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 | 26167^5794+5794^26167 | 98466 | Hans Havermann | 01/2020 |
5252 | (6883*2^327047-1)/77 | 98453 | Lelio R Paula | 05/2015 |
5253 | (71*10^98446+1)/9 | 98447 | Serge Batalov | 11/2010 |
5254 | 13^88363+94 | 98432 | Lelio R Paula | 08/2016 |
5255 | 48^58543-47^58543 | 98425 | Jean-Louis Charton | 11/2005 |
5256 | 6^126481+41 | 98422 | Lelio R Paula | 08/2016 |
5257 | 78*10^98413-7 | 98415 | Robert Price | 05/2017 |
5258 | 22634^22263+22263^22634 | 98404 | Hans Havermann | 07/2020 |
5259 | 7^116416+46 | 98383 | Lelio R Paula | 08/2016 |
5260 | 7^116407-24 | 98376 | Lelio R Paula | 07/2016 |
5261 | 439^37228+37228^439 | 98374 | Norbert Schneider | 08/2018 |
5262 | 2^326782-1860671 | 98372 | Enzo Doria | 03/2016 |
5263 | 17^79948+58 | 98372 | Lelio R Paula | 08/2016 |
5264 | 22499^22602-22602^22499 | 98368 | Norbert Schneider | 08/2020 |
5265 | 3^206143-98 | 98356 | Lelio R Paula | 08/2016 |
5266 | 8*5^140705+7 | 98350 | Lelio R Paula | 11/2014 |
5267 | (2^326632+1662)/2 | 98326 | Stefano Morozzi | 09/2020 |
5268 | 2^326585+11 | 98312 | Lelio R Paula | 12/2012 |
5269 | 2^326582-459161 | 98311 | Enzo Doria | 05/2015 |
5271 | (2^326548+9)/5 | 98301 | Lelio R Paula | 10/2013 |
5270 | (2^326549+18)/10 | 98301 | Stefano Morozzi | 03/2020 |
5272 | 2^326538+71659 | 98298 | Enzo Doria | 04/2016 |
5273 | (2^326520+2082)/2 | 98293 | Stefano Morozzi | 09/2020 |
5274 | (2^326521+1002)/2 | 98293 | Stefano Morozzi | 09/2020 |
5275 | 15^83575-58 | 98292 | Lelio R Paula | 08/2016 |
5276 | 10^98288+3 | 98289 | Robert Price | 03/2011 |
5277 | 10^98288-117017 | 98288 | Patrick De Geest | 11/2011 |
5278 | (44*10^98284-719)/9 | 98285 | Robert Price | 12/2017 |
5279 | 23466^15419+15419^23466 | 98277 | Hans Havermann | 02/2020 |
5280 | 2^326421-2797573 | 98263 | Enzo Doria | 04/2016 |
5281 | 2^326401+16095 | 98257 | Lelio R Paula | 07/2016 |
5282 | 7^116240-116240^7 | 98235 | Norbert Schneider | 05/2017 |
5283 | 17^79826-78 | 98222 | Lelio R Paula | 08/2016 |
5284 | 2^326268-809 | 98217 | Yves Minet | 04/2011 |
5285 | 22659^21590+21590^22659 | 98210 | Hans Havermann | 10/2019 |
5286 | 22268^22587-22587^22268 | 98202 | Norbert Schneider | 08/2020 |
5287 | (418*10^98199+23)/9 | 98201 | Robert Price | 08/2017 |
5288 | 12*10^98198-7 | 98200 | Robert Price | 11/2017 |
5289 | 15^83496-76 | 98199 | Lelio R Paula | 08/2016 |
5290 | (10223*2^326179+1)/6125 | 98190 | Lelio R Paula | 07/2014 |
5291 | 9*5^140471-4 | 98186 | Lelio R Paula | 11/2014 |
