PRP Records

Probable Primes Top 10000

(294113 PRPs in the top)

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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 1-250 251-500 501-750 751-1000 1001-1250 1251-1500 1501-1750 1751-2000 2001-2250 2251-2500 2501-2750 2751-3000 3001-3250 3251-3500 3501-3750 3751-4000 4001-4250 4251-4500 4501-4750 4751-5000 5001-5250 5251-5500 5501-5750 5751-6000 6001-6250 6251-6500 6501-6750 6751-7000 7001-7250 7251-7500 7501-7750 7751-8000 8001-8250 8251-8500 8501-8750 8751-9000 9001-9250 9251-9500 9501-9750 9751-10000

 Rank Probable prime Digits (> 50000) Who ? When ? 5251 2^381207-111546435 114755 Paul Bourdelais 10/2021 5252 569^41651-568^41651 114754 Jean-Louis Charton 11/2009 5253 2^381201+1873205 114753 Enzo Doria 06/2016 5254 (85*10^114737+293)/9 114738 Robert Price 12/2019 5255 (265*10^114736+17)/3 114738 Robert Price 03/2020 5256 (2^381062+2170)/2 114711 Stefano Morozzi 09/2020 5257 2^380974-112991 114685 Enzo Doria 07/2014 5258 37097^1234+1234^37097 114679 Hans Havermann 02/2021 5259 (26*10^114658-119)/3 114659 Robert Price 07/2023 5260 88^58949-87 114626 Norbert Schneider 11/2015 5261 (2^380773+662)/2 114624 Stefano Morozzi 09/2020 5262 29913^6782+6782^29913 114608 Hans Havermann 02/2021 5263 (331*10^114605-7)/9 114607 Robert Price 04/2022 5264 2^380700+91 114603 Lelio R Paula 03/2013 5265 (2^380632+2578)/2 114582 Stefano Morozzi 09/2020 5266 7*10^114577+27 114578 Robert Price 11/2020 5268 10^114575+3^114576 114576 Mike Oakes 09/2010 5267 10^114575+66561 114576 Patrick De Geest 02/2017 5269 10^114575-581081 114575 Patrick De Geest 02/2017 5270 2^380587-115315 114569 Enzo Doria 06/2015 5271 31874^3927+3927^31874 114558 Hans Havermann 02/2021 5272 2^380513-216925 114546 Enzo Doria 05/2014 5273 2^380451-1840087 114528 Enzo Doria 06/2015 5274 (2^380426+1510)/2 114520 Stefano Morozzi 09/2020 5275 (15*2^380388-1)/539 114507 Lelio R Paula 04/2014 5276 2^380279-461347 114476 Enzo Doria 07/2015 5277 (331*10^114454-7)/9 114456 Robert Price 04/2022 5278 27121^16590+16590^27121 114447 Hans Havermann 01/2021 5279 25966^25555+25555^25966 114445 Hans Havermann 01/2021 5280 (611*32^76029-53)/31 114437 Eric Chen 11/2023 5281 (11*10^114400+529)/9 114401 Robert Price 09/2021 5282 2^380021+1871147 114398 Enzo Doria 05/2016 5283 2^380005+1869707 114393 Enzo Doria 05/2016 5284 2^379958-113297 114379 Enzo Doria 07/2014 5285 (2^379897+1274)/2 114361 Stefano Morozzi 01/2021 5286 2^379881-109105 114356 Enzo Doria 04/2014 5287 (21*2^379857-1)/13 114349 Lelio R Paula 03/2014 5288 (4*10^114340+83)/3 114341 Robert Price 02/2018 5289 (26*10^114317-77)/3 114318 Robert Price 11/2019 5290 (4*10^114296+149)/9 114296 Robert Price 04/2018 5291 88^58773-87 114284 Norbert Schneider 11/2015 5292 27764^13065+13065^27764 