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) !!!
Submit your PRPs
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See the Latest PRPs
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| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 6251 | (15*2^403912+1)/271 | 121589 | Lelio R Paula | 05/2014 |
| 6252 | (211^52301-1)/210 | 121560 | Anonymous | 04/2024 |
| 6253 | (10^121543-79)/3 | 121543 | Robert Price | 01/2018 |
| 6254 | Phi(85408,1105) | 121540 | Henri Lifchitz | 12/2025 |
| 6255 | 801^41852-41852^801 | 121523 | Norman Luhn | 10/2024 |
| 6256 | 2^403676+76831 | 121519 | Enzo Doria | 05/2016 |
| 6257 | (41^75337-1)/98233421080 | 121492 | Paul Vanderveen | 05/2025 |
| 6258 | 715^42564-42564^715 | 121491 | Norman Luhn | 10/2024 |
| 6259 | (7*10^121487+143)/3 | 121488 | Robert Price | 03/2018 |
| 6260 | 27965^22086+22086^27965 | 121484 | Hans Havermann | 02/2021 |
| 6261 | (893*10^121470+7)/9 | 121472 | Robert Price | 06/2021 |
| 6262 | (206*10^121462-11)/3 | 121464 | Robert Price | 02/2022 |
| 6263 | 26282^27481-27481^26282 | 121457 | Frank Doornink | 03/2024 |
| 6264 | (77*10^121455+67)/9 | 121456 | Robert Price | 12/2021 |
| 6265 | 2^403363-113635 | 121425 | Enzo Doria | 08/2014 |
| 6266 | 25531^27552-27552^25531 | 121424 | Frank Doornink | 02/2024 |
| 6267 | (17*10^121418-113)/3 | 121419 | Robert Price | 06/2021 |
| 6268 | 2^403336-1861469 | 121417 | Enzo Doria | 03/2016 |
| 6269 | 27929^22186+22186^27929 | 121382 | Hans Havermann | 02/2021 |
| 6270 | p(24442)#/2-64 | 121381 | Robert Price | 04/2017 |
| 6271 | 11^116555-720 | 121380 | Enzo Doria | 11/2012 |
| 6272 | (873^41263+1)/874 | 121353 | Jinyuan Wang | 12/2024 |
| 6273 | 2^403100-461267 | 121346 | Enzo Doria | 07/2015 |
| 6274 | 2^403093-112213 | 121344 | Enzo Doria | 06/2014 |
| 6275 | 29404^13385+13385^29404 | 121340 | Hans Havermann | 02/2021 |
| 6276 | 28106^20745+20745^28106 | 121332 | Hans Havermann | 02/2021 |
| 6277 | (316^48539+1)/317 | 121330 | Eric Chen | 10/2017 |
| 6278 | (23*10^121320-71)/3 | 121321 | Robert Price | 07/2020 |
| 6279 | 2^403004+1866361 | 121317 | Enzo Doria | 03/2016 |
| 6280 | 2^402953+89 | 121301 | Lelio R Paula | 10/2013 |
| 6281 | 2^402944-2788319 | 121299 | Enzo Doria | 03/2016 |
| 6282 | (44*10^121297-719)/9 | 121298 | Robert Price | 12/2018 |
| 6283 | Phi(171913,7) | 121289 | Henri Lifchitz | 12/2025 |
| 6284 | (27*2^402865+1)/5 | 121276 | Lelio R Paula | 04/2014 |
| 6285 | 2^402828-113183 | 121264 | Enzo Doria | 07/2014 |
| 6286 | (17*10^121242+1)/9 | 121243 | Serge Batalov | 05/2010 |
| 6287 | (15*2^402757+1)/101 | 121242 | Lelio R Paula | 05/2014 |
| 6288 | 282^49477-49477^282 | 121231 | Norman Luhn | 10/2024 |
| 6290 | 2^402715+1874223 | 121230 | Enzo Doria | 06/2016 |