5292 | 22774^20455+20455^22774 | 98175 | Hans Havermann | 07/2020 |
5293 | 2^326069-2383 | 98157 | Yves Minet | 10/2013 |
5294 | 2^325973+1185 | 98128 | Lelio R Paula | 07/2016 |
5295 | (25*2^325949-1)/17 | 98121 | Lelio R Paula | 02/2014 |
5296 | 2^325945-1847269 | 98120 | Enzo Doria | 07/2015 |
5297 | 8*10^98111-67 | 98112 | Robert Price | 10/2017 |
5298 | (2^325902+1138)/2 | 98106 | Stefano Morozzi | 09/2020 |
5299 | 2^325866+15 | 98096 | Lelio R Paula | 12/2012 |
5300 | 22591^21952+21952^22591 | 98079 | Hans Havermann | 02/2020 |
5301 | 2^325765+1974305 | 98066 | Enzo Doria | 06/2016 |
5302 | 2^325733-58695 | 98056 | Lelio R Paula | 07/2016 |
5303 | 2^325717-3645 | 98051 | Lelio R Paula | 07/2016 |
5304 | (2^325704+718)/2 | 98047 | Stefano Morozzi | 09/2020 |
5305 | 23968^12293+12293^23968 | 98021 | Hans Havermann | 11/2019 |
5306 | (23*2^325583-1)/21 | 98011 | Lelio R Paula | 02/2014 |
5307 | (7*10^98007-13)/3 | 98008 | Robert Price | 06/2016 |
5308 | (2^325544+1110)/2 | 97999 | Stefano Morozzi | 09/2020 |
5309 | 2^325512-459959 | 97989 | Enzo Doria | 05/2015 |
5310 | (2^325492+682)/2 | 97983 | Stefano Morozzi | 09/2020 |
5311 | (3^205354-8)/17 | 97978 | Lelio R Paula | 09/2013 |
5312 | 2^325433+76817 | 97966 | Enzo Doria | 05/2016 |
5313 | 5*10^97963+81 | 97964 | Robert Price | 08/2017 |
5314 | 2^325390-109061 | 97953 | Enzo Doria | 04/2014 |
5315 | 13^87921+24 | 97940 | Lelio R Paula | 08/2016 |
5316 | 961^32831-960^32831 | 97926 | Jean-Louis Charton | 02/2011 |
5317 | 22600^21499+21499^22600 | 97913 | Hans Havermann | 05/2020 |
5318 | 2^325215+12909 | 97900 | Lelio R Paula | 07/2016 |
5319 | 22619^21286+21286^22619 | 97898 | Hans Havermann | 04/2020 |
5320 | (85*10^97876-49)/9 | 97877 | Robert Price | 12/2020 |
5321 | 7*10^97874-69 | 97875 | Robert Price | 01/2017 |
5323 | (17^79537+5^79537)/22 | 97865 | Robert Price | 06/2013 |
5322 | 15^83212+22 | 97865 | Lelio R Paula | 08/2016 |
5324 | 2^325087-109057 | 97861 | Enzo Doria | 04/2014 |
5325 | 2^325074+1870657 | 97858 | Enzo Doria | 05/2016 |
5327 | 2^325066-2111 | 97855 | Yves Minet | 08/2013 |
5326 | CopelandErdos(97855) | 97855 | Eric W. Weisstein | 10/2015 |
5328 | 26660^4677+4677^26660 | 97842 | Hans Havermann | 12/2019 |
5329 | 18^77944-89 | 97841 | Lelio R Paula | 07/2016 |
5330 | 119^47136+118 | 97833 | Norbert Schneider | 09/2018 |
5331 | 6^125720-17663 | 97830 | Enzo Doria | 02/2013 |
5332 | 2^324972-2069 | 97827 | Yves Minet | 05/2013 |
5333 | 2^324958-4691 | 97823 | Yves Minet | 05/2019 |
