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
See the Top discoverers
See the Latest PRPs
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| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 6251 | 2^413352+524287 | 124432 | Paul Underwood | 09/2018 |
| 6252 | 287117#+391613 | 124424 | Nicolas PALAU | 01/2017 |
| 6253 | (4*10^124420+83)/3 | 124421 | Robert Price | 02/2018 |
| 6254 | 34578^3965+3965^34578 | 124421 | Hans Havermann | 03/2021 |
| 6255 | (68*10^124392-329)/9 | 124393 | Robert Price | 03/2021 |
| 6256 | (27*2^413207-1)/108335 | 124385 | Lelio R Paula | 05/2014 |
| 6257 | 10^124383+58407 | 124384 | Patrick De Geest | 08/2021 |
| 6259 | 10^124383-8000001 | 124383 | Robert Price | 04/2021 |
| 6258 | 10^124383-5801 | 124383 | Patrick De Geest | 08/2021 |
| 6260 | 26091^28154-28154^26091 | 124342 | Frank Doornink | 03/2024 |
| 6261 | (41*10^124335-383)/9 | 124336 | Robert Price | 11/2018 |
| 6262 | (304*10^124329-43)/9 | 124331 | Robert Price | 02/2020 |
| 6263 | 34716^3811+3811^34716 | 124320 | Hans Havermann | 03/2021 |
| 6264 | 26892^28063-28063^26892 | 124309 | Frank Doornink | 03/2024 |
| 6265 | 2^412868-120599 | 124286 | Paul Bourdelais | 02/2012 |
| 6266 | 10^124248+899089 | 124249 | Patrick De Geest | 05/2021 |
| 6268 | 10^124248-1000001 | 124248 | Robert Price | 08/2020 |
| 6267 | 10^124248-501903 | 124248 | Patrick De Geest | 05/2021 |
| 6269 | 45^75145-2 | 124231 | Lelio R Paula | 08/2015 |
| 6270 | 29901^14272+14272^29901 | 124224 | Hans Havermann | 03/2021 |
| 6271 | 2^412645-112213 | 124219 | Enzo Doria | 06/2014 |
| 6272 | 29837^14500+14500^29837 | 124163 | Hans Havermann | 03/2021 |
| 6273 | 28074^26455+26455^28074 | 124158 | Hans Havermann | 03/2021 |
| 6274 | 954^41669-41669^954 | 124155 | Norman Luhn | 10/2024 |
| 6275 | 432^47093-47093^432 | 124113 | Norman Luhn | 10/2024 |
| 6276 | 2^412285+213317 | 124111 | Enzo Doria | 09/2023 |
| 6277 | (12^115001-1)/2530033 | 124101 | Paul Vanderveen | 06/2025 |
| 6278 | 2^412248+74611 | 124100 | Enzo Doria | 04/2016 |
| 6279 | (22*10^124096-13)/9 | 124097 | Robert Price | 06/2018 |
| 6280 | (455*10^124093+31)/9 | 124095 | Robert Price | 06/2021 |
| 6281 | 2^412192-3329 | 124083 | Yves Minet | 12/2014 |
| 6282 | (25*2^412191-1)/23 | 124082 | Lelio R Paula | 05/2014 |
| 6284 | (25*10^124076-67)/3 | 124077 | Robert Price | 06/2019 |
| 6283 | 28132^25735+25735^28132 | 124077 | Hans Havermann | 03/2021 |
| 6285 | F(593689) | 124074 | Henri Lifchitz | 01/2005 |
| 6286 | (11*2^412161+1)/19 | 124073 | Lelio R Paula | 05/2014 |
| 6287 | 1232^40143-40143^1232 | 124067 | Norman Luhn | 10/2024 |
| 6288 | 26372^28057-28057^26372 | 124045 | Frank Doornink | 03/2024 |
| 6289 | 27528^27937-27937^27528 | 124034 | Frank Doornink | 03/2024 |
