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 | (2^335562+1258)/2 | 101014 | Stefano Morozzi | 09/2020 |
5252 | (19*10^100997+737)/9 | 100998 | Robert Price | 07/2018 |
5253 | 47599!2+1024 | 100991 | Robert Price | 02/2015 |
5254 | 2^335468-18629 | 100986 | Enzo Doria | 05/2013 |
5255 | 2^335454-20961 | 100982 | Enzo Doria | 06/2013 |
5256 | (2^335454+3258)/2 | 100982 | Stefano Morozzi | 02/2021 |
5257 | 10^100978+61 | 100979 | Lelio R Paula | 09/2016 |
5258 | 10^100978-156437 | 100978 | Patrick De Geest | 11/2016 |
5259 | (2^335422+3114)/2 | 100972 | Stefano Morozzi | 09/2020 |
5260 | (15*2^335417+1)/481 | 100970 | Lelio R Paula | 12/2013 |
5261 | 2^335403-1859167 | 100967 | Enzo Doria | 03/2016 |
5262 | 23599^18976+18976^23599 | 100962 | Hans Havermann | 10/2018 |
5263 | 6*10^100958+43 | 100959 | Robert Price | 07/2020 |
5264 | 9*2^335364-5 | 100956 | Lelio R Paula | 08/2014 |
5265 | 2^335349+72287 | 100951 | Enzo Doria | 04/2016 |
5266 | 2^335329+16095 | 100945 | Lelio R Paula | 09/2016 |
5267 | 232823#+233663 | 100937 | Makoto Morimoto | 10/2017 |
5268 | (232823#+10141)/(10141*1674461) | 100927 | Makoto Morimoto | 06/2019 |
5269 | 2^335237-20893 | 100917 | Enzo Doria | 06/2013 |
5270 | 2^335222-19337 | 100912 | Enzo Doria | 05/2013 |
5271 | 2^335222-109985 | 100912 | Enzo Doria | 04/2014 |
5272 | 2^335182-17237 | 100900 | Enzo Doria | 05/2013 |
5273 | (2^335107+1634)/2 | 100877 | Stefano Morozzi | 09/2020 |
5275 | 2^335043-16737 | 100858 | Enzo Doria | 05/2013 |
5274 | (21181*2^335049+1)/1343811 | 100858 | Lelio R Paula | 07/2014 |
5276 | 2^335038-20633 | 100857 | Enzo Doria | 06/2013 |
5277 | 2^335031+1873373 | 100855 | Enzo Doria | 06/2016 |
5278 | 23489^19650+19650^23489 | 100847 | Hans Havermann | 10/2018 |
5279 | 3^211354-8816 | 100842 | Enzo Doria | 05/2014 |
5280 | 2^334984-112757 | 100841 | Enzo Doria | 06/2014 |
5281 | (746*10^100827+1)/9 | 100829 | Robert Price | 03/2020 |
5282 | 29451^2648+2648^29451 | 100809 | Hans Havermann | 09/2018 |
5283 | 25583^8716+8716^25583 | 100806 | Hans Havermann | 08/2018 |
5285 | 2^334857+48527 | 100803 | Lelio R Paula | 08/2011 |
5284 | 12^93406+29 | 100803 | Lelio R Paula | 10/2016 |
5286 | 28780^3179+3179^28780 | 100796 | Hans Havermann | 09/2018 |
5287 | (5*2^334825+1)/47 | 100792 | Lelio R Paula | 12/2013 |
5288 | 2^334809-13 | 100788 | Lelio R Paula | 04/2011 |
5289 | (82*10^100780-1)/9 | 100781 | Robert Price | 12/2014 |
5290 | 31395^1622+1622^31395 | 100780 | Hans Havermann | 09/2018 |
5291 | (2^334779+47)/5 | 100778 | Lelio R Paula | 12/2013 |
5292 | 2^334751+2049 | 100771 | Lelio R Paula | 09/2016 |
5293 | 13^90443-98 | 100749 | Lelio R Paula | 10/2016 |
5294 | (2^334674+3190)/2 | 100747 | Stefano Morozzi | 09/2020 |
5295 | (2^334651+1050)/2 | 100740 | Stefano Morozzi | 09/2020 |
5296 | (7*10^100737+71)/3 | 100738 | Robert Price | 05/2018 |
5297 | (24737*2^334628+1)/3 | 100737 | Lelio R Paula | 07/2014 |
5298 | 15^85639-28 | 100720 | Lelio R Paula | 10/2016 |
5299 | 27068^5259+5259^27068 | 100718 | Hans Havermann | 08/2018 |
5300 | 2^334562+577294575 | 100711 | Lelio R Paula | 09/2016 |
