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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Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
6251 | 99^54094+2 | 107952 | Lelio R Paula | 06/2013 |
6252 | (2^358583-9)/391 | 107942 | Lelio R Paula | 12/2013 |
6253 | (2^358562+838)/2 | 107938 | Stefano Morozzi | 02/2021 |
6254 | 2^358538+55 | 107931 | Lelio R Paula | 12/2011 |
6255 | 2^358517-109009 | 107925 | Enzo Doria | 03/2014 |
6256 | 26395^12258+12258^26395 | 107914 | Hans Havermann | 10/2020 |
6257 | 3^226159+104 | 107906 | Lelio R Paula | 03/2017 |
6258 | 7*10^107870+39 | 107871 | Robert Price | 01/2023 |
6259 | 2^358310-11655 | 107863 | Lelio R Paula | 03/2017 |
6260 | (68*10^107852-329)/9 | 107853 | Robert Price | 03/2021 |
6261 | 2^358275-112987 | 107852 | Enzo Doria | 07/2014 |
6262 | 3^226038+4 | 107848 | Tyler NeSmith | 01/2021 |
6263 | 2^358233-20005 | 107839 | Enzo Doria | 06/2013 |
6264 | 2^358194+175 | 107828 | Lelio R Paula | 12/2011 |
6265 | 107^53125-106 | 107812 | Norbert Schneider | 12/2016 |
6266 | (25*10^107804+161)/3 | 107805 | Robert Price | 09/2019 |
6267 | 3^225922-2 | 107793 | Lelio R Paula | 10/2013 |
6268 | 12^99874-95 | 107783 | Lelio R Paula | 03/2017 |
6269 | (2^358042+3042)/2 | 107782 | Stefano Morozzi | 09/2020 |
6270 | 2^358030-171 | 107778 | Lelio R Paula | 12/2011 |
6271 | 11^103488-4170 | 107772 | Enzo Doria | 12/2012 |
6272 | 2^357930-4547 | 107748 | Yves Minet | 03/2019 |
6273 | 2^357911-20089 | 107742 | Enzo Doria | 06/2013 |
6274 | 2^357885+12857 | 107735 | Yves Minet | 07/2010 |
6275 | (248587#+9289)/(7*1327*111512899) | 107733 | Makoto Morimoto | 06/2019 |
6276 | 7^127473+40 | 107728 | Lelio R Paula | 03/2017 |
6277 | 5*2^357850+9 | 107725 | Lelio R Paula | 09/2014 |
6278 | 2^357786-291191 | 107705 | Enzo Doria | 06/2015 |
6279 | 28907^5320+5320^28907 | 107705 | Hans Havermann | 10/2020 |
6280 | 18^85798-23 | 107700 | Lelio R Paula | 04/2017 |
6281 | 3*10^107697+61 | 107698 | Robert Price | 09/2020 |
6282 | (14*10^107694-83)/3 | 107695 | Robert Price | 12/2018 |
6283 | 2^357688-1854269 | 107675 | Enzo Doria | 09/2015 |
6284 | 2^357671-112225 | 107670 | Enzo Doria | 06/2014 |
6285 | 34323^1370+1370^34323 | 107662 | Hans Havermann | 11/2020 |
6286 | 2^357618-21005 | 107654 | Enzo Doria | 06/2013 |
6287 | 2^357615-17505 | 107653 | Enzo Doria | 05/2013 |
6288 | 26350^12171+12171^26350 | 107649 | Hans Havermann | 11/2020 |
6289 | (30^72871-1)/29 | 107638 | Robert Price | 12/2011 |
6290 | 25021^20026+20026^25021 | 107631 | Hans Havermann | 11/2020 |
6291 | 2^357521+1870217 | 107625 | Enzo Doria | 05/2016 |
6292 | 2^357477-1203 | 107612 | Lelio R Paula | 03/2017 |
6293 | 26008^13693+13693^26008 | 107583 | Hans Havermann | 10/2020 |
6294 | 25432^16991+16991^25432 | 107583 | Hans Havermann | 10/2020 |
6295 | (2^357371+3726)/2 | 107580 | Stefano Morozzi | 09/2020 |
6296 | 5^153894-18 | 107568 | Lelio R Paula | 02/2017 |
6297 | 2^357324-69059 | 107566 | Enzo Doria | 11/2015 |
6298 | 467^40296+40296^467 | 107563 | Norbert Schneider | 03/2019 |