114280 Hans Havermann 01/2021 5293 2^379529-2790283 114250 Enzo Doria 03/2016 5294 2^379522+1869115 114248 Enzo Doria 05/2016 5295 (145*10^114226-1)/9 114228 Serge Batalov 12/2014 5296 2^379317-115033 114186 Enzo Doria 06/2015 5297 (22*10^114178+47)/3 114179 Robert Price 06/2021 5298 (17*2^379246-1)/17407 114162 Lelio R Paula 03/2014 5299 (2^379192+226)/2 114148 Stefano Morozzi 09/2020 5300 (228^48407-1)/227 114139 Alexander Zhirkov 03/2023 5301 6*10^114091+23 114092 Robert Price 09/2020 5302 (4*10^114076+143)/3 114077 Robert Price 03/2018 5303 332*25^81584+12357 114053 Eric Chen 10/2023 5304 (2^378820+3226)/2 114036 Stefano Morozzi 01/2021 5305 (2^378754+2058)/2 114017 Stefano Morozzi 09/2020 5306 13643^27572-27572^13643 114008 Norbert Schneider 12/2022 5308 (46*10^113969+683)/9 113970 Robert Price 03/2019 5307 (83*10^113969+133)/9 113970 Robert Price 08/2021 5309 32226^3439+3439^32226 113966 Hans Havermann 02/2021 5310 (77*10^113963-149)/9 113964 Robert Price 03/2022 5311 78*10^113954-7 113956 Robert Price 10/2020 5312 2*10^113941+9 113942 Dmitry Domanov 11/2010 5313 10^113933+145897 113934 Patrick De Geest 02/2021 5316 (2^378478+1642)/2 113933 Stefano Morozzi 09/2020 5314 10^113933-8000000001 113933 Robert Price 11/2020 5315 10^113933-66167 113933 Patrick De Geest 02/2021 5317 2339662057597*10^113903+9 113916 Robert Price 03/2021 5318 4*10^113905+91 113906 Robert Price 08/2018 5319 10^113894+76609 113895 Patrick De Geest 02/2021 5321 10^113894-10000001 113894 Robert Price 09/2020 5320 10^113894-373947 113894 Patrick De Geest 02/2021 5322 33933^2270+2270^33933 113881 Hans Havermann 02/2021 5323 4*10^113874-21 113875 Robert Price 09/2018 5324 2^378272-16565 113872 Enzo Doria 04/2013 5325 2^378217-109075 113855 Enzo Doria 04/2014 5326 2^378198+67 113849 Lelio R Paula 03/2013 5327 2^378173-3249 113842 Yves Minet 12/2014 5328 (2^378155-5)/6597 113833 Lelio R Paula 03/2014 5329 92941#+(355049#)/(92941#) 113830 Makoto Morimoto 10/2017 5330 30030^6173+6173^30030 113829 Hans Havermann 01/2021 5331 2^378128-262977 113828 Enzo Doria 05/2014 5332 2^378123-113215 113827 Enzo Doria 07/2014 5333 6^146274-18893 113824 Enzo Doria 03/2013 5334 34596^1949+1949^34596 113815 Hans Havermann 02/2021 5335 2^378078+75 113813 Lelio R Paula 03/2013 5336 (28*10^113810+449)/9 113811 Robert Price 11/2021 5337 26273^21448+21448^26273 113799 Hans Havermann 02/2021 5338 2^377966+255255 113780 Paul Bourdelais 10/2021 5339 2^377940+63 113772 Lelio R Paula 03/2013 5340 2^377941-2785843 113772 Enzo Doria 04/2016 5341 (7*10^113757+11)/9 113757 Tyler Busby 01/2023 5342 2^377810+1875109 113733 Enzo Doria 09/2016 5343 2^377803-1838635 113731 Enzo Doria 05/2015 5344 2^377799+52223 113729 Yves Minet 08/2010 5345 (2^377791+3258)/2 113727 Stefano Morozzi 