5301 | 4*3^211077-5 | 100710 | Lelio R Paula | 08/2014 |
5302 | 2^334524+145 | 100702 | Lelio R Paula | 07/2009 |
5303 | (2^334451+714)/2 | 100680 | Stefano Morozzi | 09/2020 |
5304 | 27648^4375+4375^27648 | 100666 | Hans Havermann | 09/2018 |
5305 | (1017*2^334391-1)/3535 | 100662 | Lelio R Paula | 05/2015 |
5306 | (2^334309+3122)/2 | 100637 | Stefano Morozzi | 09/2020 |
5307 | 2^334294-113111 | 100633 | Enzo Doria | 07/2014 |
5308 | 25581^8582+8582^25581 | 100626 | Hans Havermann | 08/2018 |
5309 | 6^129308-17723 | 100622 | Enzo Doria | 03/2013 |
5310 | 6^129305+95 | 100619 | Lelio R Paula | 10/2016 |
5311 | 2^334244-1167 | 100618 | Lelio R Paula | 09/2016 |
5312 | (2^334233+3066)/2 | 100614 | Stefano Morozzi | 09/2020 |
5313 | (76*10^100611+77)/9 | 100612 | Robert Price | 10/2019 |
5314 | 7*10^100606-93 | 100607 | Robert Price | 08/2020 |
5315 | (26*10^100566+49)/3 | 100567 | Robert Price | 08/2019 |
5316 | (21*2^334050+1)/935 | 100558 | Lelio R Paula | 12/2013 |
5317 | 24885^10984+10984^24885 | 100555 | Hans Havermann | 07/2018 |
5318 | (78557*2^334018+1)/4326021 | 100548 | Lelio R Paula | 07/2014 |
5319 | (35*10^100542+1)/9 | 100543 | Serge Batalov | 11/2010 |
5320 | 23578^18367+18367^23578 | 100538 | Hans Havermann | 07/2018 |
5321 | 13^90251+24 | 100535 | Lelio R Paula | 10/2016 |
5322 | 2^333963+789 | 100533 | Lelio R Paula | 08/2011 |
5323 | 2^333919-1840087 | 100520 | Enzo Doria | 06/2015 |
5324 | (2^333916+1698)/2 | 100519 | Stefano Morozzi | 09/2020 |
5325 | 2^333911+72623 | 100518 | Enzo Doria | 04/2016 |
5326 | 24605^12168+12168^24605 | 100517 | Hans Havermann | 08/2018 |
5327 | 66*10^100502+7 | 100504 | Robert Price | 07/2020 |
5328 | 18^80064-67 | 100503 | Lelio R Paula | 10/2016 |
5329 | 5^143742-48 | 100472 | Lelio R Paula | 10/2016 |
5330 | 24095^14784+14784^24095 | 100472 | Hans Havermann | 08/2018 |
5331 | 2^333757-112123 | 100471 | Enzo Doria | 06/2014 |
5332 | 7*10^100457-57 | 100458 | Robert Price | 06/2020 |
5333 | 27358^4693+4693^27358 | 100444 | Hans Havermann | 07/2018 |
5334 | 8*10^100439-51 | 100440 | Robert Price | 08/2019 |
5335 | 2^333603-108861 | 100425 | Enzo Doria | 03/2014 |
5336 | 9*7^118818-2 | 100414 | Lelio R Paula | 11/2014 |
5337 | 2^333546-17097 | 100408 | Enzo Doria | 05/2013 |
5338 | 17^81597+72 | 100401 | Lelio R Paula | 10/2016 |
5339 | p(20559)#/2+8 | 100384 | Robert Price | 01/2017 |
5340 | 11^96390-24 | 100380 | Lelio R Paula | 10/2016 |
5341 | (2^333385+2730)/2 | 100359 | Stefano Morozzi | 09/2020 |
5343 | 4832563059*2^333333+30029 | 100353 | Donovan Johnson | 01/2008 |
5342 | 23565^18136+18136^23565 | 100353 | Hans Havermann | 07/2018 |
5344 | 2^333354+763 | 100350 | Lelio R Paula | 08/2011 |
5345 | (25*10^100343-67)/3 | 100344 | Robert Price | 06/2019 |
5346 | 2^333289-109483 | 100330 | Enzo Doria | 04/2014 |
5347 | 2^333240-2790209 | 100316 | Enzo Doria | 03/2016 |
5348 | 23601^17798+17798^23601 | 100314 | Hans Havermann | 05/2018 |
5350 | (2^333227-2^166614+1)/5 | 100311 | | 11/2006 |
5349 | 2^333225+719 | 100311 | Lelio R Paula | 08/2011 |
5351 | 2^333221-2785333 | 100310 | Enzo Doria | 10/2015 |