5334 | 2^324944-2788319 | 97818 | Enzo Doria | 03/2016 |
5335 | 22845^19112+19112^22845 | 97807 | Hans Havermann | 10/2019 |
5336 | (2^324898+1270)/2 | 97804 | Stefano Morozzi | 09/2020 |
5338 | 4*10^97799-9 | 97800 | Erik Branger | 11/2013 |
5337 | 2^324882+577294575 | 97800 | Lelio R Paula | 09/2016 |
5339 | 2^324863-1867921 | 97794 | Enzo Doria | 04/2016 |
5340 | 6^125662-18473 | 97785 | Enzo Doria | 03/2013 |
5341 | 12^90604+11 | 97779 | Lelio R Paula | 07/2016 |
5342 | 5^139830+24 | 97737 | Lelio R Paula | 04/2016 |
5343 | (2^324672+1198)/2 | 97736 | Stefano Morozzi | 09/2020 |
5344 | 2^324612+1155 | 97718 | Lelio R Paula | 07/2016 |
5345 | (2^324597+3542)/2 | 97714 | Stefano Morozzi | 09/2020 |
5346 | 19^76404-44 | 97702 | Lelio R Paula | 07/2016 |
5347 | 2^324505-2983 | 97686 | Yves Minet | 04/2011 |
5348 | (144^45259+1)/145 | 97684 | Paul Bourdelais | 08/2019 |
5349 | (31*2^324496-1)/45 | 97683 | Lelio R Paula | 02/2014 |
5350 | 6^125488-17843 | 97649 | Enzo Doria | 02/2013 |
5351 | (2^324350+3198)/2 | 97639 | Stefano Morozzi | 09/2020 |
5352 | 7^115515-2 | 97622 | Lelio R Paula | 09/2013 |
5353 | (89^50069-1)/88 | 97603 | Paul Bourdelais | 08/2017 |
5354 | 6^125418-5 | 97595 | Lelio R Paula | 11/2014 |
5355 | (2^324193+3522)/2 | 97592 | Stefano Morozzi | 09/2020 |
5356 | (2^324172+666)/2 | 97586 | Stefano Morozzi | 09/2020 |
5357 | 2^324076+1155 | 97557 | Lelio R Paula | 07/2016 |
5358 | (2^324074+9)/13 | 97555 | Lelio R Paula | 10/2013 |
5359 | (55459*2^323993+1)/21 | 97536 | Lelio R Paula | 07/2014 |
5360 | 13^87557-12^87557 | 97534 | Jean-Louis Charton | 12/2008 |
5361 | 2^323946+73939 | 97518 | Enzo Doria | 04/2016 |
5362 | 2^323937+1866947 | 97515 | Enzo Doria | 03/2016 |
5364 | 6^125290-18533 | 97495 | Enzo Doria | 03/2013 |
5363 | (2^323870+1650)/2 | 97495 | Stefano Morozzi | 09/2020 |
5365 | 2^323845+101 | 97488 | Lelio R Paula | 12/2012 |
5366 | 18^77662+65 | 97487 | Lelio R Paula | 07/2016 |
5367 | 22634^20265+20265^22634 | 97479 | Hans Havermann | 04/2020 |
5368 | 2^323772+76771 | 97466 | Enzo Doria | 05/2016 |
5369 | 2^323765-112213 | 97463 | Enzo Doria | 06/2014 |
5370 | 22730^19389+19389^22730 | 97457 | Hans Havermann | 02/2020 |
5371 | 2^323720-6555 | 97450 | Lelio R Paula | 07/2016 |
5372 | 2^323694-1860401 | 97442 | Enzo Doria | 03/2016 |
5373 | 20^74886+3 | 97429 | Lelio R Paula | 06/2016 |
5374 | 24476^9561+9561^24476 | 97427 | Hans Havermann | 01/2020 |
5375 | (2^323623+1766)/2 | 97420 | Stefano Morozzi | 09/2020 |
5377 | 3*10^97399+73 | 97400 | Robert Price | 04/2016 |