02/2021 5346 11^109190-270 113710 Enzo Doria 12/2012 5347 28206^10739+10739^28206 113698 Hans Havermann 01/2021 5348 7*10^113693+9 113694 Robert Price 09/2015 5349 13899^27442+27442^13899 113692 Norbert Schneider 12/2020 5350 (82*10^113681+161)/9 113682 Robert Price 10/2019 5351 26121^22478+22478^26121 113673 Hans Havermann 01/2021 5352 4*10^113658+49 113659 Robert Price 01/2019 5353 (10^113656+7)/40231/6439001 113645 Alfred Reich 06/2021 5354 (2*10^113631+529)/9 113631 Robert Price 01/2018 5355 2^377408-2798279 113612 Enzo Doria 04/2016 5356 13706^27459+27459^13706 113596 Norbert Schneider 12/2020 5357 5*10^113586+57 113587 Robert Price 12/2018 5358 (2^377242+2794)/2 113561 Stefano Morozzi 02/2021 5359 2^377222+93679 113556 Yves Minet 02/2011 5361 262147#+316847 113552 Makoto Morimoto 02/2016 5360 27172^15101+15101^27172 113552 Hans Havermann 01/2021 5362 (2^377131+2018)/2 113528 Stefano Morozzi 09/2020 5363 2^377026-458903 113497 Enzo Doria 04/2015 5364 (2^377014+2202)/2 113493 Stefano Morozzi 09/2020 5365 34791^1828+1828^34791 113488 Hans Havermann 02/2021 5366 (2^376967+258)/2 113479 Stefano Morozzi 09/2020 5367 (29*10^113468-17)/3 113469 Robert Price 09/2019 5368 35^73477-34^73477 113454 Robert Price 05/2012 5369 (14*10^113451-89)/3 113452 Robert Price 05/2020 5370 2^376790+27 113426 Lelio R Paula 03/2013 5371 2^376786-112701 113424 Enzo Doria 06/2014 5372 2^376731+21 113408 Lelio R Paula 03/2013 5373 9*10^113394-73 113395 Robert Price 01/2021 5374 29660^6651+6651^29660 113387 Hans Havermann 01/2021 5376 2^376634+1871245 113379 Enzo Doria 05/2016 5375 (4^188318+17)/3 113379 Robert Price 02/2017 5377 E(29532)/492842728006750534663978950979381235 113367 Thomas Ritschel 01/2021 5378 2^376576-344369 113361 Enzo Doria 07/2015 5379 2^376549-4543 113353 Yves Minet 03/2019 5380 (17*2^376526-1)/223 113345 Lelio R Paula 03/2014 5381 (27*2^376441-1)/811 113319 Lelio R Paula 03/2014 5382 (2^376350+3538)/2 113293 Stefano Morozzi 09/2020 5383 27265^14272+14272^27265 113273 Hans Havermann 02/2021 5384 32174^3315+3315^32174 113269 Hans Havermann 02/2021 5385 (2*10^113248+73)/3 113248 Robert Price 09/2020 5386 2^376128-21237 113226 Enzo Doria 06/2013 5387 5*10^113224-81 113225 Robert Price 01/2019 5388 10^113220+51409 113221 Patrick De Geest 02/2021 5390 10^113220-1000001 113220 Robert Price 08/2020 5389 10^113220-61779 113220 Patrick De Geest 02/2021 5391 (2^376102+1578)/2 113218 Stefano Morozzi 09/2020 5392 (2^375996+3102)/2 113186 Stefano Morozzi 09/2020 5393 37258^1091+1091^37258 113184 Hans Havermann 02/2021 5394 (94*10^113176+11)/3 113178 Robert Price 04/2020 5395 (46*10^113162+521)/9 113163 Robert Price 02/2019 5396 (2^375885+3614)/2 113153 Stefano Morozzi 09/2020 5397 (2^375873+2006)/2 113149 Stefano Morozzi 09/2020 5398 