| 6290 | 35364^3215+3215^35364 | 124028 | Hans Havermann | 03/2021 |
| 6292 | (266*10^124022-11)/3 | 124024 | Robert Price | 04/2020 |
| 6291 | 29987^13674+13674^29987 | 124024 | Hans Havermann | 03/2021 |
| 6293 | 2^411932-111546435 | 124004 | Paul Bourdelais | 10/2021 |
| 6294 | 2^411884-113279 | 123990 | Enzo Doria | 07/2014 |
| 6295 | (2^411832+1)/257 | 123972 | Lelio R Paula | 05/2014 |
| 6296 | (2^411833+2)/514 | 123972 | Stefano Morozzi | 03/2020 |
| 6297 | (26*10^123970-89)/9 | 123971 | Robert Price | 06/2018 |
| 6298 | 2^411790-1853531 | 123962 | Enzo Doria | 08/2015 |
| 6300 | (5^177337+1)/6 | 123953 | Paul Bourdelais | 11/2008 |
| 6299 | Phi(177337,-5) | 123953 | Henri Lifchitz | 12/2025 |
| 6301 | (101*10^123950+7)/9 | 123952 | Robert Price | 02/2022 |
| 6302 | 2^411711-113257 | 123938 | Enzo Doria | 07/2014 |
| 6303 | (23*2^411675-1)/3 | 123928 | Lelio R Paula | 05/2014 |
| 6304 | 36289^2598+2598^36289 | 123914 | Hans Havermann | 03/2021 |
| 6305 | (11*10^123899-179)/3 | 123900 | Robert Price | 09/2018 |
| 6306 | 32276^6879+6879^32276 | 123860 | Hans Havermann | 02/2021 |
| 6307 | 2^411325-351103 | 123822 | Enzo Doria | 06/2015 |
| 6308 | (646*10^123817+11)/9 | 123819 | Robert Price | 10/2021 |
| 6309 | 30738^10643+10643^30738 | 123784 | Hans Havermann | 03/2021 |
| 6310 | 31074^9607+9607^31074 | 123755 | Hans Havermann | 03/2021 |
| 6311 | Phi(395949,3) | 123754 | Henri Lifchitz | 02/2026 |
| 6312 | 2^411052+1872481 | 123739 | Enzo Doria | 05/2016 |
| 6313 | 34365^3986+3986^34365 | 123733 | Hans Havermann | 03/2021 |
| 6314 | 2^410997+39 | 123723 | Lelio R Paula | 05/2014 |
| 6315 | (649^43987-1)/648 | 123700 | Michael Stocker | 05/2020 |
| 6316 | (148*10^123688-1)/3 | 123690 | Robert Price | 03/2020 |
| 6317 | 36825^2284+2284^36825 | 123684 | Hans Havermann | 03/2021 |
| 6318 | 29582^15171+15171^29582 | 123683 | Hans Havermann | 03/2021 |
| 6319 | 10^123671+3593037 | 123672 | Paul Bourdelais | 10/2021 |
| 6320 | 8*10^123657+87 | 123658 | Robert Price | 10/2019 |
| 6321 | 30505^11302+11302^30505 | 123642 | Hans Havermann | 03/2021 |
| 6322 | 29956^13401+13401^29956 | 123633 | Hans Havermann | 03/2021 |
| 6323 | 19*35^80065+19442 | 123628 | Eric Chen | 05/2025 |
| 6324 | 155^56438+154 | 123618 | Norbert Schneider | 01/2019 |
| 6325 | 2^410596-39 | 123602 | Lelio R Paula | 05/2014 |
| 6326 | (41*10^123600-221)/9 | 123601 | Robert Price | 10/2021 |
| 6327 | 28995^18302+18302^28995 | 123592 | Hans Havermann | 03/2021 |
| 6328 | 28302^23269+23269^28302 | 123589 | Hans Havermann | 03/2021 |
| 6329 | (41^76630+40)/37 | 123587 | Alfred Reich | 06/2024 |
| 6330 | 2^410540-115079 | 123585 | Enzo Doria | 06/2015 |
| 6331 | (7*10^123563+107)/3 | 123564 | Robert Price | 02/2018 |