6299 | 29446^4495+4495^29446 | 107559 | Hans Havermann | 10/2020 |
6300 | (8*10^107556-149)/3 | 107557 | Robert Price | 12/2021 |
6301 | 2^357283-869688105 | 107553 | Lelio R Paula | 01/2017 |
6302 | 2^357280-16805 | 107552 | Enzo Doria | 05/2013 |
6303 | 10^107547+481719 | 107548 | Patrick De Geest | 03/2017 |
6304 | 10^107547-47 | 107547 | Lelio R Paula | 02/2017 |
6305 | (23*10^107540+37)/3 | 107541 | Robert Price | 02/2022 |
6306 | 17^87396-32 | 107537 | Lelio R Paula | 04/2017 |
6307 | (746*10^107505+1)/9 | 107507 | Robert Price | 03/2020 |
6308 | (2^357125+1730)/2 | 107506 | Stefano Morozzi | 09/2020 |
6309 | 2^357081+107 | 107493 | Lelio R Paula | 12/2011 |
6310 | 2^357058-3911 | 107486 | Yves Minet | 04/2017 |
6311 | 3^225274+64 | 107484 | Lelio R Paula | 03/2017 |
6312 | 5*10^107482-57 | 107483 | Robert Price | 03/2021 |
6313 | 18^85619-95 | 107476 | Lelio R Paula | 04/2017 |
6314 | (2^357013+2526)/2 | 107472 | Stefano Morozzi | 09/2020 |
6315 | 3^225248-130 | 107471 | Lelio R Paula | 03/2017 |
6316 | (5*2^356961+1)/143 | 107455 | Lelio R Paula | 03/2014 |
6317 | 27029^9448+9448^27029 | 107450 | Hans Havermann | 11/2020 |
6318 | 2^356935-18085 | 107449 | Enzo Doria | 05/2013 |
6319 | 55396^87+87^55396 | 107442 | Hans Havermann | 10/2020 |
6320 | (14*10^107439-137)/3 | 107440 | Robert Price | 04/2021 |
6321 | 10^107409+37 | 107410 | Lelio R Paula | 02/2017 |
6322 | 10^107409-329633 | 107409 | Patrick De Geest | 03/2017 |
6323 | (2^356799+3134)/2 | 107407 | Stefano Morozzi | 09/2020 |
6324 | 2^356787-109027 | 107404 | Enzo Doria | 04/2014 |
6325 | (2^356767+78557)/5 | 107397 | Lelio R Paula | 12/2013 |
6326 | 3*10^107389+77 | 107390 | Robert Price | 09/2018 |
6327 | (11*10^107385+61)/9 | 107386 | Tyler Busby | 01/2023 |
6328 | 5^153622-42 | 107378 | Lelio R Paula | 02/2017 |
6329 | 2^356699-97305 | 107378 | Lelio R Paula | 03/2017 |
6330 | 13129^26072-26072^13129 | 107371 | Norbert Schneider | 09/2022 |
6331 | 2^356654+85 | 107364 | Lelio R Paula | 11/2011 |
6332 | 2^356641-19921 | 107360 | Enzo Doria | 06/2013 |
6333 | 5*10^107355+11 | 107356 | Robert Price | 08/2019 |
6334 | 2^356623-465 | 107355 | Lelio R Paula | 03/2017 |
6335 | 19^83945-92 | 107345 | Lelio R Paula | 02/2017 |
6336 | 25491^16246+16246^25491 | 107337 | Hans Havermann | 11/2020 |
6337 | 10^107334+28149 | 107335 | Patrick De Geest | 03/2017 |
6338 | 10^107334-83 | 107334 | Lelio R Paula | 02/2017 |
6339 | 2^356518+885 | 107323 | Lelio R Paula | 03/2017 |
6340 | (59*10^107322+391)/9 | 107323 | Robert Price | 03/2021 |
6341 | (3*2^356506-1)/467 | 107317 | Lelio R Paula | 03/2014 |
6342 | (2^356468+1162)/2 | 107308 | Stefano Morozzi | 09/2020 |
6343 | 2^356442-114713 | 107300 | Enzo Doria | 04/2015 |
6344 | 2^356425+72257 | 107295 | Enzo Doria | 04/2016 |
6345 | 2^356351-112237 | 107273 | Enzo Doria | 06/2014 |
6347 | (6^137845-11)/5 | 107264 | Paul Bourdelais | 11/2011 |
6346 | 2^356322+74539 | 107264 | Enzo Doria | 04/2016 |
6348 | 2^356274+1874479 | 107250 | Enzo Doria | 06/2016 |
6349 | 24606^22819+22819^24606 | 107241 | Hans Havermann | 10/2020 |