5352 | 76^53332-75 | 100308 | Norbert Schneider | 02/2015 |
5353 | 6^128892-17573 | 100298 | Enzo Doria | 03/2013 |
5354 | (47*10^100283-119)/9 | 100284 | Robert Price | 05/2019 |
5355 | 2^333105-113215 | 100275 | Enzo Doria | 07/2014 |
5356 | (31*2^333102+1)/2375 | 100272 | Lelio R Paula | 11/2013 |
5357 | 4*10^100257-83 | 100258 | Robert Price | 10/2018 |
5358 | 17^81476-74 | 100253 | Lelio R Paula | 10/2016 |
5359 | 23392^19207+19207^23392 | 100199 | Hans Havermann | 06/2018 |
5360 | (2^332830+750)/2 | 100192 | Stefano Morozzi | 09/2020 |
5361 | (206*10^100189-17)/9 | 100191 | Robert Price | 01/2020 |
5362 | 17^81417-16 | 100180 | Theodore Burton | 11/2005 |
5363 | (2^332773+590)/2 | 100175 | Stefano Morozzi | 09/2020 |
5364 | 2^332739-113215 | 100165 | Enzo Doria | 07/2014 |
5365 | 2^332730-1865621 | 100162 | Enzo Doria | 03/2016 |
5366 | 91^51127-2 | 100160 | Lelio R Paula | 09/2013 |
5367 | 15^85159-32 | 100155 | Lelio R Paula | 10/2016 |
5368 | 6^128661+97 | 100118 | Lelio R Paula | 10/2016 |
5369 | 19^78285+40 | 100108 | Lelio R Paula | 07/2016 |
5370 | 6^128640+5 | 100102 | Lelio R Paula | 11/2014 |
5371 | 22779^22970-22970^22779 | 100093 | Norbert Schneider | 08/2020 |
5372 | (2^332468+3130)/2 | 100083 | Stefano Morozzi | 09/2020 |
5373 | (14*10^100075+61)/3 | 100076 | Robert Price | 12/2018 |
5374 | (2^332435+3098)/2 | 100073 | Stefano Morozzi | 09/2020 |
5375 | 28562^3189+3189^28562 | 100072 | Hans Havermann | 05/2018 |
5376 | 6^128565-127 | 100044 | Lelio R Paula | 08/2016 |
5377 | (2^332317+2106)/2 | 100038 | Stefano Morozzi | 09/2020 |
5378 | 2^332309-133 | 100035 | Lelio R Paula | 02/2011 |
5379 | 2^332307+731 | 100035 | Lelio R Paula | 07/2011 |
5380 | 2^332301+12927 | 100033 | Lelio R Paula | 04/2013 |
5381 | 23406^18781+18781^23406 | 100031 | Hans Havermann | 04/2018 |
5382 | 2^332277-4573 | 100026 | Yves Minet | 03/2019 |
5383 | 12^92684-13 | 100023 | Lelio R Paula | 07/2016 |
5384 | 78557*2^332193+55669 | 100005 | Jorge Menendez | 04/2019 |
5385 | 78557*2^332192+72689 | 100005 | Jorge Menendez | 04/2019 |
5386 | 10^100003+45799 | 100004 | Stefano Morozzi | 04/2019 |
5387 | 10^100003+155461 | 100004 | Stefano Morozzi | 04/2019 |
5388 | 10^100003+211389 | 100004 | Stefano Morozzi | 04/2019 |
5389 | 10^100003+381027 | 100004 | Stefano Morozzi | 04/2019 |
5390 | 10^100003+540703 | 100004 | Stefano Morozzi | 04/2019 |
5391 | 10^100003+823977 | 100004 | Stefano Morozzi | 04/2019 |
5403 | 10^100002+236023 | 100003 | Stefano Morozzi | 05/2018 |
5404 | 10^100002+433741 | 100003 | Stefano Morozzi | 05/2018 |
5392 | 2^332202+104659 | 100003 | Stefano Morozzi | 04/2019 |
5393 | 2^332202+857539 | 100003 | Stefano Morozzi | 04/2019 |
5394 | 2^332202+181773 | 100003 | Stefano Morozzi | 04/2019 |
5395 | 2^332202+687543 | 100003 | Stefano Morozzi | 04/2019 |
5396 | 2^332202+941595 | 100003 | Stefano Morozzi | 04/2019 |
5397 | 2^332202+445813 | 100003 | Stefano Morozzi | 04/2019 |
5398 | 2^332202+1599727 | 100003 | Stefano Morozzi | 04/2019 |
5399 | 2^332202+1389567 | 100003 | Stefano Morozzi | 04/2019 |