| 6332 | 9*10^123549+89 | 123550 | Robert Price | 11/2019 |
| 6333 | (197*10^123545+7)/3 | 123547 | Robert Price | 12/2020 |
| 6334 | (3*2^410392-1)/9229 | 123537 | Lelio R Paula | 05/2014 |
| 6335 | 2^410342+212449 | 123526 | Enzo Doria | 08/2023 |
| 6336 | (29*10^123510+277)/9 | 123511 | Robert Price | 11/2021 |
| 6337 | 28118^24687+24687^28118 | 123508 | Hans Havermann | 03/2021 |
| 6338 | 39994^1225+1225^39994 | 123507 | Hans Havermann | 03/2021 |
| 6339 | 2^410206-113081 | 123485 | Enzo Doria | 07/2014 |
| 6340 | (25*2^410192+1)/10397 | 123478 | Lelio R Paula | 04/2014 |
| 6341 | 28974^18215+18215^28974 | 123442 | Hans Havermann | 03/2021 |
| 6342 | 28901^18618+18618^28901 | 123406 | Hans Havermann | 03/2021 |
| 6343 | 2^409909-189 | 123395 | Enzo Doria | 05/2014 |
| 6344 | 135^57922-57922^135 | 123394 | Norman Luhn | 10/2024 |
| 6345 | 2^409896-109043 | 123391 | Enzo Doria | 04/2014 |
| 6346 | 2^409890+75409 | 123390 | Enzo Doria | 04/2016 |
| 6347 | 81254^33+33^81254 | 123386 | Hans Havermann | 03/2021 |
| 6348 | Sm(26896)/9570596907856 | 123361 | Youcef Lemsafer | 06/2026 |
| 6349 | 33463^4854+4854^33463 | 123348 | Hans Havermann | 03/2021 |
| 6350 | 34061^4182+4182^34061 | 123348 | Hans Havermann | 03/2021 |
| 6351 | 133^58076-2 | 123345 | Lelio R Paula | 10/2017 |
| 6352 | L(2*409661)%(2^409661) | 123320 | Henri Lifchitz | 06/2025 |
| 6353 | F(590041) | 123311 | Henri Lifchitz | 01/2005 |
| 6354 | (82*10^123299+377)/9 | 123300 | Robert Price | 03/2022 |
| 6355 | 2^409566-113501 | 123292 | Enzo Doria | 08/2014 |
| 6356 | 2^409533+77747 | 123282 | Enzo Doria | 05/2016 |
| 6357 | 2^409436-112799 | 123253 | Enzo Doria | 06/2014 |
| 6358 | 28212^23321+23321^28212 | 123223 | Hans Havermann | 03/2021 |
| 6359 | 2^409225+1873787 | 123189 | Enzo Doria | 06/2016 |
| 6360 | 2^409174+73009 | 123174 | Enzo Doria | 04/2016 |
| 6361 | (4893*35^79754-31)/34 | 123148 | Eric Chen | 05/2025 |
| 6362 | 2^409058-112685 | 123139 | Enzo Doria | 06/2014 |
| 6363 | (13*10^123137-61)/3 | 123138 | Robert Price | 11/2018 |
| 6364 | 4*10^123113+21 | 123114 | Robert Price | 12/2018 |
| 6365 | 2^408778+77689 | 123055 | Enzo Doria | 05/2016 |
| 6366 | 660^43643-43643^660 | 123054 | Norman Luhn | 10/2024 |
| 6367 | 2^408690-75 | 123028 | Lelio R Paula | 11/2013 |
| 6368 | 28327^22032+22032^28327 | 123026 | Hans Havermann | 03/2021 |
| 6369 | (29*10^122996+673)/9 | 122997 | Robert Price | 12/2018 |
| 6370 | (65*10^122994-101)/9 | 122995 | Robert Price | 01/2022 |
| 6371 | 2^408574-2787341 | 122994 | Enzo Doria | 03/2016 |
| 6372 | 3*10^122977+37 | 122978 | Robert Price | 08/2018 |
| 6373 | (7*10^122976-67)/3 | 122977 | Robert Price | 10/2021 |
