## PRP Records

### Probable Primes Top 10000

#### (295756 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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See the Latest PRPs
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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 ? 6251 (301*10^110903+23)/9 110905 Robert Price 06/2021 6252 (9179*2^368330-1)/35 110881 Lelio R Paula 05/2015 6253 25830^19619+19619^25830 110880 Hans Havermann 10/2020 6254 (34*10^110882-7)/9/13/29/1019374319 110871 Makoto Morimoto 05/2016 6255 26022^18191+18191^26022 110850 Hans Havermann 10/2020 6256 (2^368211+2250)/2 110843 Stefano Morozzi 01/2021 6257 (37*10^110813+251)/9 110814 Robert Price 09/2021 6258 2^368050-64875 110795 Lelio R Paula 05/2017 6259 2^368048+25 110794 Lelio R Paula 02/2013 6260 (2^368017+2262)/2 110784 Stefano Morozzi 02/2021 6261 69^60239-2 110771 Lelio R Paula 10/2013 6262 (23*2^367952+1)/15717 110762 Lelio R Paula 03/2014 6263 2^367924-69 110757 Lelio R Paula 02/2013 6264 (23*10^110738+61)/3 110739 Robert Price 01/2022 6265 (2^367779+3750)/2 110713 Stefano Morozzi 01/2021 6266 2^367709-109723 110692 Enzo Doria 04/2014 6267 2^367687+213413 110685 Enzo Doria 09/2023 6268 (3*2^367644-1)/107 110671 Lelio R Paula 03/2014 6269 (2^367626+3514)/2 110667 Stefano Morozzi 09/2020 6270 (1288676*34^72242-455)/33 110642 Eric Chen 03/2023 6271 (23*2^367398+1)/57963 110595 Lelio R Paula 03/2014 6272 140^51515-139 110558 Norbert Schneider 04/2019 6273 2^367215+1879223 110543 Enzo Doria 09/2016 6274 25782^19375+19375^25782 110534 Hans Havermann 10/2020 6275 26117^17058+17058^26117 110526 Hans Havermann 10/2020 6276 2^367141+41 110521 Lelio R Paula 02/2013 6277 2^367126+29835 110516 Lelio R Paula 05/2017 6278 (10^110503-1)/9+2*(10^59183-1)/9*10^25660 110503 Makoto Morimoto 09/2020 6279 (10^110503-1)/9+2*(10^65511-1)/9*10^22496 110503 Makoto Morimoto 09/2020 6280 (10^110503-1)/9+2*10^108327+2*10^2175 110503 Makoto Morimoto 09/2020 6281 (10^110503-1)/9+2*10^66251+2*10^44251 110503 Makoto Morimoto 09/2020 6282 (10^110503-1)/9+3*(10^28813-1)/9*10^40845 110503 Makoto Morimoto 09/2020 6283 (10^110503-1)/9+3*(10^82573-1)/9*10^13965 110503 Makoto Morimoto 09/2020 6284 (10^110503-1)/9+4*(10^43305-1)/9*10^33599 110503 Makoto Morimoto 09/2020 6285 (10^110503-1)/9+5*10^70327+5*10^40175 110503 Makoto Morimoto 09/2020 6286 (10^110503-1)/9+5*10^99423+5*10^11079 110503 Makoto Morimoto 09/2020 6287 (10^110503-1)/9+7*(10^23617-1)/9*10^43443 110503 Makoto Morimoto 09/2020 6288 (10^110503-1)/9+8*(10^30251-1)/9*10^40126 110503 Makoto Morimoto 09/2020 6289 3*(10^110503-1)/9+1*10^106036+1*10^4466 110503 Makoto Morimoto 09/2020 6290 3*(10^110503-1)/9+1*10^58962+1*10^51540 110503 Makoto Morimoto 09/2020 6291 3*(10^110503-1)/9+1*10^78213+1*10^32289 110503 Makoto Morimoto 09/2020 6292 3*(10^110503-1)/9+2*10^76898+2*10^33604 110503 Makoto Morimoto 09/2020 6293 