6350 | (2^356243+3686)/2 | 107240 | Stefano Morozzi | 09/2020 |
6351 | 20^82422-93 | 107234 | Lelio R Paula | 02/2017 |
6352 | 2^356157-20365 | 107214 | Enzo Doria | 06/2013 |
6353 | 8*10^107209+99 | 107210 | Robert Price | 03/2021 |
6354 | 2^356129-18949 | 107206 | Enzo Doria | 05/2013 |
6355 | 2^356100-109587 | 107197 | Enzo Doria | 04/2014 |
6356 | 2*10^107173-37 | 107174 | Robert Price | 11/2021 |
6357 | (2^355978+3262)/2 | 107160 | Stefano Morozzi | 02/2021 |
6358 | (31*2^355970+1)/5 | 107159 | Lelio R Paula | 03/2014 |
6359 | 2^355968-64875 | 107158 | Lelio R Paula | 01/2017 |
6360 | 2^355952+1870321 | 107153 | Enzo Doria | 05/2016 |
6361 | 27069^9088+9088^27069 | 107152 | Hans Havermann | 11/2020 |
6362 | 2^355915-117 | 107142 | Lelio R Paula | 11/2011 |
6363 | (16*10^107140+77)/3 | 107141 | Robert Price | 03/2019 |
6364 | 24628^22369+22369^24628 | 107124 | Hans Havermann | 11/2020 |
6365 | (19*2^355838-1)/15 | 107119 | Lelio R Paula | 03/2014 |
6366 | 3^224495-8 | 107112 | Lelio R Paula | 12/2013 |
6367 | 3*10^107096+23 | 107097 | Robert Price | 03/2022 |
6368 | 25077^18632+18632^25077 | 107086 | Hans Havermann | 10/2020 |
6369 | 7^126691-44 | 107067 | Lelio R Paula | 03/2017 |
6370 | 4^177830-8243 | 107065 | Mike Oakes | 02/2011 |
6371 | (509*10^107057+13)/9 | 107059 | Robert Price | 05/2022 |
6372 | 2^355604+214051 | 107048 | Enzo Doria | 10/2023 |
6373 | (2^355562+1702)/2 | 107035 | Stefano Morozzi | 09/2020 |
6374 | 10^107028+3593037 | 107029 | Paul Bourdelais | 10/2021 |
6375 | 2^355524-21237 | 107024 | Enzo Doria | 06/2013 |
6376 | (10223*2^355515+1)/4855 | 107022 | Lelio R Paula | 07/2014 |
6377 | 24843^20320+20320^24843 | 107022 | Hans Havermann | 10/2020 |
6378 | 2^355494-19901 | 107015 | Enzo Doria | 06/2013 |
6379 | 2^355454-869688105 | 107003 | Lelio R Paula | 01/2017 |
6380 | 4*10^106997+13 | 106998 | Robert Price | 02/2021 |
6381 | (8*10^106985-629)/9 | 106985 | Robert Price | 01/2022 |
6382 | 2^355366+54615 | 106976 | Lelio R Paula | 01/2017 |
6383 | (31*2^355346-1)/1563 | 106969 | Lelio R Paula | 03/2014 |
6385 | 2^355275-19861 | 106949 | Enzo Doria | 06/2013 |
6384 | 27503^7738+7738^27503 | 106949 | Hans Havermann | 11/2020 |
6386 | (85*10^106943+77)/9 | 106944 | Robert Price | 07/2022 |
6387 | (9179*2^355234-1)/1915 | 106937 | Lelio R Paula | 05/2015 |
6388 | 4*10^106914-93 | 106915 | Robert Price | 07/2020 |
6389 | 4*10^106892-3 | 106893 | Robert Price | 10/2015 |
6390 | (66^58741+1)/67 | 106881 | Paul Bourdelais | 08/2017 |
6391 | 2^354946-3 | 106850 | M. Frind & P. Underwood | 08/2002 |
6392 | (2^354945+3134)/2 | 106849 | Stefano Morozzi | 09/2020 |
6393 | (46^64384+1)/(46^128+1) | 106843 | Martin Hopf | 12/2023 |
6394 | 2^354873-18693 | 106828 | Enzo Doria | 05/2013 |
6395 | (2^354831+3186)/2 | 106815 | Stefano Morozzi | 09/2020 |
6397 | 2^354828+4257 | 106814 | Lelio R Paula | 01/2017 |
6396 | 25216^17217+17217^25216 | 106814 | Hans Havermann | 10/2020 |
6398 | (2^354799+1218)/2 | 106805 | Stefano Morozzi | 09/2020 |
6399 | 436^40459+40459^436 | 106791 | Norbert Schneider | 03/2019 |