| 6374 | Phi(157825,10) | 122961 | Maksym Voznyy | 06/2015 |
| 6375 | 25493^27902-27902^25493 | 122948 | Frank Doornink | 02/2024 |
| 6376 | 26749^27768-27768^26749 | 122938 | Frank Doornink | 03/2024 |
| 6377 | (68*10^122933-419)/9 | 122934 | Robert Price | 07/2019 |
| 6378 | 29712^13721+13721^29712 | 122931 | Hans Havermann | 03/2021 |
| 6379 | (13*2^408283+1)/1665 | 122904 | Lelio R Paula | 05/2014 |
| 6380 | (266*10^122872-17)/3 | 122874 | Robert Price | 07/2020 |
| 6381 | (16*10^122871+77)/3 | 122872 | Robert Price | 03/2019 |
| 6382 | 30395^11022+11022^30395 | 122865 | Hans Havermann | 03/2021 |
| 6383 | 4*10^122859-69 | 122860 | Robert Price | 01/2022 |
| 6384 | (10^122857+167)/3 | 122857 | Robert Price | 05/2021 |
| 6385 | 33331^4852+4852^33331 | 122856 | Hans Havermann | 03/2021 |
| 6386 | (11*2^408100-1)/35 | 122850 | Lelio R Paula | 04/2014 |
| 6387 | (19*10^122836-43)/3 | 122837 | Robert Price | 05/2019 |
| 6388 | 315^49162-49162^315 | 122822 | Norman Luhn | 10/2024 |
| 6389 | 28420^20969+20969^28420 | 122820 | Hans Havermann | 03/2021 |
| 6390 | (16*10^122818+179)/3 | 122819 | Robert Price | 11/2021 |
| 6391 | 29865^12934+12934^29865 | 122797 | Hans Havermann | 03/2021 |
| 6392 | (2^407821-lucasV(1,2,407821)+1)/2 | 122767 | Mike Oakes | 11/2016 |
| 6393 | 17^99766+18 | 122757 | Anonymous | 09/2024 |
| 6394 | (32*10^122733-77)/9 | 122734 | Robert Price | 06/2018 |
| 6395 | (21*2^407604-1)/215 | 122701 | Lelio R Paula | 04/2014 |
| 6397 | (22*10^122681+161)/3 | 122682 | Robert Price | 05/2019 |
| 6396 | 29513^14350+14350^29513 | 122682 | Hans Havermann | 03/2021 |
| 6398 | (21*2^407433-1)/13 | 122650 | Lelio R Paula | 04/2014 |
| 6399 | Phi(149534,2^7) | 122640 | Henri Lifchitz | 10/2025 |
| 6400 | 395^47226+394 | 122627 | Alfred Reich | 03/2026 |
| 6402 | (26*10^122625-131)/3 | 122626 | Robert Price | 10/2019 |
| 6401 | (643*33^80753+3709)/32 | 122626 | Eric Chen | 12/2023 |
| 6403 | 27925^24562+24562^27925 | 122599 | Hans Havermann | 03/2021 |
| 6404 | (92365^24691-1)/92364 | 122599 | Anonymous | 09/2025 |
| 6405 | (73*10^122592-1)/9 | 122593 | Robert Price | 01/2015 |
| 6406 | (5*10^122592+91)/3 | 122593 | Robert Price | 04/2018 |
| 6407 | 36751^2166+2166^36751 | 122589 | Hans Havermann | 03/2021 |
| 6408 | (85*10^122585-1)/3 | 122587 | Robert Price | 02/2020 |
| 6409 | 29368^14931+14931^29368 | 122585 | Hans Havermann | 03/2021 |
| 6410 | 2^407179-112075 | 122574 | Enzo Doria | 06/2014 |
| 6411 | (21*2^407131+1)/207517523 | 122552 | Lelio R Paula | 04/2014 |
| 6412 | (66^67349+1)/67 | 122543 | Paul Bourdelais | 09/2017 |
| 6413 | (646*10^122533+11)/9 | 122535 | Robert Price | 10/2021 |
| 6414 | 2^407008-1867919 | 122522 | Enzo Doria | 04/2016 |
| 6415 | 11^117642-300 | 122512 | Enzo Doria | 10/2012 |