3*10^113137+23 113138 Robert Price 03/2022 5399 (8*10^113135-269)/9 113135 Robert Price 09/2021 5400 (2^375726+694)/2 113105 Stefano Morozzi 09/2020 5401 26050^21959+21959^26050 113100 Hans Havermann 02/2021 5402 2^375638-1787171 113079 Enzo Doria 03/2016 5403 (2^375563+2178)/2 113056 Stefano Morozzi 09/2020 5404 2^375537+4847 113048 Yves Minet 02/2011 5405 (17^91837+16^91837)/33 113000 Robert Price 08/2013 5406 5*F(270343)*(F(270343)+1)+1 112997 Serge Batalov 04/2015 5407 2^375350-3221 112992 Yves Minet 07/2011 5408 (13*2^375306+1)/7 112979 Lelio R Paula 03/2014 5409 2^375305+76757 112979 Enzo Doria 05/2016 5410 2^375258+1874989 112964 Enzo Doria 07/2016 5411 (29^77237-1)/28 112950 Robert Price 04/2012 5412 26620^17483+17483^26620 112939 Hans Havermann 01/2021 5413 2^375154+74959 112933 Enzo Doria 04/2016 5414 (266*10^112930-17)/3 112932 Robert Price 07/2020 5415 (2^375134+778)/2 112927 Stefano Morozzi 09/2020 5416 (85*10^112919+293)/9 112920 Robert Price 12/2019 5417 29412^6899+6899^29412 112907 Hans Havermann 02/2021 5418 (191*10^112903-17)/3 112905 Robert Price 11/2021 5419 (2^375022+1210)/2 112893 Stefano Morozzi 09/2020 5420 25992^22039+22039^25992 112889 Hans Havermann 02/2021 5421 2^374993-2787163 112885 Enzo Doria 11/2015 5422 (697*10^112869+23)/9 112871 Robert Price 04/2021 5423 (19*10^112851+377)/9 112852 Alfred Reich 11/2022 5424 30420^5111+5111^30420 112813 Hans Havermann 02/2021 5425 13699^27268+27268^13699 112800 Norbert Schneider 12/2020 5426 123^53970+2 112793 Lelio R Paula 06/2013 5427 12308*27^78796+23 112790 Eric Chen 07/2023 5428 28942^7887+7887^28942 112785 Hans Havermann 01/2021 5429 2^374640-4685 112778 Yves Minet 05/2019 5430 57290^93+93^57290 112775 Hans Havermann 01/2021 5431 13608^27277-27277^13608 112758 Norbert Schneider 12/2022 5432 (2^374556+682)/2 112753 Stefano Morozzi 09/2020 5433 p(22852)#/2+512 112745 Robert Price 05/2017 5434 (11*10^112742-131)/3 112743 Robert Price 09/2018 5435 2^374441-21049 112718 Enzo Doria 06/2013 5436 4*10^112706-93 112707 Robert Price 07/2020 5437 (2^374321+1)/3 112682 H.&R. Lifchitz 12/2000 5438 (2^374213+1766)/2 112650 Stefano Morozzi 09/2020 5439 (2^374094+2674)/2 112614 Stefano Morozzi 09/2020 5440 (13^101089-1)/12 112607 Paul Bourdelais 03/2010 5441 3^236011-8828 112606 Enzo Doria 05/2014 5442 31854^3427+3427^31854 112602 Hans Havermann 02/2021 5443 (85*10^112530-373)/9 112531 Robert Price 05/2021 5444 (2^373748+1090)/2 112510 Stefano Morozzi 09/2020 5445 (2^373727+1806)/2 112503 Stefano Morozzi 01/2021 5446 27618^11821+11821^27618 112479 Hans Havermann 01/2021 5447 26343^18580+18580^26343 112460 Hans Havermann 01/2021 5448 39^70666+2 112435 Lelio R Paula 11/2013 5449 (134*10^112400+7)/3 112402 Robert Price 02/2020 5450 (2^373365+326)/2 112394 Stefano Morozzi 