| 6289 | (35*10^121229-593)/9 | 121230 | Robert Price | 07/2018 |
| 6291 | (91^61879+1)/92 | 121222 | Paul Bourdelais | 09/2017 |
| 6292 | 291^49190-49190^291 | 121199 | Norman Luhn | 10/2024 |
| 6293 | (10^121243)/(121243^10) | 121193 | Henri Lifchitz | 05/2025 |
| 6294 | 28719^16568+16568^28719 | 121174 | Hans Havermann | 02/2021 |
| 6295 | Phi(24773,-17#) | 121170 | Henri Lifchitz | 12/2025 |
| 6296 | 7*10^121144+9 | 121145 | Robert Price | 09/2015 |
| 6297 | 27490^25467+25467^27490 | 121121 | Hans Havermann | 02/2021 |
| 6298 | 34575^3182+3182^34575 | 121106 | Hans Havermann | 02/2021 |
| 6299 | 5*10^121100-37 | 121101 | Robert Price | 11/2021 |
| 6300 | F(579521)/516247738177 | 121101 | Serge Batalov | 07/2024 |
| 6301 | 25592^27467-27467^25592 | 121078 | Frank Doornink | 02/2024 |
| 6302 | 29954^10935+10935^29954 | 120979 | Hans Havermann | 02/2021 |
| 6303 | 33585^3992+3992^33585 | 120946 | Hans Havermann | 02/2021 |
| 6304 | 40296^1003+1003^40296 | 120941 | Hans Havermann | 02/2021 |
| 6305 | 2^401725-113251 | 120932 | Enzo Doria | 07/2014 |
| 6306 | (15*2^401677-1)/19 | 120917 | Lelio R Paula | 05/2014 |
| 6307 | 2^401652+73711 | 120910 | Enzo Doria | 04/2016 |
| 6308 | (2^401632+3)/79 | 120902 | Lelio R Paula | 04/2014 |
| 6309 | 40450^973+973^40450 | 120870 | Hans Havermann | 01/2021 |
| 6310 | (8*10^120851-11)/3 | 120852 | Robert Price | 07/2023 |
| 6311 | 10^120841+88417 | 120842 | Patrick De Geest | 04/2020 |
| 6312 | 10^120841-123456789 | 120841 | Robert Price | 02/2020 |
| 6313 | 10^120841-176853 | 120841 | Patrick De Geest | 04/2020 |
| 6314 | 2^401406-2791331 | 120836 | Enzo Doria | 03/2016 |
| 6315 | (28^83497+1)/29 | 120832 | Robert Price | 07/2013 |
| 6316 | (22*10^120828+161)/3 | 120829 | Robert Price | 05/2019 |
| 6317 | 2^401369+1867367 | 120825 | Enzo Doria | 03/2016 |
| 6318 | (5*10^120821+43)/3 | 120822 | Robert Price | 12/2021 |
| 6319 | 26990^27263-27263^26990 | 120808 | Frank Doornink | 03/2024 |
| 6320 | (10^120782+29)/3 | 120782 | Serge Batalov | 12/2014 |
| 6321 | 2^401215-1657 | 120778 | Yves Minet | 07/2014 |
| 6322 | 2^401159+53 | 120761 | Lelio R Paula | 10/2013 |
| 6323 | 27782^22179+22179^27782 | 120739 | Hans Havermann | 01/2021 |
| 6324 | 242^50649-50649^242 | 120738 | Norman Luhn | 09/2024 |
| 6325 | 32974^4585+4585^32974 | 120730 | Hans Havermann | 02/2021 |
| 6326 | 2^401031-113047 | 120723 | Enzo Doria | 07/2014 |
| 6327 | 30598^8813+8813^30598 | 120713 | Hans Havermann | 02/2021 |
| 6328 | (71*10^120703-287)/9 | 120704 | Robert Price | 09/2019 |
| 6329 | 25671^27370-27370^25671 | 120687 | Frank Doornink | 02/2024 |
| 6330 | (29*2^400909-1)/303 | 120685 | Lelio R Paula | 04/2014 |
| 6331 | 34793^2940+2940^34793 | 120675 | Hans Havermann | 02/2021 |