5376 | 7^115252-50 | 97400 | Lelio R Paula | 07/2016 |
5378 | 224737#+393581 | 97389 | Nicolas PALAU | 12/2016 |
5379 | (2^323468+3186)/2 | 97374 | Stefano Morozzi | 09/2020 |
5380 | (2^323456+538)/2 | 97370 | Stefano Morozzi | 09/2020 |
5381 | 23277^15236+15236^23277 | 97365 | Hans Havermann | 07/2020 |
5383 | (26*10^97353+31)/3 | 97354 | Robert Price | 07/2016 |
5382 | (2^323403+3510)/2 | 97354 | Stefano Morozzi | 09/2020 |
5384 | 23756^12519+12519^23756 | 97342 | Hans Havermann | 07/2020 |
5385 | 23991^11402+11402^23991 | 97332 | Hans Havermann | 07/2020 |
5386 | 61^54517-60^54517 | 97331 | Jean-Louis Charton | 09/2005 |
5387 | (38*10^97329+187)/9 | 97330 | Robert Price | 11/2017 |
5388 | 86455!4+8 | 97319 | Robert Price | 09/2019 |
5389 | 22591^20310+20310^22591 | 97316 | Hans Havermann | 06/2020 |
5390 | 25101^7520+7520^25101 | 97297 | Hans Havermann | 05/2020 |
5391 | p(19982)#/2-1024 | 97293 | Robert Price | 09/2017 |
5392 | 6^125021-85 | 97286 | Lelio R Paula | 08/2016 |
5393 | 2^323164-47355 | 97283 | Lelio R Paula | 07/2016 |
5394 | (3^203902+4)/36051015157 | 97276 | Lelio R Paula | 09/2013 |
5395 | 2^323054-6555 | 97249 | Lelio R Paula | 07/2016 |
5396 | 22822^18247+18247^22822 | 97249 | Hans Havermann | 02/2020 |
5397 | 9*10^97247-29 | 97248 | Robert Price | 05/2017 |
5398 | 24382^9735+9735^24382 | 97244 | Hans Havermann | 02/2020 |
5399 | (31*10^97242+41)/9 | 97243 | Robert Price | 04/2015 |
5400 | GoldenRatioPrime[97241] | 97241 | Eric W. Weisstein | 06/2009 |
5401 | 12^90098-41 | 97233 | Lelio R Paula | 07/2016 |
5402 | 2^322928-216929 | 97212 | Enzo Doria | 05/2014 |
5403 | (7*2^322896-1)/57 | 97201 | Lelio R Paula | 02/2014 |
5404 | (2^322897+5)/3146107489 | 97193 | Lelio R Paula | 10/2013 |
5405 | (2^322789+2214)/2 | 97169 | Stefano Morozzi | 09/2020 |
5406 | 2^322725+75761 | 97150 | Enzo Doria | 04/2016 |
5407 | (13*2^322686+1)/119 | 97138 | Lelio R Paula | 11/2013 |
5408 | 22402^21639+21639^22402 | 97118 | Hans Havermann | 07/2020 |
5409 | 23399^14128+14128^23399 | 97108 | Hans Havermann | 06/2020 |
5410 | (2^322525+2606)/2 | 97090 | Stefano Morozzi | 09/2020 |
5411 | (41*10^97085+373)/9 | 97086 | Robert Price | 04/2017 |
5412 | 2^322413+77 | 97056 | Lelio R Paula | 12/2012 |
5413 | 2^322406+177 | 97054 | Lelio R Paula | 12/2012 |
5414 | (14*10^97044+31)/9 | 97045 | Robert Price | 02/2015 |
5415 | 2^322302+255255 | 97023 | Lelio R Paula | 07/2016 |
5416 | 2^322196-113093 | 96991 | Enzo Doria | 07/2014 |
5417 | (2^322169+2690)/2 | 96983 | Stefano Morozzi | 09/2020 |