3*(10^110503-1)/9-1*10^100802-1*10^9700 110503 Makoto Morimoto 09/2020 6294 3*(10^110503-1)/9-1*10^76355-1*10^34147 110503 Makoto Morimoto 09/2020 6295 3*(10^110503-1)/9-2*10^105704-2*10^4798 110503 Makoto Morimoto 09/2020 6296 7*(10^110503-1)/9+1*(10^27685-1)/9*10^41409 110503 Makoto Morimoto 09/2020 6297 7*(10^110503-1)/9+1*(10^91035-1)/9*10^9734 110503 Makoto Morimoto 09/2020 6298 7*(10^110503-1)/9-1*(10^23717-1)/9*10^43393 110503 Makoto Morimoto 09/2020 6299 7*(10^110503-1)/9-1*10^57906-1*10^52596 110503 Makoto Morimoto 09/2020 6300 7*(10^110503-1)/9-1*10^72287-1*10^38215 110503 Makoto Morimoto 09/2020 6301 7*(10^110503-1)/9-2*(10^53823-1)/9*10^28340 110503 Makoto Morimoto 09/2020 6302 7*(10^110503-1)/9-2*(10^88659-1)/9*10^10922 110503 Makoto Morimoto 09/2020 6303 7*(10^110503-1)/9-3*(10^79921-1)/9*10^15291 110503 Makoto Morimoto 09/2020 6304 7*(10^110503-1)/9-3*10^60024-3*10^50478 110503 Makoto Morimoto 09/2020 6305 7*(10^110503-1)/9-4*(10^103091-1)/9*10^3706 110503 Makoto Morimoto 09/2020 6306 7*(10^110503-1)/9-4*10^103658-4*10^6844 110503 Makoto Morimoto 09/2020 6307 7*(10^110503-1)/9-4*10^78188-4*10^32314 110503 Makoto Morimoto 09/2020 6308 7*(10^110503-1)/9-5*(10^35035-1)/9*10^37734 110503 Makoto Morimoto 09/2020 6309 7*(10^110503-1)/9-6*(10^67347-1)/9*10^21578 110503 Makoto Morimoto 09/2020 6310 7*(10^110503-1)/9-6*10^60391-6*10^50111 110503 Makoto Morimoto 09/2020 6311 (10^110503-1)-4*(10^96247-1)/9*10^7128 110503 Makoto Morimoto 09/2020 6312 (10^110503-1)-4*10^74037-4*10^36465 110503 Makoto Morimoto 09/2020 6313 (10^110503-1)-4*10^77787-4*10^32715 110503 Makoto Morimoto 09/2020 6314 (10^110503-1)-4*10^91179-4*10^19323 110503 Makoto Morimoto 09/2020 6315 (10^110503-1)-5*(10^99143-1)/9*10^5680 110503 Makoto Morimoto 09/2020 6316 (10^110503-1)-7*(10^85075-1)/9*10^12714 110503 Makoto Morimoto 09/2020 6317 (10^110503-1)-7*10^100712-7*10^9790 110503 Makoto Morimoto 09/2020 6318 (10^110503-1)-7*10^76427-7*10^34075 110503 Makoto Morimoto 09/2020 6319 (10^110503-1)-7*10^90451-7*10^20051 110503 Makoto Morimoto 09/2020 6320 (10^110503-1)-8*10^106252-8*10^4250 110503 Makoto Morimoto 09/2020 6321 (11*10^110496+49)/3 110497 Robert Price 07/2018 6322 25447^21958+21958^25447 110481 Hans Havermann 11/2020 6323 (31*2^366976+1)/7 110472 Lelio R Paula 03/2014 6324 7*10^110468-23 110469 Robert Price 07/2019 6325 5*3^231464-2^231464 110438 Jon Grantham 08/2023 6326 2^366853+5711 110434 Lelio R Paula 05/2017 6327 (21181*2^366833+1)/3 110432 Lelio R Paula 07/2014 6328 2^366816+315 110423 Lelio R Paula 05/2017 6329 2^366775-2787037 110411 Enzo Doria 03/2016 6330 (112*10^110405-1)/3 110407 Serge Batalov 12/2014 6331 2^366751+2797553 110404 Enzo Doria 03/2016 6332 25276^23331+23331^25276 110404 Hans Havermann 10/2020 6333 2^366748+255 110403 Lelio R Paula 05/2017 6334 2^366738-2985 110400 Yves Minet 09/2014 6335 (23*2^366739+1)/74575 110396 Lelio R Paula 03/2014 6336 (2^366722+1314)/2 110395 Stefano Morozzi 02/2021 6337 2^366716+1871791 110393 Enzo Doria 05/2016 6338 (239*23^81066-349)/22 110391 Eric Chen 08/2023 6339 2^366649+1871687 110373 Enzo Doria 05/2016 6340 2^366629-351205 110367 Enzo Doria 06/2015 6341 (31*10^110363+257)/9 110364 Robert Price 12/2021 6342 (17*19^86292-215)/18 110347 Eric Chen 01/2023 6344 2^366558+1874479 110345 Enzo Doria 06/2016 6343 25132^24581+24581^25132 110345 Hans Havermann 10/2020 6345 (2^366539+770)/2 110339 Stefano Morozzi 09/2020 6346 26368^15285+15285^26368 110331 Hans Havermann 10/2020 6347 (23*10^110290+19)/3 110291 Robert Price 07/2019 6348 18^87853-4409 110280 Enzo Doria 03/2013 6349 28490^7419+7419^28490 110267 Hans Havermann 11/2020 6350 2^366218-23 110243 Lelio R Paula 02/2013 6351 (21*2^366193-1)/197 110235 Lelio R Paula 03/2014 6352 2^366178-343991 110231 Enzo Doria 07/2015 6353 12^102123-11 110210 Riley Fisher 09/2023 6354 25777^18798+18798^25777 110174 Hans Havermann 10/2020 6355 2^365944+1871341 110161 Enzo Doria 05/2016 6356 2^365838-461267 110129 Enzo Doria 07/2015 6357 30152^4491+4491^30152 110126 Hans Havermann 11/2020 6358 2^365802+23359 110118 Enzo Doria 10/2023 6359 10^110111+464019 110112 Patrick De Geest 05/2021 6360 10^110111-40001 110111 Robert Price 01/2021 6361 2^365763-6555 110106 Lelio R Paula 04/2017 6362 (2^365689+2^182845+1)/5 110083 11/2006 6363 2^365666-459161 110077 Enzo Doria 05/2015 6364 3*10^110076-7 110077 Robert Price 08/2015 6365 13^98785-72 110041 Lelio R Paula 03/2017 6367 (25^78707+1)/26 110027 Robert Price 06/2013 6366 (7*10^110027-277)/9 110027 Robert Price 02/2022 6368 (16*10^110014-73)/3 110015 Robert Price 07/2020 6369 (7*10^110006-151)/9 110006 Robert Price 02/2018 6370 6^141361-7 110001 Lelio R Paula 11/2014 6371 20^84536+81 109984 Lelio R Paula 03/2017 6372 5*2^365347-9 109982 Lelio R Paula 09/2014 6373 9*6^141303+7 109957 Lelio R Paula 11/2014 6374 27635^9522+9522^27635 109953 Hans Havermann 11/2020 6375 78^58099+77 109929 Norbert Schneider 02/2015 6376 2*10^109928-7 109929 Robert Price 10/2015 6377 30580^3933+3933^30580 109927 Hans Havermann 11/2020 6378 26380^14689+14689^26380 109926 Hans Havermann 11/2020 6379 (2^365161+1130)/2 109925 Stefano Morozzi 09/2020 6380 (27*2^365137-1)/2021 109916 Lelio R Paula 03/2014 6381 (4441*29^75152-24)/7 109905 Curtis Bright 05/2015 6382 (2^365087+7)/6015 109899 Lelio R Paula 01/2014 6383 (2^365069+3774)/2 109897 Stefano Morozzi 02/2021 6384 29652^5083+5083^29652 109894 Mark Rodenkirch 10/2020 6385 (2^365049+722)/2 109891 Stefano Morozzi 09/2020 6386 (35*10^109888-89)/9 109889 Robert Price 02/2022 6387 18^87533-11 109878 Lelio R Paula 04/2017 6388 2^364982-5 109871 Henri Lifchitz 04/2006 6389 3*10^109861+59 109862 Robert Price 08/2018 6390 5*10^109860-69 109861 Robert Price 02/2021 6391 2^364936-1867979 109857 Enzo Doria 04/2016 6392 27013^11652+11652^27013 109846 Hans Havermann 