| 6332 | 26028^27329-27329^26028 | 120670 | Frank Doornink | 03/2024 |
| 6333 | (2^400846+538)/2 | 120667 | Stefano Morozzi | 09/2020 |
| 6334 | (166*10^120654+11)/3 | 120656 | Robert Price | 03/2021 |
| 6335 | 34066^3481+3481^34066 | 120652 | Hans Havermann | 02/2021 |
| 6336 | 8*10^120637-27 | 120638 | Robert Price | 10/2021 |
| 6337 | (2^400709+3546)/2 | 120626 | Stefano Morozzi | 09/2020 |
| 6338 | (2^400700+3126)/2 | 120623 | Stefano Morozzi | 09/2020 |
| 6339 | (2^400693+2634)/2 | 120621 | Stefano Morozzi | 09/2020 |
| 6340 | 9*10^120617-61 | 120618 | Robert Price | 06/2021 |
| 6341 | (29*10^120590-71)/3 | 120591 | Robert Price | 07/2021 |
| 6342 | 2^400571-15 | 120584 | Lelio R Paula | 10/2013 |
| 6343 | (10^120574+359)/9 | 120574 | Serge Batalov | 12/2014 |
| 6344 | (8*10^120552-17)/9 | 120552 | Serge Batalov | 11/2022 |
| 6345 | 27431^24810+24810^27431 | 120550 | Hans Havermann | 02/2021 |
| 6346 | 2^400424-216413 | 120540 | Enzo Doria | 04/2013 |
| 6347 | 29090^13911+13911^29090 | 120531 | Hans Havermann | 02/2021 |
| 6348 | (2^400346+1722)/2 | 120516 | Stefano Morozzi | 09/2020 |
| 6349 | 27899^20868+20868^27899 | 120510 | Hans Havermann | 02/2021 |
| 6350 | 33740^3729+3729^33740 | 120506 | Hans Havermann | 02/2021 |
| 6351 | (17*2^400200-1)/587 | 120471 | Lelio R Paula | 05/2014 |
| 6352 | 17228^28437-28437^17228 | 120466 | Norbert Schneider | 08/2025 |
| 6353 | 1069^39770-39770^1069 | 120463 | Norbert Schneider | 05/2025 |
| 6355 | 2^400166+1874899 | 120462 | Enzo Doria | 06/2016 |
| 6354 | (2^400165+1602)/2 | 120462 | Stefano Morozzi | 09/2020 |
| 6356 | 2739^35038-35038^2739 | 120447 | Norbert Schneider | 05/2025 |
| 6357 | 37078^1771+1771^37078 | 120438 | Hans Havermann | 02/2021 |
| 6358 | (2^400084+1638)/2 | 120437 | Stefano Morozzi | 09/2020 |
| 6359 | (3*2^400045-1)/865 | 120424 | Lelio R Paula | 04/2014 |
| 6360 | 12857^29306-29306^12857 | 120423 | Norbert Schneider | 07/2025 |
| 6361 | 2^399999+54173 | 120412 | Norman Luhn | 08/2023 |
| 6362 | (2^399974+2790)/2 | 120404 | Stefano Morozzi | 02/2021 |
| 6363 | 2^399966+73759 | 120402 | Enzo Doria | 04/2016 |
| 6364 | (2^399961+2306)/2 | 120400 | Stefano Morozzi | 02/2021 |
| 6365 | (112*10^120395-1)/3 | 120397 | Serge Batalov | 12/2014 |
| 6366 | 2^399918-95 | 120388 | Lelio R Paula | 04/2013 |
| 6367 | 2^399918+214009 | 120388 | Enzo Doria | 10/2023 |
| 6368 | (28*10^120381-67)/3 | 120382 | Robert Price | 10/2020 |
| 6369 | (49*10^120380-139)/9 | 120381 | Robert Price | 03/2019 |
| 6370 | (2^399874+2194)/2 | 120374 | Stefano Morozzi | 09/2020 |
| 6371 | 2^399792-1849259 | 120350 | Enzo Doria | 08/2015 |
| 6372 | 9*10^120342-7 | 120343 | Robert Price | 09/2015 |
| 6373 | (2^399751+786)/2 | 120337 | Stefano Morozzi | 09/2020 |
| 6374 | (331*10^120332-7)/9 | 120334 | Robert Price | 04/2022 |