5418 | 23109^15668+15668^23109 | 96943 | Hans Havermann | 07/2020 |
5419 | 2^322000-1861469 | 96932 | Enzo Doria | 03/2016 |
5420 | 2^321971-112747 | 96923 | Enzo Doria | 06/2014 |
5421 | 23754^12023+12023^23754 | 96917 | Hans Havermann | 07/2020 |
5422 | 11^93062-92 | 96915 | Lelio R Paula | 06/2016 |
5423 | (2^321922+2214)/2 | 96908 | Stefano Morozzi | 09/2020 |
5424 | (2^321900+2086)/2 | 96902 | Stefano Morozzi | 09/2020 |
5425 | (11*2^321841-7)/15 | 96884 | Renaud Lifchitz | 03/2011 |
5426 | 3^203051+34 | 96880 | Lelio R Paula | 05/2016 |
5427 | 2*10^96867-51 | 96868 | Robert Price | 11/2017 |
5428 | (2^321779+2618)/2 | 96865 | Stefano Morozzi | 09/2020 |
5429 | (64*10^96863-1)/27 | 96864 | Serge Batalov | 05/2010 |
5430 | 2^321716-2786939 | 96847 | Enzo Doria | 03/2016 |
5431 | 22496^20181+20181^22496 | 96844 | Hans Havermann | 03/2020 |
5432 | 2^321701-113053 | 96842 | Enzo Doria | 07/2014 |
5433 | 2^321700-28635 | 96842 | Lelio R Paula | 06/2016 |
5434 | (5*2^321691-1)/27 | 96838 | Lelio R Paula | 02/2014 |
5435 | 6^124433-124433 | 96828 | Robert Price | 01/2014 |
5436 | 2^321631+69 | 96821 | Lelio R Paula | 12/2012 |
5437 | (13*2^321606+1)/119 | 96813 | Lelio R Paula | 11/2013 |
5438 | (46*10^96798-1)/9 | 96799 | Serge Batalov | 10/2014 |
5439 | (59*10^96798+31)/9 | 96799 | Robert Price | 09/2015 |
5440 | (2^321536+2062)/2 | 96792 | Stefano Morozzi | 09/2020 |
5441 | 223319#+231223 | 96790 | Makoto Morimoto | 02/2016 |
5442 | 2^321519-28635 | 96787 | Lelio R Paula | 06/2016 |
5443 | 2^321487-1867237 | 96778 | Enzo Doria | 03/2016 |
5444 | 2^321461-63 | 96770 | Lelio R Paula | 12/2012 |
5445 | 2^321439+123 | 96763 | Lelio R Paula | 12/2012 |
5446 | 2^321434+709 | 96762 | Lelio R Paula | 02/2013 |
5447 | (2^321415+554)/2 | 96756 | Stefano Morozzi | 09/2020 |
5448 | 14^84413+89 | 96749 | Lelio R Paula | 07/2016 |
5449 | (28*10^96743+71)/9 | 96744 | Serge Batalov | 12/2008 |
5450 | 13^86847+96 | 96743 | Lelio R Paula | 06/2016 |
5451 | 9*2^321336-7 | 96733 | Lelio R Paula | 08/2014 |
5452 | (209*10^96722-17)/3 | 96724 | Robert Price | 05/2017 |
5453 | 2^321237-4615 | 96702 | Yves Minet | 05/2019 |
5454 | 2^321187-1159 | 96687 | Yves Minet | 11/2012 |
5455 | 2^321182-1850081 | 96686 | Enzo Doria | 08/2015 |
5456 | 23359^13768+13768^23359 | 96680 | Hans Havermann | 06/2020 |
5457 | 2^321116-112829 | 96666 | Enzo Doria | 06/2014 |
5458 | 2^321108-109499 | 96664 | Enzo Doria | 04/2014 |
5459 | 2^321098+2793859 | 96661 | Enzo Doria | 03/2016 |