| 6416 | (F(3*97700+1)^2+L(3*97700+1)^2)/2 | 122509 | Henri Lifchitz | 10/2017 |
| 6417 | 2^406949+72197 | 122504 | Enzo Doria | 04/2016 |
| 6418 | (19*10^122501+149)/3 | 122502 | Robert Price | 05/2019 |
| 6419 | 28632^18977+18977^28632 | 122495 | Hans Havermann | 03/2021 |
| 6420 | 31815^7076+7076^31815 | 122481 | Hans Havermann | 03/2021 |
| 6421 | 2^406826-65 | 122467 | Lelio R Paula | 11/2013 |
| 6422 | 2^406821-2797363 | 122466 | Enzo Doria | 04/2016 |
| 6423 | (7*10^122456-331)/9 | 122456 | Robert Price | 03/2022 |
| 6424 | 2^406758-17 | 122447 | Lelio R Paula | 11/2013 |
| 6425 | 411^46842+410 | 122438 | Alfred Reich | 03/2026 |
| 6426 | 29941^12282+12282^29941 | 122437 | Hans Havermann | 03/2021 |
| 6428 | (30^82883-1)/29 | 122427 | Robert Price | 12/2011 |
| 6427 | Phi(82883,5#) | 122427 | Henri Lifchitz | 12/2025 |
| 6429 | 27496^27577+27577^27496 | 122422 | Norbert Schneider | 12/2020 |
| 6430 | 28732^18215+18215^28732 | 122411 | Hans Havermann | 03/2021 |
| 6431 | (2^406583-1)/813167 | 122388 | Jens K. Andersen | 02/2009 |
| 6432 | 4*10^122377+19 | 122378 | Robert Price | 10/2018 |
| 6433 | 28227^21634+21634^28227 | 122368 | Hans Havermann | 03/2021 |
| 6434 | Phi(246362,10) | 122365 | Makoto Kamada | 09/2019 |
| 6435 | 3*10^122345-97 | 122346 | Robert Price | 07/2018 |
| 6436 | 97^61575-2 | 122336 | Lelio R Paula | 12/2014 |
| 6437 | 2*10^122319+47 | 122320 | Robert Price | 12/2021 |
| 6438 | 208^52765+52765^208 | 122313 | Norbert Schneider | 11/2020 |
| 6440 | 2^406298+2799109 | 122308 | Enzo Doria | 04/2016 |
| 6439 | 2^406296+213691 | 122308 | Enzo Doria | 09/2023 |
| 6441 | 7*10^122294+57 | 122295 | Robert Price | 06/2019 |
| 6442 | (27*2^406241-1)/10277 | 122289 | Lelio R Paula | 04/2014 |
| 6443 | 2^406229-1849993 | 122288 | Enzo Doria | 08/2015 |
| 6444 | 4^203111-203111 | 122286 | Anonymous | 08/2026 |
| 6445 | 3*10^122274+7 | 122275 | Robert Price | 07/2015 |
| 6446 | 2^406117+1876577 | 122254 | Enzo Doria | 07/2016 |
| 6447 | 29308^14835+14835^29308 | 122253 | Hans Havermann | 03/2021 |
| 6448 | 28119^22268+22268^28119 | 122253 | Hans Havermann | 03/2021 |
| 6449 | 32167^6312+6312^32167 | 122240 | Hans Havermann | 03/2021 |
| 6450 | 3^256199-2^256199 | 122238 | Mike Oakes | 06/2005 |
| 6451 | 27678^26053+26053^27678 | 122223 | Hans Havermann | 03/2021 |
| 6452 | 2^405992-78557 | 122216 | Jorge Menendez | 03/2018 |
| 6453 | (8*10^122203+43)/3 | 122204 | Robert Price | 06/2018 |
| 6454 | (58*10^122170+329)/9 | 122171 | Robert Price | 05/2019 |
| 6455 | 2^405774+179149 | 122151 | Enzo Doria | 06/2016 |
| 6456 | 2^405693+20417 | 122126 | Enzo Doria | 07/2023 |
| 6457 | (218*10^122109+7)/9 | 122111 | Robert Price | 06/2022 |