09/2020 5451 (2^373350-7)/3 112390 Lelio R Paula 03/2014 5452 2^373306-1840931 112377 Enzo Doria 06/2015 5453 8*10^112371-37 112372 Robert Price 03/2022 5454 (2^373262+270)/2 112363 Stefano Morozzi 09/2020 5455 6*10^112359-79 112360 Robert Price 03/2022 5456 34409^1842+1842^34409 112356 Hans Havermann 02/2021 5457 (142*10^112352-7)/9 112354 Robert Price 12/2019 5458 25580^24633+24633^25580 112336 Hans Havermann 01/2021 5459 2^373117+1872107 112320 Enzo Doria 05/2016 5460 (2^373083+2226)/2 112309 Stefano Morozzi 01/2021 5461 (35*10^112308+37)/9 112309 Robert Price 05/2022 5462 27963^10376+10376^27963 112301 Hans Havermann 01/2021 5463 2^373040+2792761 112297 Enzo Doria 03/2016 5464 EPrime(112280) 112280 Eric W. Weisstein 10/2010 5465 2^372950+7 112270 Lelio R Paula 03/2013 5466 2^372945+1872167 112268 Enzo Doria 05/2016 5467 36274^1243+1243^36274 112249 Hans Havermann 02/2021 5468 (55*10^112246+629)/9 112247 Robert Price 01/2022 5469 (2^372872+3798)/2 112246 Stefano Morozzi 02/2021 5470 25513^25060+25060^25513 112232 Hans Havermann 02/2021 5471 (53*10^112229-611)/9 112230 Robert Price 02/2022 5472 (2^372754+3094)/2 112210 Stefano Morozzi 09/2020 5473 6*10^112208+43 112209 Robert Price 07/2020 5474 (2^372728+3058)/2 112203 Stefano Morozzi 09/2020 5475 32061^3158+3158^32061 112195 Hans Havermann 02/2021 5476 2^372695+72113 112193 Enzo Doria 04/2016 5477 2^372689-2563 112191 Yves Minet 07/2014 5478 2^372638-1859441 112176 Enzo Doria 03/2016 5479 3^235074-113056 112159 Enzo Doria 07/2014 5480 -E(29242)/489848365125303139750087 112140 Thomas Ritschel 01/2021 5481 (2^372514+1822)/2 112138 Stefano Morozzi 02/2021 5482 29468^6387+6387^29468 112135 Hans Havermann 02/2021 5483 (2^372428+3742)/2 112112 Stefano Morozzi 01/2021 5484 25375^25454-25454^25375 112110 Norbert Schneider 01/2021 5485 131^52949-130 112108 Norbert Schneider 02/2019 5486 (91*10^112098-1)/9 112100 Robert Price 04/2015 5487 (68*10^112087-149)/9 112088 Robert Price 07/2022 5488 2^372314+212419 112078 Enzo Doria 08/2023 5489 2^372310-85061 112077 Paul Bourdelais 02/2012 5490 (10^112067+53)/9 112067 Serge Batalov 07/2015 5491 (2^372237+2082)/2 112055 Stefano Morozzi 09/2020 5492 75^59760+2 112054 Lelio R Paula 08/2013 5493 (2^372200+1710)/2 112044 Stefano Morozzi 09/2020 5494 (10^112048+7)/8747/373157 112039 Alfred Reich 06/2021 5495 (2^372181+2250)/2 112038 Stefano Morozzi 01/2021 5496 (2^372161+2574)/2 112032 Stefano Morozzi 09/2020 5497 8*10^112018-49 112019 Robert Price 08/2019 5499 2^372108+74221 112016 Enzo Doria 04/2016 5498 (2^372109+2046)/2 112016 Stefano Morozzi 09/2020 5500 8*10^112011-73 112012 Robert Price 01/2022

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 05 2023 08:12 (Time in France)

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