| 6375 | 14609^28890-28890^14609 | 120316 | Norbert Schneider | 09/2025 |
| 6376 | (13*10^120306-37)/3 | 120307 | Robert Price | 01/2019 |
| 6377 | (23*10^120299+37)/3 | 120300 | Robert Price | 02/2022 |
| 6378 | 25935^27254-27254^25935 | 120297 | Frank Doornink | 03/2024 |
| 6379 | (2^399604+3070)/2 | 120293 | Stefano Morozzi | 09/2020 |
| 6380 | (2^399549+1062)/2 | 120276 | Stefano Morozzi | 09/2020 |
| 6381 | 2^399526-1861721 | 120270 | Enzo Doria | 11/2015 |
| 6382 | 12199^29430-29430^12199 | 120261 | Norbert Schneider | 08/2025 |
| 6383 | (10^(2*60126+1)+36*10^60126-1)/9 | 120253 | Robert Price | 10/2015 |
| 6384 | 32016^5687+5687^32016 | 120217 | Hans Havermann | 01/2021 |
| 6385 | (205*10^120212-1)/3 | 120214 | Robert Price | 11/2021 |
| 6386 | 13302^29149-29149^13302 | 120209 | Norbert Schneider | 08/2025 |
| 6387 | 2^399322-2798111 | 120208 | Enzo Doria | 04/2016 |
| 6388 | 30438^8867+8867^30438 | 120163 | Hans Havermann | 02/2021 |
| 6389 | 3^251841-5*2^251841 | 120159 | Jon Grantham | 08/2023 |
| 6391 | 72^64693-71^64693 | 120157 | Robert Price | 03/2014 |
| 6390 | (17*10^120156-161)/9 | 120157 | Robert Price | 02/2021 |
| 6392 | Phi(81997,-5#) | 120150 | Henri Lifchitz | 12/2025 |
| 6393 | 2^399111-28489 | 120145 | Enzo Doria | 08/2015 |
| 6394 | 2958^34607-34607^2958 | 120121 | Norbert Schneider | 04/2025 |
| 6395 | (2^399014+1318)/2 | 120115 | Stefano Morozzi | 02/2021 |
| 6396 | 30254^9333+9333^30254 | 120110 | Hans Havermann | 02/2021 |
| 6397 | 2^398972+6561 | 120103 | Henri Lifchitz | 10/2024 |
| 6398 | 30882^7745+7745^30882 | 120101 | Hans Havermann | 02/2021 |
| 6399 | 23687^27452-27452^23687 | 120090 | Norbert Schneider | 08/2025 |
| 6401 | 2^398877+105 | 120074 | Donovan Johnson | 01/2006 |
| 6400 | (101*10^120072-87)/7 | 120074 | Hans Havermann | 02/2015 |
| 6402 | (88^61751+1)/89 | 120072 | Paul Bourdelais | 09/2017 |
| 6403 | U(686581)/4280145953 | 120067 | Serge Batalov | 07/2024 |
| 6404 | 16651^28442-28442^16651 | 120067 | Norbert Schneider | 07/2025 |
| 6405 | 12284^29359-29359^12284 | 120059 | Norbert Schneider | 06/2025 |
| 6406 | 3207^34240-34240^3207 | 120049 | Norbert Schneider | 04/2025 |
| 6407 | 2^398710+57 | 120024 | Lelio R Paula | 04/2013 |
| 6408 | (2^398698+1138)/2 | 120020 | Stefano Morozzi | 09/2020 |
| 6409 | 2^398691-115057 | 120018 | Enzo Doria | 06/2015 |
| 6410 | 12134^29385-29385^12134 | 120009 | Norbert Schneider | 06/2025 |
| 6411 | 6089^31710-31710^6089 | 120008 | Norbert Schneider | 05/2025 |
| 6412 | L(574219) | 120005 | Renaud Lifchitz | 03/2004 |
| 6413 | 2^398571+60413 | 119982 | Yves Minet | 03/2011 |
| 6414 | 28623^15538+15538^28623 | 119971 | Hans Havermann | 02/2021 |
| 6415 | p(24179)#/2-64 | 119949 | Robert Price | 04/2017 |