| 6458 | 29189^15246+15246^29189 | 122103 | Hans Havermann | 03/2021 |
| 6459 | (42^75217-5^75217)/37 | 122095 | Robert Price | 06/2026 |
| 6461 | 34*10^122082-9 | 122084 | Robert Price | 06/2020 |
| 6460 | 33442^4473+4473^33442 | 122084 | Hans Havermann | 03/2021 |
| 6462 | 5*10^122082+41 | 122083 | Robert Price | 03/2019 |
| 6463 | 31849^6808+6808^31849 | 122078 | Hans Havermann | 03/2021 |
| 6465 | 2^405514-3311 | 122072 | Yves Minet | 12/2014 |
| 6466 | 2^405514-115511 | 122072 | Enzo Doria | 07/2015 |
| 6464 | 23*10^122070-7 | 122072 | Robert Price | 02/2020 |
| 6467 | 2^405422-113261 | 122045 | Enzo Doria | 07/2014 |
| 6468 | 95^61698-61698^95 | 122022 | Norman Luhn | 10/2024 |
| 6469 | 2^405173+71237 | 121970 | Enzo Doria | 04/2016 |
| 6470 | fibonacci(583574)+2 | 121960 | Jon Grantham | 08/2023 |
| 6471 | (154*10^121953+17)/9 | 121955 | Robert Price | 06/2022 |
| 6472 | (34*10^121924+191)/9 | 121925 | Robert Price | 08/2021 |
| 6473 | (2^405016+1)/257 | 121920 | Lelio R Paula | 04/2014 |
| 6474 | 28557^18590+18590^28557 | 121918 | Hans Havermann | 03/2021 |
| 6475 | 28641^18002+18002^28641 | 121877 | Hans Havermann | 03/2021 |
| 6476 | 2^404858+71329 | 121875 | Enzo Doria | 04/2016 |
| 6477 | 2^404813-114703 | 121861 | Enzo Doria | 04/2015 |
| 6478 | 2^404764+77791 | 121847 | Enzo Doria | 05/2016 |
| 6479 | 28830^16841+16841^28830 | 121847 | Hans Havermann | 03/2021 |
| 6480 | (4*10^121825+89)/3 | 121826 | Robert Price | 08/2021 |
| 6481 | 317^48694+48694^317 | 121787 | Norbert Schneider | 08/2015 |
| 6482 | 2^404536-115259 | 121778 | Enzo Doria | 06/2015 |
| 6483 | 2^404501-631 | 121767 | Yves Minet | 07/2012 |
| 6484 | 5*10^121764-69 | 121765 | Robert Price | 02/2021 |
| 6485 | (34^79493-3^79493)/31 | 121741 | Robert Price | 07/2025 |
| 6486 | 28236^20485+20485^28236 | 121738 | Hans Havermann | 02/2021 |
| 6487 | (382*10^121694-31)/9 | 121696 | Robert Price | 06/2022 |
| 6488 | 63^67620+2 | 121672 | Lelio R Paula | 08/2015 |
| 6489 | (25*34^79445-28062367)/33 | 121669 | Eric Chen | 08/2023 |
| 6490 | (13*33^80110-121453)/32 | 121648 | Eric Chen | 12/2023 |
| 6491 | (16*10^121633+167)/3 | 121634 | Robert Price | 06/2019 |
| 6492 | 29955^11494+11494^29955 | 121632 | Hans Havermann | 02/2021 |
| 6493 | (17*10^121621+1)/9 | 121622 | Serge Batalov | 05/2010 |
| 6494 | 31088^8163+8163^31088 | 121612 | Hans Havermann | 02/2021 |
| 6495 | (15*2^403912+1)/271 | 121589 | Lelio R Paula | 05/2014 |
| 6496 | (211^52301-1)/210 | 121560 | Anonymous | 04/2024 |
| 6497 | (10^121543-79)/3 | 121543 | Robert Price | 01/2018 |
| 6498 | Phi(85408,1105) | 121540 | Henri Lifchitz | 12/2025 |
| 6499 | 801^41852-41852^801 | 121523 | Norman Luhn | 10/2024 |
| 6500 | 2^403676+76831 | 121519 | Enzo Doria | 05/2016 |