6400 | (21^80761+1)/22 | 106783 | Paul Bourdelais | 03/2010 |
6401 | (115*10^106772-7)/9 | 106774 | Robert Price | 02/2020 |
6402 | 2^354640-354640+1 | 106758 | Robert Price | 10/2014 |
6403 | (2^354603+2606)/2 | 106746 | Stefano Morozzi | 09/2020 |
6404 | 2^354585+95 | 106741 | Lelio R Paula | 10/2011 |
6405 | (206*10^106737+1)/9 | 106739 | Robert Price | 04/2022 |
6406 | 2^354553+189 | 106732 | Lelio R Paula | 10/2011 |
6408 | (2^354546+1338)/2 | 106729 | Stefano Morozzi | 02/2021 |
6407 | (8*10^106729-71)/9 | 106729 | Serge Batalov | 11/2022 |
6409 | 2^354514-109031 | 106720 | Enzo Doria | 04/2014 |
6410 | 2^354509-109465 | 106718 | Enzo Doria | 04/2014 |
6411 | fibonacci(510628)+2 | 106715 | Jon Grantham | 08/2023 |
6412 | (15*2^354478-1)/26983 | 106706 | Lelio R Paula | 03/2014 |
6413 | Phi(217618,10)/899798636917 | 106693 | Makoto Kamada | 06/2019 |
6414 | 15^90710+28 | 106684 | Lelio R Paula | 04/2017 |
6415 | 7^126237+34 | 106683 | Lelio R Paula | 03/2017 |
6416 | 2^354385-115315 | 106681 | Enzo Doria | 06/2015 |
6417 | 2^354327-19305 | 106664 | Enzo Doria | 06/2013 |
6418 | (35*10^106649+1)/9 | 106650 | Serge Batalov | 11/2010 |
6419 | 10^106636+97 | 106637 | Lelio R Paula | 02/2017 |
6420 | 10^106636-22923 | 106636 | Patrick De Geest | 03/2017 |
6421 | 2^354220-57 | 106631 | Lelio R Paula | 10/2011 |
6422 | (68*10^106628-329)/9 | 106629 | Robert Price | 03/2021 |
6423 | (29*10^106620-77)/3 | 106621 | Robert Price | 02/2020 |
6424 | (746*10^106618+1)/9 | 106620 | Robert Price | 03/2020 |
6425 | 2*10^106613+29 | 106614 | Robert Price | 02/2021 |
6426 | 2^354157-17041 | 106612 | Enzo Doria | 05/2013 |
6427 | 12^98778+73 | 106600 | Lelio R Paula | 02/2017 |
6428 | 33333^1576+1576^33333 | 106585 | Hans Havermann | 11/2020 |
6429 | 2^354064+1870651 | 106584 | Enzo Doria | 05/2016 |
6430 | 24568^21779+21779^24568 | 106577 | Hans Havermann | 11/2020 |
6431 | 2^353992-57 | 106563 | Lelio R Paula | 10/2011 |
6432 | 9*10^106559+59 | 106560 | Robert Price | 01/2020 |
6433 | 7*10^106553+27 | 106554 | Robert Price | 11/2020 |
6434 | 28847^4938+4938^28847 | 106548 | Hans Havermann | 10/2020 |
6436 | NSW(139160) | 106535 | Robert Price | 12/2018 |
6435 | f(278321) | 106535 | Robert Price | 07/2023 |
6437 | (7*10^106516+113)/3 | 106517 | Robert Price | 02/2018 |
6438 | 2^353832-1853849 | 106515 | Enzo Doria | 09/2015 |
6439 | (7^126037-1)/6 | 106513 | Paul Bourdelais | 09/2008 |
6440 | 2^353794-18453 | 106503 | Enzo Doria | 05/2013 |
6441 | (2^353761+2094)/2 | 106493 | Stefano Morozzi | 09/2020 |
6442 | 2^353728+7695 | 106483 | Lelio R Paula | 01/2017 |
6443 | 26476^10509+10509^26476 | 106475 | Hans Havermann | 10/2020 |
6444 | 2^353672-303 | 106466 | Yves Minet | 02/2012 |
6445 | 6^136811+101 | 106460 | Lelio R Paula | 02/2017 |
6446 | 2^353641+1871981 | 106457 | Enzo Doria | 05/2016 |
6447 | (8*10^106454-29)/3 | 106455 | Robert Price | 07/2018 |
6448 | 27845^6654+6654^27845 | 106454 | Hans Havermann | 11/2020 |
6449 | 10^106449-700001 | 106449 | Robert Price | 08/2021 |
6450 | 25316^16017+16017^25316 | 106444 | Hans Havermann | 11/2020 |
