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 ? |
5251 | 2^361497+767 | 108822 | Lelio R Paula | 01/2012 |
5252 | 28019^7630+7630^28019 | 108785 | Hans Havermann | 10/2020 |
5253 | 24723^24758-24758^24723 | 108765 | Norbert Schneider | 11/2020 |
5254 | 2^361280-112349 | 108757 | Enzo Doria | 06/2014 |
5255 | 2^361271-5955 | 108754 | Lelio R Paula | 04/2017 |
5256 | 12^100757+19 | 108736 | Lelio R Paula | 03/2017 |
5257 | 25368^19333+19333^25368 | 108735 | Hans Havermann | 11/2020 |
5258 | (2^361195+3618)/2 | 108731 | Stefano Morozzi | 09/2020 |
5259 | 2^361153-111546435 | 108718 | Paul Bourdelais | 10/2021 |
5260 | 14^94849-61 | 108710 | Lelio R Paula | 05/2017 |
5261 | 27267^9700+9700^27267 | 108708 | Hans Havermann | 11/2020 |
5262 | (19^85009-5^85009)/14 | 108705 | Robert Price | 07/2013 |
5263 | 24832^23853+23853^24832 | 108704 | Hans Havermann | 11/2020 |
5264 | 27502^8963+8963^27502 | 108701 | Hans Havermann | 11/2020 |
5265 | 25807^16278+16278^25807 | 108689 | Hans Havermann | 11/2020 |
5266 | (11*2^361027+1)/40463 | 108677 | Lelio R Paula | 03/2014 |
5267 | 2^360973+1299 | 108664 | Lelio R Paula | 04/2017 |
5268 | 2^360959-109101 | 108660 | Enzo Doria | 04/2014 |
5269 | 6*5^155454+7 | 108659 | Lelio R Paula | 11/2014 |
5270 | 10^108656+79 | 108657 | Lelio R Paula | 02/2017 |
5271 | 10^108656-50001 | 108656 | Patrick De Geest | 03/2017 |
5272 | 2^360918-35 | 108648 | Lelio R Paula | 01/2012 |
5273 | 4*10^108646-47 | 108647 | Robert Price | 10/2021 |
5274 | (11*2^360886-1)/7 | 108638 | Lelio R Paula | 03/2014 |
5275 | 3*10^108624-49 | 108625 | Robert Price | 07/2018 |
5276 | (2^360831+666)/2 | 108621 | Stefano Morozzi | 09/2020 |
5277 | (134*10^108610+7)/3 | 108612 | Robert Price | 02/2020 |
5278 | 2*10^108609+29 | 108610 | Robert Price | 02/2021 |
5279 | (10^108604+7)/71/191 | 108600 | Alfred Reich | 06/2021 |
5280 | (2^360742+3222)/2 | 108594 | Stefano Morozzi | 09/2020 |
5281 | 2^360706-458903 | 108584 | Enzo Doria | 04/2015 |
5282 | 31112^3087+3087^31112 | 108567 | Hans Havermann | 11/2020 |
5283 | 2^360641-113185 | 108564 | Enzo Doria | 07/2014 |
5284 | (29*10^108559-71)/3 | 108560 | Robert Price | 07/2021 |
5285 | 2^360618+75019 | 108557 | Enzo Doria | 04/2016 |
5286 | 2^360607-216367 | 108554 | Harrison Mesh | 06/2022 |
5287 | (14*10^108545-221)/9 | 108546 | Robert Price | 04/2018 |
5288 | (44*10^108544-233)/9 | 108545 | Robert Price | 01/2019 |
5289 | 3*5^155286+2 | 108541 | Lelio R Paula | 11/2014 |
5290 | 7^128422+4 | 108530 | Lelio R Paula | 11/2014 |
5291 | 7^128421-80 | 108529 | Lelio R Paula | 03/2017 |
5292 | 2^360497+53807 | 108521 | Yves Minet | 07/2010 |
5293 | 2^360468-4559 | 108512 | Yves Minet | 03/2019 |
5294 | (2^360451+578)/2 | 108507 | Stefano Morozzi | 09/2020 |
5295 | 2^360366+1459 | 108481 | Lelio R Paula | 09/2011 |
5296 | 2^360364-1499 | 108481 | Yves Minet | 05/2013 |
5297 | 25662^16871+16871^25662 | 108477 | Hans Havermann | 10/2020 |
5298 | 25009^21748+21748^25009 | 108475 | Hans Havermann | 10/2020 |
5299 | 14^94642-23 | 108472 | Lelio R Paula | 05/2017 |