10/2020 6393 2^364867-112087 109836 Enzo Doria 06/2014 6394 4^182415-85061 109825 Mike Oakes 06/2011 6395 (2^364809+1034)/2 109819 Stefano Morozzi 09/2020 6396 (53*10^109809-287)/9 109810 Robert Price 02/2022 6397 (52*10^109807-133)/9 109808 Robert Price 09/2021 6398 25708^18675+18675^25708 109806 Hans Havermann 10/2020 6399 (17^89227+16^89227)/33 109788 Robert Price 08/2013 6400 2^364687-187 109782 Lelio R Paula 01/2012 6401 2^364644+67 109769 Lelio R Paula 01/2012 6402 (9787*2^364625-1)/24947 109763 Lelio R Paula 05/2015 6403 (2^364616+5)/9 109760 Lelio R Paula 01/2014 6404 (55*10^109759+89)/9 109760 Robert Price 03/2019 6405 (14*32^72921+4171)/31 109757 Eric Chen 04/2023 6406 12^101694+73 109747 Lelio R Paula 03/2017 6407 13^98518-66 109744 Lelio R Paula 03/2017 6408 (8*10^109721-269)/9 109721 Robert Price 09/2021 6409 2^364478-113261 109719 Enzo Doria 07/2014 6410 (2^364513+1)/(3*44290516579) 109719 Gord Palameta 08/2018 6411 (24737*2^364454+1)/3 109716 Lelio R Paula 07/2014 6412 27814^8777+8777^27814 109681 Hans Havermann 10/2020 6413 (62*10^109673+1)/9 109674 Serge Batalov 11/2010 6414 3^229824+340 109654 Lelio R Paula 03/2017 6415 (16623*33^72206-8095)/16 109649 Eric Chen 05/2023 6416 (2*10^109645-71)/3 109645 Robert Price 12/2017 6417 V(786978) 109644 Serge Batalov 07/2024 6418 2^364169-112813 109626 Enzo Doria 06/2014 6419 28822^6359+6359^28822 109622 Hans Havermann 11/2020 6420 10^109615+21 109616 Lelio R Paula 03/2017 6421 10^109615-456267 109615 Patrick De Geest 03/2017 6422 2^364094-113 109604 Lelio R Paula 01/2012 6423 25251^21898+21898^25251 109600 Hans Havermann 11/2020 6424 (4^182026+11)/3 109591 Robert Price 02/2017 6425 2^364041-6883 109588 Lelio R Paula 09/2011 6426 12^101545+11 109586 Lelio R Paula 03/2017 6427 26536^13475+13475^26536 109582 Hans Havermann 11/2020 6428 2^363842-2787101 109528 Enzo Doria 03/2016 6429 (2^363812+3570)/2 109519 Stefano Morozzi 09/2020 6430 (22699*2^363782+1)/763 109511 Lelio R Paula 07/2014 6431 2^363769+5711 109506 Lelio R Paula 04/2017 6432 (31*2^363748+1)/49 109499 Lelio R Paula 03/2014 6433 (2^363670+100280245065) 109476 Paul Bourdelais 05/2022 6434 p(22245)#/2-8 109462 Robert Price 01/2017 6435 2^363556+55 109442 Lelio R Paula 01/2012 6436 (509*10^109414+31)/9 109416 Robert Price 08/2022 6437 (2^363437+1682)/2 109406 Stefano Morozzi 09/2020 6438 (55459*2^363411+1)/81 109401 Lelio R Paula 07/2014 6439 2^363406+1871569 109397 Enzo Doria 05/2016 6440 (129^51829-1)/128 109388 Anonymous 06/2024 6441 (2^363370+1338)/2 109385 Stefano Morozzi 02/2021 6442 (2^363349+7)/9 109378 Lelio R Paula 01/2014 6443 (13869^26569-1)/(13869^163-1) 109375 Ryan Propper 11/2023 6444 3^229236+100 109374 Lelio R Paula 03/2017 6445 (2^363315+3258)/2 109369 Stefano Morozzi 02/2021 6446 2^363268-58695 109355 Lelio R Paula 04/2017 6447 2^363191-112321 109332 Enzo Doria 06/2014 6448 26231^14718+14718^26231 109327 Hans