5460 | (2^321100+1170)/2 | 96661 | Stefano Morozzi | 09/2020 |
5461 | 2^321057+4097 | 96648 | Lelio R Paula | 06/2016 |
5463 | (4435*29^66081-4)/7 | 96640 | Curtis Bright | 05/2015 |
5462 | 22743^17750+17750^22743 | 96640 | Hans Havermann | 04/2020 |
5464 | 22882^16679+16679^22882 | 96612 | Hans Havermann | 02/2020 |
5465 | 23452^13163+13163^23452 | 96608 | Hans Havermann | 02/2020 |
5466 | (2^320863+666)/2 | 96590 | Stefano Morozzi | 09/2020 |
5467 | p(19849)#/2-64 | 96581 | Robert Price | 04/2017 |
5469 | 2^320817+189 | 96576 | Lelio R Paula | 12/2012 |
5468 | 2^320816-4685 | 96576 | Yves Minet | 05/2019 |
5470 | (361*10^96567-163)/9 | 96569 | Robert Price | 10/2017 |
5471 | 2^320788-110327 | 96567 | Enzo Doria | 05/2014 |
5472 | 2^320764+793 | 96560 | Lelio R Paula | 02/2013 |
5473 | (9179*2^320652-1)/221 | 96528 | Lelio R Paula | 05/2015 |
5474 | 23288^13947+13947^23288 | 96517 | Hans Havermann | 07/2020 |
5475 | 2^320616-78795 | 96516 | Lelio R Paula | 03/2016 |
5476 | 2^320612-461939 | 96514 | Enzo Doria | 07/2015 |
5477 | 10^96504+987654321 | 96505 | Robert Price | 12/2019 |
5478 | 10^96504+71887 | 96505 | Patrick De Geest | 02/2020 |
5479 | 22654^18195+18195^22654 | 96505 | Hans Havermann | 07/2020 |
5480 | 10^96504-139277 | 96504 | Patrick De Geest | 02/2020 |
5481 | 5*2^320431+7 | 96461 | Lelio R Paula | 08/2014 |
5482 | 19^75431-90 | 96458 | Lelio R Paula | 06/2016 |
5483 | (2^320370+3)/67 | 96440 | Lelio R Paula | 10/2013 |
5484 | 2^320309+1871477 | 96423 | Enzo Doria | 05/2016 |
5485 | tau(809^6028) | 96410 | Nik Lygeros / Olivier Rozier / LR team | 10/2013 |
5486 | (21*2^320252-1)/1895 | 96404 | Lelio R Paula | 02/2014 |
5487 | 2^320232-173 | 96400 | Lelio R Paula | 12/2012 |
5488 | 175^42975-2 | 96395 | Lelio R Paula | 10/2017 |
5489 | (2^320170+2718)/2 | 96381 | Stefano Morozzi | 09/2020 |
5490 | 10^96377+199911 | 96378 | Patrick De Geest | 12/2016 |
5491 | 10^96377-20001 | 96377 | Robert Price | 11/2016 |
5492 | 2^320124-2790449 | 96367 | Enzo Doria | 03/2016 |
5493 | 22488^19255+19255^22488 | 96351 | Hans Havermann | 11/2019 |
5494 | 23248^13939+13939^23248 | 96346 | Hans Havermann | 11/2019 |
5496 | 2^320043-108775 | 96343 | Enzo Doria | 04/2014 |
5495 | 24989^7168+7168^24989 | 96343 | Hans Havermann | 11/2019 |
5497 | 10^96338+424939 | 96339 | Patrick De Geest | 03/2016 |
5498 | 10^96338-9281 | 96338 | Robert Price | 09/2015 |
5499 | (3*2^320008+1)/7 | 96332 | Lelio R Paula | 09/2013 |
5500 | 25699^5596+5596^25699 | 96317 | Hans Havermann | 07/2020 |