5300 | (197*10^108446-11)/3 | 108448 | Robert Price | 03/2020 |
5301 | (2^360229+1290)/2 | 108440 | Stefano Morozzi | 01/2021 |
5302 | 4*10^108412+9 | 108413 | Robert Price | 05/2015 |
5303 | (259*10^108409-1)/3 | 108411 | Robert Price | 12/2020 |
5304 | (2^360122+1194)/2 | 108408 | Stefano Morozzi | 09/2020 |
5305 | 133^51042-132 | 108406 | Norbert Schneider | 02/2019 |
5306 | 2^360093-351103 | 108399 | Enzo Doria | 06/2015 |
5307 | 2^360042+723 | 108384 | Lelio R Paula | 01/2012 |
5308 | 85^56164-2 | 108364 | Lelio R Paula | 10/2013 |
5309 | 2^359937-29323 | 108352 | Enzo Doria | 07/2015 |
5310 | (2^359922+1762)/2 | 108348 | Stefano Morozzi | 09/2020 |
5311 | (2^359903+758)/2 | 108342 | Stefano Morozzi | 09/2020 |
5312 | 2^359898-19997 | 108341 | Enzo Doria | 06/2013 |
5313 | (2^359886+2122)/2 | 108337 | Stefano Morozzi | 09/2020 |
5314 | 2*5^154948-7 | 108305 | Lelio R Paula | 11/2014 |
5315 | 10^108303+13 | 108304 | Lelio R Paula | 02/2017 |
5316 | 10^108303-207959 | 108303 | Patrick De Geest | 03/2017 |
5317 | 7*10^108300+69 | 108301 | Robert Price | 07/2019 |
5318 | 2^359730+753 | 108290 | Lelio R Paula | 12/2011 |
5319 | (8*10^108273+13)/3 | 108274 | Robert Price | 06/2018 |
5320 | 2^359650-19797 | 108266 | Enzo Doria | 06/2013 |
5321 | (47*10^108261+259)/9 | 108262 | Robert Price | 03/2022 |
5322 | 91^55259-90^55259 | 108255 | Robert Price | 07/2015 |
5323 | 10^108251+85749 | 108252 | Patrick De Geest | 02/2021 |
5324 | 10^108251-50000000001 | 108251 | Robert Price | 12/2020 |
5325 | 10^108251-252081 | 108251 | Patrick De Geest | 02/2021 |
5326 | 4*10^108238-71 | 108239 | Robert Price | 12/2018 |
5327 | 3^226845+68 | 108233 | Lelio R Paula | 03/2017 |
5328 | 31836^2509+2509^31836 | 108227 | Hans Havermann | 10/2020 |
5329 | 5^154822-12866 | 108216 | Enzo Doria | 05/2014 |
5330 | (9*2^359480+1)/5 | 108215 | Lelio R Paula | 03/2014 |
5331 | 2^359454-177 | 108207 | Lelio R Paula | 12/2011 |
5332 | (19*10^108184+191)/3 | 108185 | Robert Price | 05/2019 |
5333 | 6^139022-59 | 108181 | Lelio R Paula | 02/2017 |
5334 | (19*10^108176-43)/3 | 108177 | Robert Price | 05/2019 |
5335 | 2^359352-179 | 108176 | Lelio R Paula | 12/2011 |
5336 | 2^359338-1858781 | 108172 | Enzo Doria | 04/2016 |
5337 | 12^100230-97 | 108167 | Lelio R Paula | 03/2017 |
5338 | 27028^10043+10043^27028 | 108163 | Hans Havermann | 11/2020 |
5339 | (25*2^359297-1)/137 | 108159 | Lelio R Paula | 03/2014 |
5340 | (2^359262-509203)/9 | 108148 | Lelio R Paula | 12/2013 |
5341 | 26583^11702+11702^26583 | 108147 | Hans Havermann | 11/2020 |
5342 | (3^226648-8)/352715633 | 108131 | Lelio R Paula | 12/2013 |
5343 | 6^138956-59 | 108129 | Lelio R Paula | 02/2017 |
5344 | 2^359184+30285 | 108126 | Lelio R Paula | 04/2017 |
5345 | 13^97059+10 | 108119 | Lelio R Paula | 03/2017 |
5346 | 2^359137-81 | 108112 | Lelio R Paula | 12/2011 |
5348 | (15185*2^359105-1)/567 | 108103 | Lelio R Paula | 05/2015 |
5347 | 2^359110-11655 | 108103 | Lelio R Paula | 04/2017 |
5349 | 2^359069-933075 | 108091 | Paul Bourdelais | 06/2021 |