5400 | 2^332202+1206315 | 100003 | Stefano Morozzi | 04/2019 |
5401 | 2^332202+1958647 | 100003 | Stefano Morozzi | 04/2019 |
5402 | 10^100003-562857 | 100003 | Patrick De Geest | 07/2019 |
5405 | (10^100002-1)/9-10^33441 | 100002 | Akihiko Yoshida | 03/2018 |
5406 | (10^100002-1)/9-10^44692 | 100002 | Akihiko Yoshida | 03/2018 |
5407 | 10^100002-249519 | 100002 | Patrick De Geest | 07/2018 |
5408 | 10^100001+314199 | 100002 | Patrick De Geest | 07/2018 |
5498 | 10^100000+1751769 | 100001 | Robert Price | 08/2012 |
5499 | 10^100000+2155489 | 100001 | Robert Price | 10/2012 |
5500 | 10^100000+2483527 | 100001 | Robert Price | 12/2012 |
5445 | 10^100000+3938473 | 100001 | Robert Price | 05/2015 |
5446 | 10^100000+3979761 | 100001 | Robert Price | 05/2015 |
5447 | 10^100000+4293973 | 100001 | Robert Price | 09/2015 |
5451 | 10^100000+4858267 | 100001 | Robert Price | 12/2015 |
5452 | 10^100000+5113299 | 100001 | Robert Price | 02/2016 |
5453 | 10^100000+5169411 | 100001 | Robert Price | 02/2016 |
5454 | 10^100000+5354043 | 100001 | Robert Price | 05/2016 |
5455 | 10^100000+5717979 | 100001 | Robert Price | 05/2016 |
5456 | 10^100000+6080631 | 100001 | Robert Price | 07/2016 |
5457 | 10^100000+6308469 | 100001 | Robert Price | 07/2016 |
5458 | 10^100000+6512023 | 100001 | Robert Price | 08/2016 |
5459 | 10^100000+6596557 | 100001 | Robert Price | 08/2016 |
5460 | 10^100000+7115409 | 100001 | Robert Price | 10/2016 |
5461 | 10^100000+7235803 | 100001 | Robert Price | 10/2016 |
5485 | 10^100000+7867333 | 100001 | Robert Price | 12/2016 |
5486 | 10^100000+8743093 | 100001 | Robert Price | 02/2017 |
5487 | 10^100000+8955391 | 100001 | Robert Price | 03/2017 |
5488 | 10^100000+9180019 | 100001 | Robert Price | 03/2017 |
5489 | 10^100000+9225987 | 100001 | Robert Price | 04/2017 |
5490 | 10^100000+9265587 | 100001 | Robert Price | 04/2017 |
5491 | 10^100000+9287049 | 100001 | Robert Price | 04/2017 |
5492 | 10^100000+9425053 | 100001 | Robert Price | 05/2017 |
5493 | 10^100000+9450769 | 100001 | Robert Price | 05/2017 |
5494 | 10^100000+9528747 | 100001 | Robert Smith | 05/2017 |
5495 | 10^100000+9548071 | 100001 | Robert Price | 06/2017 |
5496 | 10^100000+10064287 | 100001 | Robert Price | 08/2017 |
5497 | 10^100000+10229569 | 100001 | Robert Price | 10/2017 |
5409 | 10^100000+11187931 | 100001 | Robert Price | 03/2018 |
5410 | 10^100000+11264721 | 100001 | Robert Price | 04/2018 |
5411 | 10^100000+11477661 | 100001 | Robert Price | 05/2018 |
5412 | 10^100000+11644653 | 100001 | Robert Price | 07/2018 |
5413 | 10^100001-431439 | 100001 | Patrick De Geest | 07/2018 |
5414 | 10^100000+11769399 | 100001 | Robert Price | 08/2018 |
5415 | 10^100000+11848159 | 100001 | Robert Price | 08/2018 |
5416 | 10^100000+11863467 | 100001 | Robert Price | 08/2018 |
5448 | 10^100000+11992051 | 100001 | Robert Price | 09/2018 |
5449 | 2^332196-1-2*29696 | 100001 | Matt Stath | 11/2018 |
5450 | 10^100000+12363957 | 100001 | Robert Price | 11/2018 |
5417 | 2^332196+1+2*17152 | 100001 | Matt Stath | 12/2018 |
5418 | 10^100000+12778033 | 100001 | Robert Price | 02/2019 |