6451 | 2^353553+54615 | 106431 | Lelio R Paula | 01/2017 |
6452 | 2^353544-18897 | 106428 | Enzo Doria | 05/2013 |
6453 | 28894^4823+4823^28894 | 106426 | Hans Havermann | 11/2020 |
6454 | (19*10^106422+29)/3 | 106423 | Robert Price | 12/2021 |
6455 | (694*10^106418+53)/9 | 106420 | Robert Price | 02/2022 |
6456 | 6*10^106412-13 | 106413 | Robert Price | 07/2022 |
6457 | 25696^13829+13829^25696 | 106402 | Hans Havermann | 11/2020 |
6458 | 6^136729-133 | 106396 | Lelio R Paula | 02/2017 |
6459 | 2^353418+1605 | 106390 | Lelio R Paula | 01/2017 |
6460 | 2^353387+65 | 106381 | Lelio R Paula | 10/2011 |
6461 | 2^353372+74311 | 106376 | Enzo Doria | 04/2016 |
6462 | 2^353344-3693 | 106368 | Yves Minet | 03/2017 |
6463 | (772*10^106365-7)/9 | 106367 | Robert Price | 06/2022 |
6464 | (56*10^106351+619)/9 | 106352 | Robert Price | 05/2021 |
6466 | 2^353277-20089 | 106347 | Enzo Doria | 06/2013 |
6465 | 2^353275+72173 | 106347 | Enzo Doria | 04/2016 |
6467 | 2^353268-17705 | 106345 | Enzo Doria | 05/2013 |
6468 | 2^353267-19857 | 106344 | Enzo Doria | 06/2013 |
6469 | (46*10^106343+143)/9 | 106344 | Robert Price | 01/2019 |
6471 | (2^353189+3054)/2 | 106321 | Stefano Morozzi | 09/2020 |
6470 | 35087^1072+1072^35087 | 106321 | Hans Havermann | 10/2020 |
6472 | (2^353184+1290)/2 | 106319 | Stefano Morozzi | 01/2021 |
6473 | 26985^8684+8684^26985 | 106287 | Hans Havermann | 10/2020 |
6474 | (2^353051+606)/2 | 106279 | Stefano Morozzi | 09/2020 |
6476 | 222748^3+3^222748 | 106278 | Anatoly F. Selevich | 12/2010 |
6475 | (46*10^106277+107)/9 | 106278 | Robert Price | 06/2022 |
6477 | (9179*2^353019-1)/9 | 106273 | Lelio R Paula | 05/2015 |
6478 | 2^353025+72257 | 106272 | Enzo Doria | 04/2016 |
6481 | 2^352932-20345 | 106244 | Enzo Doria | 06/2013 |
6479 | (2^353011-3)/745325861246794515484535 | 106244 | Lelio R Paula | 12/2013 |
6480 | 25628^13983+13983^25628 | 106244 | Hans Havermann | 10/2020 |
6482 | 2^352883-187 | 106229 | Lelio R Paula | 10/2011 |
6483 | 20^81649-19^81649 | 106228 | Jean-Louis Charton | 03/2011 |
6484 | (55*10^106222+377)/9 | 106223 | Robert Price | 02/2019 |
6485 | 2^352814-131 | 106208 | Lelio R Paula | 10/2011 |
6486 | 2^352752+73951 | 106189 | Enzo Doria | 04/2016 |
6487 | 11876*25^75945+357 | 106171 | Eric Chen | 10/2023 |
6488 | 6^136434+5 | 106167 | Lelio R Paula | 11/2014 |
6489 | 25296^15737+15737^25296 | 106166 | Hans Havermann | 09/2020 |
6490 | 8*10^106157-13 | 106158 | Robert Price | 08/2019 |
6491 | 7*5^151872-8 | 106155 | Lelio R Paula | 11/2014 |
6492 | 105^52520-2 | 106153 | Lelio R Paula | 10/2017 |
6493 | (23*10^106152-29)/3 | 106153 | Robert Price | 03/2022 |
6494 | 2^352601-1604809 | 106144 | Enzo Doria | 05/2015 |
6495 | 12^98353-43 | 106141 | Lelio R Paula | 02/2017 |
6496 | 2^352585-18901 | 106139 | Enzo Doria | 05/2013 |
6497 | 26363^10614+10614^26363 | 106135 | Hans Havermann | 09/2020 |
6498 | (2^352554-3)/193 | 106128 | Lelio R Paula | 12/2013 |
6499 | 2^352540+15015 | 106126 | Lelio R Paula | 01/2017 |
6500 | 25068^17119+17119^25068 | 106125 | Hans Havermann | 09/2020 |