5350 | 26227^13222+13222^26227 | 108090 | Hans Havermann | 10/2020 |
5351 | 8*6^138875+5 | 108067 | Lelio R Paula | 11/2014 |
5352 | 2^358987-216919 | 108066 | Enzo Doria | 05/2014 |
5353 | (2^358977+2714)/2 | 108063 | Stefano Morozzi | 09/2020 |
5354 | 39^67918-67918^39 | 108062 | Norbert Schneider | 02/2017 |
5355 | 24^78283-1*78283^24 | 108048 | Dylan Delgado | 12/2019 |
5356 | 25282^18767+18767^25282 | 108040 | Hans Havermann | 11/2020 |
5357 | 2^358785-16933 | 108006 | Enzo Doria | 05/2013 |
5358 | (2^358783+5)/33383 | 108000 | Lelio R Paula | 12/2013 |
5359 | 6^138770-77 | 107985 | Lelio R Paula | 02/2017 |
5360 | (2^358727-1017)/94178479 | 107980 | Lelio R Paula | 12/2013 |
5361 | 10^107976+19 | 107977 | Lelio R Paula | 02/2017 |
5362 | 10^107976-202103 | 107976 | Patrick De Geest | 03/2017 |
5363 | 2^358684+75781 | 107975 | Enzo Doria | 04/2016 |
5364 | 24928^21411+21411^24928 | 107955 | Hans Havermann | 10/2020 |
5365 | 99^54094+2 | 107952 | Lelio R Paula | 06/2013 |
5366 | (2^358583-9)/391 | 107942 | Lelio R Paula | 12/2013 |
5367 | (2^358562+838)/2 | 107938 | Stefano Morozzi | 02/2021 |
5368 | 2^358538+55 | 107931 | Lelio R Paula | 12/2011 |
5369 | 2^358517-109009 | 107925 | Enzo Doria | 03/2014 |
5370 | 26395^12258+12258^26395 | 107914 | Hans Havermann | 10/2020 |
5371 | 3^226159+104 | 107906 | Lelio R Paula | 03/2017 |
5372 | 7*10^107870+39 | 107871 | Robert Price | 01/2023 |
5373 | 2^358310-11655 | 107863 | Lelio R Paula | 03/2017 |
5374 | (68*10^107852-329)/9 | 107853 | Robert Price | 03/2021 |
5375 | 2^358275-112987 | 107852 | Enzo Doria | 07/2014 |
5376 | 3^226038+4 | 107848 | Tyler NeSmith | 01/2021 |
5377 | 2^358233-20005 | 107839 | Enzo Doria | 06/2013 |
5378 | 2^358194+175 | 107828 | Lelio R Paula | 12/2011 |
5379 | 107^53125-106 | 107812 | Norbert Schneider | 12/2016 |
5380 | (25*10^107804+161)/3 | 107805 | Robert Price | 09/2019 |
5381 | 3^225922-2 | 107793 | Lelio R Paula | 10/2013 |
5382 | 12^99874-95 | 107783 | Lelio R Paula | 03/2017 |
5383 | (2^358042+3042)/2 | 107782 | Stefano Morozzi | 09/2020 |
5384 | 2^358030-171 | 107778 | Lelio R Paula | 12/2011 |
5385 | 11^103488-4170 | 107772 | Enzo Doria | 12/2012 |
5386 | 2^357930-4547 | 107748 | Yves Minet | 03/2019 |
5387 | 2^357911-20089 | 107742 | Enzo Doria | 06/2013 |
5388 | 2^357885+12857 | 107735 | Yves Minet | 07/2010 |
5389 | (248587#+9289)/(7*1327*111512899) | 107733 | Makoto Morimoto | 06/2019 |
5390 | 7^127473+40 | 107728 | Lelio R Paula | 03/2017 |
5391 | 5*2^357850+9 | 107725 | Lelio R Paula | 09/2014 |
5392 | 2^357786-291191 | 107705 | Enzo Doria | 06/2015 |
5393 | 28907^5320+5320^28907 | 107705 | Hans Havermann | 10/2020 |
5394 | 18^85798-23 | 107700 | Lelio R Paula | 04/2017 |
5395 | 3*10^107697+61 | 107698 | Robert Price | 09/2020 |
5396 | (14*10^107694-83)/3 | 107695 | Robert Price | 12/2018 |
5397 | 2^357688-1854269 | 107675 | Enzo Doria | 09/2015 |
5398 | 2^357671-112225 | 107670 | Enzo Doria | 06/2014 |
5399 | 34323^1370+1370^34323 | 107662 | Hans Havermann | 11/2020 |
5400 | 2^357618-21005 | 107654 | Enzo Doria | 06/2013 |
