211 (20^393257+1)/21 511638 Paul Bourdelais 12/2014 212 10^509546+3 509547 Paul Bourdelais 01/2021 213 (72^273149-1)/71 507327 Paul Bourdelais 02/2022 214 107890^49423+49423^107890 506429 Miklos Levai 02/2022 215 (14^441697-1)/13 506241 Paul Bourdelais 12/2014 216 101645^94522+94522^101645 505739 Gabor Levai 02/2023 217 3^1059503-2^1059503 505512 Mike Oakes 04/2012 218 101542^92885+92885^101542 504465 Gabor Levai 04/2022 219 105098^61113+61113^105098 503014 Miklos Levai 09/2022 220 2^1670703+60293 502932 Enzo Doria 11/2017 221 (2^1669219-2^834610+1)/5 502485 Borys Jaworski 01/2011 222 101311^90816+90816^101311 502317 Gabor Levai 12/2021 223 101643^87368+87368^101643 502254 Gabor Levai 11/2022 224 101863^84922+84922^101863 502085 Gabor Levai 10/2022 225 100207^99856+99856^100207 500973 Gabor Levai 11/2021 226 101839^83028+83028^101839 500969 Gabor Levai 11/2022 227 100263^98600+98600^100263 500702 Gabor Levai 09/2021 228 101761^82168+82168^101761 500126 Gabor Levai 03/2022 229 2^1661176+336631 500064 Tony Prest / Never Odd Or Even 09/2019 230 101070^88579+88579^101070 500027 Gabor Levai 01/2022 231 (85^259159-1)/84 500025 Paul Bourdelais 11/2021 232 2^1660973+368139 500003 Tony Prest / Never Odd Or Even 08/2020 233 2^1660964-382425 500000 Tony Prest / Never Odd Or Even 05/2020 234 (87^257689-1)/86 499791 Paul Bourdelais 01/2021 235 (64*10^499210+53)/9 499211 Serge Batalov 03/2015 236 Tau(631^32370) 498503 Nik Lygeros / Olivier Rozier 05/2015 237 29^339887-28^339887 497051 Jean-Louis Charton 05/2019 238 (2^1629469-1)/644908484660139264379223 490496 Gord Palameta 11/2017 239 10^487291+7 487292 Alfred Reich 06/2021 240 2^1617579+1889543 486940 Enzo Doria 09/2017 241 L(2316773) 484177 Serge Batalov 06/2017 242 (57^275669-1)/56 484039 Paul Bourdelais 04/2021 243 2^1599120-5 481384 Stefano Morozzi 12/2022 244 10^480684-3 480684 Paul Bourdelais 01/2021 245 2^1595483+184133 480289 Enzo Doria 07/2017 246 2^1594947+3 480127 Paul Bourdelais 07/2019 247 (94^241993-1)/93 477482 Paul Bourdelais 09/2020 248 2^1585195+1888373 477192 Enzo Doria 08/2017 249 (33^313553+1)/34 476134 Paul Bourdelais 02/2021 250 3^994536+16 474515 Robert Price 10/2020

Find by discoverer :

Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 20 2023 09:01 (Time in France)

Go back