| 6416 | 2^398448+1872001 | 119945 | Enzo Doria | 05/2016 |
| 6417 | (10^119946*19-91)/6093 | 119944 | Alfred Reich | 10/2023 |
| 6418 | (19*10^119946-91)/9/677 | 119944 | Alfred Reich | 11/2023 |
| 6419 | (191*10^119941-17)/3 | 119943 | Robert Price | 11/2021 |
| 6420 | 634^42803+42803^634 | 119938 | Norbert Schneider | 07/2019 |
| 6421 | 31083^7220+7220^31083 | 119935 | Hans Havermann | 01/2021 |
| 6422 | (68*10^119931-11)/3 | 119933 | Robert Price | 01/2020 |
| 6423 | 8*10^119930-3 | 119931 | Ray Chandler | 04/2011 |
| 6424 | (2^398398+774)/2 | 119930 | Stefano Morozzi | 09/2020 |
| 6425 | (10^119880+179)/9 | 119880 | Serge Batalov | 12/2014 |
| 6426 | (9*2^398145+1)/73 | 119853 | Lelio R Paula | 04/2014 |
| 6427 | (10^119836+77)/3 | 119836 | Robert Price | 01/2018 |
| 6428 | 26681^27074-27074^26681 | 119835 | Frank Doornink | 03/2024 |
| 6429 | 28179^17870+17870^28179 | 119821 | Hans Havermann | 02/2021 |
| 6430 | 2^398029+1872527 | 119819 | Enzo Doria | 05/2016 |
| 6431 | 33142^4119+4119^33142 | 119802 | Hans Havermann | 01/2021 |
| 6432 | 2^397897-113541 | 119779 | Enzo Doria | 08/2014 |
| 6433 | 28636^15171+15171^28636 | 119728 | Hans Havermann | 02/2021 |
| 6434 | 87^61730-61730^87 | 119727 | Norman Luhn | 09/2024 |
| 6435 | (10556^29929-1)/(10556^173-1) | 119724 | Ryan Propper | 11/2023 |
| 6436 | (2^397696+1042)/2 | 119719 | Stefano Morozzi | 09/2020 |
| 6438 | (19*10^119716+101)/3 | 119717 | Robert Price | 09/2019 |
| 6437 | 29563^11208+11208^29563 | 119717 | Hans Havermann | 02/2021 |
| 6439 | 458^44991-44991^458 | 119715 | Norman Luhn | 09/2024 |
| 6440 | 2^397655-933075 | 119707 | Paul Bourdelais | 06/2021 |
| 6441 | (21*2^397661-1)/27593 | 119705 | Lelio R Paula | 04/2014 |
| 6442 | 28243^17308+17308^28243 | 119701 | Hans Havermann | 02/2021 |
| 6443 | 77*10^119688+3 | 119690 | Robert Price | 06/2020 |
| 6444 | 586*25^85601+3717 | 119668 | Eric Chen | 10/2023 |
| 6445 | (2^397504+1698)/2 | 119661 | Stefano Morozzi | 09/2020 |
| 6446 | (58^67853-1)/57 | 119653 | Paul Bourdelais | 09/2017 |
| 6447 | 2^397426+73849 | 119638 | Enzo Doria | 04/2016 |
| 6448 | 8*10^119509+29 | 119510 | Robert Price | 11/2021 |
| 6449 | 2^396933-112723 | 119489 | Enzo Doria | 06/2014 |
| 6450 | 11^114738-150 | 119488 | Enzo Doria | 10/2012 |
| 6451 | (4*10^119474+149)/9 | 119474 | Robert Price | 04/2018 |
| 6452 | 26964^26964-13^13 | 119472 | Henri Lifchitz | 08/2024 |
| 6453 | 2^396790-21 | 119446 | Lelio R Paula | 04/2013 |
| 6454 | 32061^5300+5300^32061 | 119405 | Hans Havermann | 01/2021 |
| 6455 | (2^396633-7)/5 | 119398 | Lelio R Paula | 04/2014 |
| 6456 | 27382^22913+22913^27382 | 119388 | Hans Havermann | 03/2021 |
| 6457 | (2^396577+2522)/2 | 119382 | Stefano Morozzi | 09/2020 |