5401 | 2^357615-17505 | 107653 | Enzo Doria | 05/2013 |
5402 | 26350^12171+12171^26350 | 107649 | Hans Havermann | 11/2020 |
5403 | (30^72871-1)/29 | 107638 | Robert Price | 12/2011 |
5404 | 25021^20026+20026^25021 | 107631 | Hans Havermann | 11/2020 |
5405 | 2^357521+1870217 | 107625 | Enzo Doria | 05/2016 |
5406 | 2^357477-1203 | 107612 | Lelio R Paula | 03/2017 |
5407 | 26008^13693+13693^26008 | 107583 | Hans Havermann | 10/2020 |
5408 | 25432^16991+16991^25432 | 107583 | Hans Havermann | 10/2020 |
5409 | (2^357371+3726)/2 | 107580 | Stefano Morozzi | 09/2020 |
5410 | 5^153894-18 | 107568 | Lelio R Paula | 02/2017 |
5411 | 2^357324-69059 | 107566 | Enzo Doria | 11/2015 |
5412 | 467^40296+40296^467 | 107563 | Norbert Schneider | 03/2019 |
5413 | 29446^4495+4495^29446 | 107559 | Hans Havermann | 10/2020 |
5414 | (8*10^107556-149)/3 | 107557 | Robert Price | 12/2021 |
5415 | 2^357283-869688105 | 107553 | Lelio R Paula | 01/2017 |
5416 | 2^357280-16805 | 107552 | Enzo Doria | 05/2013 |
5417 | 10^107547+481719 | 107548 | Patrick De Geest | 03/2017 |
5418 | 10^107547-47 | 107547 | Lelio R Paula | 02/2017 |
5419 | (23*10^107540+37)/3 | 107541 | Robert Price | 02/2022 |
5420 | 17^87396-32 | 107537 | Lelio R Paula | 04/2017 |
5421 | (746*10^107505+1)/9 | 107507 | Robert Price | 03/2020 |
5422 | (2^357125+1730)/2 | 107506 | Stefano Morozzi | 09/2020 |
5423 | 2^357081+107 | 107493 | Lelio R Paula | 12/2011 |
5424 | 2^357058-3911 | 107486 | Yves Minet | 04/2017 |
5425 | 3^225274+64 | 107484 | Lelio R Paula | 03/2017 |
5426 | 5*10^107482-57 | 107483 | Robert Price | 03/2021 |
5427 | 18^85619-95 | 107476 | Lelio R Paula | 04/2017 |
5428 | (2^357013+2526)/2 | 107472 | Stefano Morozzi | 09/2020 |
5429 | 3^225248-130 | 107471 | Lelio R Paula | 03/2017 |
5430 | (5*2^356961+1)/143 | 107455 | Lelio R Paula | 03/2014 |
5431 | 27029^9448+9448^27029 | 107450 | Hans Havermann | 11/2020 |
5432 | 2^356935-18085 | 107449 | Enzo Doria | 05/2013 |
5433 | 55396^87+87^55396 | 107442 | Hans Havermann | 10/2020 |
5434 | (14*10^107439-137)/3 | 107440 | Robert Price | 04/2021 |
5435 | 10^107409+37 | 107410 | Lelio R Paula | 02/2017 |
5436 | 10^107409-329633 | 107409 | Patrick De Geest | 03/2017 |
5437 | (2^356799+3134)/2 | 107407 | Stefano Morozzi | 09/2020 |
5438 | 2^356787-109027 | 107404 | Enzo Doria | 04/2014 |
5439 | (2^356767+78557)/5 | 107397 | Lelio R Paula | 12/2013 |
5440 | 3*10^107389+77 | 107390 | Robert Price | 09/2018 |
5441 | (11*10^107385+61)/9 | 107386 | Tyler Busby | 01/2023 |
5442 | 5^153622-42 | 107378 | Lelio R Paula | 02/2017 |
5443 | 2^356699-97305 | 107378 | Lelio R Paula | 03/2017 |
5444 | 13129^26072-26072^13129 | 107371 | Norbert Schneider | 09/2022 |
5445 | 2^356654+85 | 107364 | Lelio R Paula | 11/2011 |
5446 | 2^356641-19921 | 107360 | Enzo Doria | 06/2013 |
5447 | 5*10^107355+11 | 107356 | Robert Price | 08/2019 |
5448 | 2^356623-465 | 107355 | Lelio R Paula | 03/2017 |
5449 | 19^83945-92 | 107345 | Lelio R Paula | 02/2017 |
5450 | 25491^16246+16246^25491 | 107337 | Hans Havermann | 11/2020 |