Havermann 10/2020 6449 25461^19672+19672^25461 109326 Hans Havermann 10/2020 6450 4*10^109316-63 109317 Robert Price 10/2018 6451 2^363120+3 109311 Donovan Johnson 04/2006 6452 (10^109297-1)/9 109297 Paul Bourdelais, Harvey Dubner 04/2007 6453 2^363042-114641 109287 Enzo Doria 04/2015 6454 2^363020-112793 109280 Enzo Doria 06/2014 6455 (8732^27889-1)/(8732^167-1) 109256 Ryan Propper 11/2023 6456 (85*10^109253+203)/9 109254 Robert Price 09/2020 6457 24990^23431+23431^24990 109202 Hans Havermann 10/2020 6458 (2^362746+3738)/2 109198 Stefano Morozzi 09/2020 6459 (2^362716+1282)/2 109189 Stefano Morozzi 01/2021 6460 (67607*2^362695+1)/70499 109183 Lelio R Paula 07/2014 6461 25060^22737+22737^25060 109180 Hans Havermann 10/2020 6462 (9*2^362644+1)/5 109167 Lelio R Paula 03/2014 6463 5^156181+38 109166 Lelio R Paula 02/2017 6464 (2^362623+3618)/2 109161 Stefano Morozzi 09/2020 6465 25138^21993+21993^25138 109157 Hans Havermann 10/2020 6466 4*10^109142+91 109143 Robert Price 08/2018 6467 3^228750+68 109142 Lelio R Paula 03/2017 6468 (2^362561+786)/2 109142 Stefano Morozzi 09/2020 6469 (23*10^109113+61)/3 109114 Robert Price 01/2022 6470 2*10^109100-49 109101 Robert Price 09/2020 6471 (10223*2^362376+1)/9 109090 Lelio R Paula 07/2014 6472 65^60167-64^60167 109078 Robert Price 08/2013 6473 7*3^228589-2 109066 Lelio R Paula 09/2014 6474 24874^24243+24243^24874 109063 Hans Havermann 11/2020 6475 (17*10^109059-161)/9 109060 Robert Price 02/2021 6476 29158^5495+5495^29158 109050 Hans Havermann 11/2020 6477 (78557*2^362188+1)/189 109033 Lelio R Paula 07/2014 6478 2*7^129008+9 109025 Lelio R Paula 11/2014 6479 88*10^109022+7 109024 Robert Price 03/2020 6480 28194^7337+7337^28194 108985 Hans Havermann 10/2020 6481 (5*10^108960+91)/3 108961 Robert Price 04/2018 6482 2^361957+76367 108960 Enzo Doria 05/2016 6483 2^361873-1411 108935 Yves Minet 01/2013 6484 (24737*2^361857+1)/35 108933 Lelio R Paula 07/2014 6485 115^52842-114 108892 Norbert Schneider 07/2018 6486 13^97745-24 108883 Lelio R Paula 03/2017 6487 (2^361696+2562)/2 108882 Stefano Morozzi 09/2020 6488 17^88475+8 108864 Lelio R Paula 04/2017 6489 2^361567+51 108843 Lelio R Paula 01/2012 6490 2^361563-109501 108842 Enzo Doria 04/2014 6491 12^100852+83 108838 Lelio R Paula 03/2017 6492 2^361497+767 108822 Lelio R Paula 01/2012 6493 L(520691)/78103651/1057002731/42794551909 108791 Serge Batalov 07/2024 6494 28019^7630+7630^28019 108785 Hans Havermann 10/2020 6495 24723^24758-24758^24723 108765 Norbert Schneider 11/2020 6496 2^361280-112349 108757 Enzo Doria 06/2014 6497 2^361271-5955 108754 Lelio R Paula 04/2017 6498 12^100757+19 108736 Lelio R Paula 03/2017 6499 25368^19333+19333^25368 108735 Hans Havermann 11/2020 6500 (2^361195+3618)/2 108731 Stefano Morozzi 09/2020

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 12 2024 08:27 (Time in France)

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