5419 | 10^100000+13581679 | 100001 | Robert Price | 05/2019 |
5420 | 10^100000+13613199 | 100001 | Robert Price | 05/2019 |
5421 | 10^100000+13752327 | 100001 | Robert Price | 05/2019 |
5422 | 10^100000+14139243 | 100001 | Robert Price | 06/2019 |
5423 | 10^100000+14151057 | 100001 | Robert Price | 06/2019 |
5424 | 10^100000+14218923 | 100001 | Robert Price | 06/2019 |
5425 | 10^100000+15136771 | 100001 | Robert Price | 09/2019 |
5426 | 10^100000+15219873 | 100001 | Robert Price | 10/2019 |
5427 | 10^100000+15274039 | 100001 | Robert Price | 10/2019 |
5428 | 10^100000+15394069 | 100001 | Robert Price | 10/2019 |
5429 | 10^100000+15547119 | 100001 | Robert Price | 10/2019 |
5430 | 10^100000+15932923 | 100001 | Robert Price | 11/2019 |
5431 | 10^100000+16345467 | 100001 | Robert Price | 12/2019 |
5432 | 10^100000+16672143 | 100001 | Robert Price | 01/2020 |
5433 | 10^100000+16731939 | 100001 | Robert Price | 02/2020 |
5434 | 10^100000+16907049 | 100001 | Robert Price | 03/2020 |
5435 | 10^100000+17652523 | 100001 | Robert Price | 05/2020 |
5436 | 10^100000+18047167 | 100001 | Robert Price | 05/2020 |
5437 | 10^100000+18471819 | 100001 | Robert Price | 06/2020 |
5438 | 10^100000+18494793 | 100001 | Robert Price | 07/2020 |
5439 | 10^100000+18762609 | 100001 | Robert Price | 07/2020 |
5440 | 10^100000+19204141 | 100001 | Robert Price | 08/2020 |
5441 | 10^100000+19349793 | 100001 | Robert Price | 08/2020 |
5442 | 10^100000+19495699 | 100001 | Robert Price | 09/2020 |
5443 | 10^100000+19668927 | 100001 | Robert Price | 09/2020 |
5444 | 10^100000+19704313 | 100001 | Robert Price | 09/2020 |
5462 | 10^100000+19956229 | 100001 | Robert Price | 09/2020 |
5463 | 10^100000+3*(10^37093-1)/9*10^31454+1 | 100001 | Makoto Morimoto | 09/2020 |
5464 | 10^100000+4*(10^36149-1)/9*10^31926+1 | 100001 | Makoto Morimoto | 09/2020 |
5465 | 10^100000+6*(10^41029-1)/9*10^29486+1 | 100001 | Makoto Morimoto | 09/2020 |
5466 | 10^100000+7*(10^55505-1)/9*10^22248+1 | 100001 | Makoto Morimoto | 09/2020 |
5467 | 10^100000+20234607 | 100001 | Robert Price | 10/2020 |
5468 | 10^100000+20752303 | 100001 | Robert Price | 11/2020 |
5469 | 10^100000+20774041 | 100001 | Robert Price | 11/2020 |
5470 | 10^100000+20854741 | 100001 | Robert Price | 11/2020 |
5471 | 10^100000+20908917 | 100001 | Robert Price | 11/2020 |
5472 | 10^100000+20994793 | 100001 | Robert Price | 11/2020 |
5473 | 10^100000+21354249 | 100001 | Robert Price | 12/2020 |
5474 | 10^100000+21455559 | 100001 | Robert Price | 12/2020 |
5475 | 10^100000+21538873 | 100001 | Robert Price | 12/2020 |
5476 | 10^100000+21830901 | 100001 | Robert Price | 01/2021 |
5477 | 10^100000+21842629 | 100001 | Robert Price | 01/2021 |
5478 | 10^100000+21930861 | 100001 | Robert Price | 01/2021 |
5479 | 10^100000+22092943 | 100001 | Robert Price | 03/2021 |
5480 | 10^100000+22278417 | 100001 | Robert Price | 03/2021 |
5481 | 10^100000+22388581 | 100001 | Robert Price | 03/2021 |
5482 | 10^100000+22390933 | 100001 | Robert Price | 03/2021 |
5483 | 10^100000+22436169 | 100001 | Robert Price | 03/2021 |
5484 | 10^100000+22714557 | 100001 | Robert Price | 04/2021 |