5451 | 10^107334+28149 | 107335 | Patrick De Geest | 03/2017 |
5452 | 10^107334-83 | 107334 | Lelio R Paula | 02/2017 |
5453 | 2^356518+885 | 107323 | Lelio R Paula | 03/2017 |
5454 | (59*10^107322+391)/9 | 107323 | Robert Price | 03/2021 |
5455 | (3*2^356506-1)/467 | 107317 | Lelio R Paula | 03/2014 |
5456 | (2^356468+1162)/2 | 107308 | Stefano Morozzi | 09/2020 |
5457 | 2^356442-114713 | 107300 | Enzo Doria | 04/2015 |
5458 | 2^356425+72257 | 107295 | Enzo Doria | 04/2016 |
5459 | 2^356351-112237 | 107273 | Enzo Doria | 06/2014 |
5461 | (6^137845-11)/5 | 107264 | Paul Bourdelais | 11/2011 |
5460 | 2^356322+74539 | 107264 | Enzo Doria | 04/2016 |
5462 | 2^356274+1874479 | 107250 | Enzo Doria | 06/2016 |
5463 | 24606^22819+22819^24606 | 107241 | Hans Havermann | 10/2020 |
5464 | (2^356243+3686)/2 | 107240 | Stefano Morozzi | 09/2020 |
5465 | 20^82422-93 | 107234 | Lelio R Paula | 02/2017 |
5466 | 2^356157-20365 | 107214 | Enzo Doria | 06/2013 |
5467 | 8*10^107209+99 | 107210 | Robert Price | 03/2021 |
5468 | 2^356129-18949 | 107206 | Enzo Doria | 05/2013 |
5469 | 2^356100-109587 | 107197 | Enzo Doria | 04/2014 |
5470 | 2*10^107173-37 | 107174 | Robert Price | 11/2021 |
5471 | (2^355978+3262)/2 | 107160 | Stefano Morozzi | 02/2021 |
5472 | (31*2^355970+1)/5 | 107159 | Lelio R Paula | 03/2014 |
5473 | 2^355968-64875 | 107158 | Lelio R Paula | 01/2017 |
5474 | 2^355952+1870321 | 107153 | Enzo Doria | 05/2016 |
5475 | 27069^9088+9088^27069 | 107152 | Hans Havermann | 11/2020 |
5476 | 2^355915-117 | 107142 | Lelio R Paula | 11/2011 |
5477 | (16*10^107140+77)/3 | 107141 | Robert Price | 03/2019 |
5478 | 24628^22369+22369^24628 | 107124 | Hans Havermann | 11/2020 |
5479 | (19*2^355838-1)/15 | 107119 | Lelio R Paula | 03/2014 |
5480 | 3^224495-8 | 107112 | Lelio R Paula | 12/2013 |
5481 | 3*10^107096+23 | 107097 | Robert Price | 03/2022 |
5482 | 25077^18632+18632^25077 | 107086 | Hans Havermann | 10/2020 |
5483 | 7^126691-44 | 107067 | Lelio R Paula | 03/2017 |
5484 | 4^177830-8243 | 107065 | Mike Oakes | 02/2011 |
5485 | (509*10^107057+13)/9 | 107059 | Robert Price | 05/2022 |
5486 | (2^355562+1702)/2 | 107035 | Stefano Morozzi | 09/2020 |
5487 | 10^107028+3593037 | 107029 | Paul Bourdelais | 10/2021 |
5488 | 2^355524-21237 | 107024 | Enzo Doria | 06/2013 |
5489 | (10223*2^355515+1)/4855 | 107022 | Lelio R Paula | 07/2014 |
5490 | 24843^20320+20320^24843 | 107022 | Hans Havermann | 10/2020 |
5491 | 2^355494-19901 | 107015 | Enzo Doria | 06/2013 |
5492 | 2^355454-869688105 | 107003 | Lelio R Paula | 01/2017 |
5493 | 4*10^106997+13 | 106998 | Robert Price | 02/2021 |
5494 | (8*10^106985-629)/9 | 106985 | Robert Price | 01/2022 |
5495 | 2^355366+54615 | 106976 | Lelio R Paula | 01/2017 |
5496 | (31*2^355346-1)/1563 | 106969 | Lelio R Paula | 03/2014 |
5498 | 2^355275-19861 | 106949 | Enzo Doria | 06/2013 |
5497 | 27503^7738+7738^27503 | 106949 | Hans Havermann | 11/2020 |
5499 | (85*10^106943+77)/9 | 106944 | Robert Price | 07/2022 |
5500 | (9179*2^355234-1)/1915 | 106937 | Lelio R Paula | 05/2015 |