| 6458 | (2^396492+2230)/2 | 119356 | Stefano Morozzi | 01/2021 |
| 6459 | (47*10^119354+259)/9 | 119355 | Robert Price | 03/2022 |
| 6461 | 105^59050+104 | 119352 | Norbert Schneider | 11/2016 |
| 6460 | 126^56824-125 | 119352 | Norbert Schneider | 12/2018 |
| 6462 | 2^396469+111546435 | 119350 | Paul Bourdelais | 10/2021 |
| 6463 | 139^55690-138 | 119345 | Norbert Schneider | 04/2019 |
| 6464 | Phi(66220,p(66220)) | 119337 | Henri Lifchitz | 12/2025 |
| 6465 | Phi(132889,-9) | 119334 | Henri Lifchitz | 12/2025 |
| 6466 | 790^41179+41179^790 | 119322 | Norbert Schneider | 04/2019 |
| 6467 | 2^396374+73729 | 119321 | Enzo Doria | 04/2016 |
| 6469 | 88*10^119295+3 | 119297 | Robert Price | 05/2020 |
| 6468 | 21*29^81575+129664 | 119297 | Eric Chen | 06/2025 |
| 6470 | 2^396258-459491 | 119286 | Enzo Doria | 05/2015 |
| 6471 | (2^396248+3126)/2 | 119283 | Stefano Morozzi | 09/2020 |
| 6472 | 2^396128-396128-1 | 119247 | Karsten Bonath | 06/2018 |
| 6473 | (893*10^119228+7)/9 | 119230 | Robert Price | 06/2021 |
| 6474 | (31*10^119229+257)/9 | 119230 | Robert Price | 12/2021 |
| 6475 | (28*10^119206-67)/3 | 119207 | Robert Price | 10/2020 |
| 6476 | (2^395986+5)/76881 | 119199 | Lelio R Paula | 04/2014 |
| 6477 | 11^114458+6 | 119196 | Paul Bourdelais | 02/2021 |
| 6478 | (23*2^395942-1)/91 | 119190 | Lelio R Paula | 04/2014 |
| 6479 | (2^395902+202)/2 | 119179 | Stefano Morozzi | 09/2020 |
| 6480 | (2^395825+582)/2 | 119155 | Stefano Morozzi | 09/2020 |
| 6481 | (2^395733+1130)/2 | 119128 | Stefano Morozzi | 09/2020 |
| 6482 | (23^119099)%(10^119099) | 119099 | Henri Lifchitz | 05/2025 |
| 6483 | 29548^10725+10725^29548 | 119091 | Hans Havermann | 02/2021 |
| 6484 | (11*2^395548+1)/3 | 119073 | Lelio R Paula | 04/2014 |
| 6486 | (30^80599+1)/31 | 119054 | Robert Price | 07/2013 |
| 6485 | Phi(80599,-5#) | 119054 | Henri Lifchitz | 12/2025 |
| 6487 | (232*10^119047+17)/3 | 119049 | Robert Price | 04/2021 |
| 6488 | (43*10^119024-403)/9 | 119025 | Robert Price | 01/2019 |
| 6489 | (4*10^119021+47)/3 | 119022 | Robert Price | 01/2022 |
| 6490 | fibonacci(569433)+3 | 119005 | Jon Grantham | 08/2023 |
| 6491 | 26603^26888-26888^26603 | 118978 | Norbert Schneider | 07/2021 |
| 6492 | 912^40193-40193^912 | 118972 | Norman Luhn | 09/2024 |
| 6493 | 681^41992-41992^681 | 118970 | Norman Luhn | 09/2024 |
| 6494 | 6*10^118964+43 | 118965 | Robert Price | 07/2020 |
| 6495 | (8*10^118960+49)/3 | 118961 | Robert Price | 05/2020 |
| 6496 | 31253^6402+6402^31253 | 118959 | Hans Havermann | 02/2021 |
| 6497 | (194*10^118925-17)/3 | 118927 | Robert Price | 09/2020 |
| 6498 | 2^395062-109121 | 118926 | Enzo Doria | 04/2014 |
| 6499 | 2^395055-4627 | 118924 | Yves Minet | 05/2019 |
| 6500 | (2^395054+702)/2 | 118923 | Stefano Morozzi | 09/2020 |
