PRP Records

Probable Primes Top 10000

(259919 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 ?
4252(3*2^328311+1)/598832Lelio R Paula11/2013
4251287^40210+40210^28798832Norbert Schneider11/2014
4253(2^328284+9)/132598821Lelio R Paula10/2013
4254(21*2^328258+1)/212598814Lelio R Paula11/2013
425565^54491+4898788Lelio R Paula04/2016
42563^207042+9898785Lelio R Paula08/2016
42573^206977-11275698754Enzo Doria07/2014
42587^116846-5098747Lelio R Paula08/2016
42592^327967-2863598728Lelio R Paula08/2016
4260707^34642+34642^70798710Norbert Schneider12/2017
42616^126850-4798709Lelio R Paula08/2016
42628*6^126830-798694Lelio R Paula11/2014
426311^94770-27098693Enzo Doria08/2012
42642^327832+4398688Lelio R Paula12/2012
42652^327795+76198677Lelio R Paula02/2013
426610^98669+14741198670Patrick De Geest11/2016
426810^98669-9^(98669-1)98669Robert Price05/2016
426710^98669-10524998669Patrick De Geest11/2016
42692^327671-10980198639Enzo Doria04/2014
427024398^11037+11037^2439898638Hans Havermann10/2019
42715^141090-1498618Lelio R Paula08/2016
427220^75799+4798617Lelio R Paula08/2016
42732^327515-101798592Lelio R Paula08/2016
42746^126692+9768198586Mike Oakes04/2011
42752^327467-74198578Lelio R Paula08/2016
4276(2^327329+9)/1998535Lelio R Paula10/2013
42777^116577-6698519Lelio R Paula08/2016
4279(3*2^327250+1)/798512Lelio R Paula11/2013
427823220^17479+17479^2322098512Hans Havermann03/2020
4280(19*2^327192+1)/27598494Lelio R Paula11/2013
42812^327162-6694598486Lelio R Paula08/2016
428230139^1852+1852^3013998484Hans Havermann02/2020
428323182^17703+17703^2318298479Hans Havermann01/2020
42844*10^98472-398473Erik Branger11/2013
428526167^5794+5794^2616798466Hans Havermann01/2020
4286(6883*2^327047-1)/7798453Lelio R Paula05/2015
4287(71*10^98446+1)/998447Serge Batalov11/2010
428813^88363+9498432Lelio R Paula08/2016
428948^58543-47^5854398425Jean-Louis Charton11/2005
42906^126481+4198422Lelio R Paula08/2016
429178*10^98413-798415Robert Price05/2017
42927^116416+4698383Lelio R Paula08/2016
42937^116407-2498376Lelio R Paula07/2016
4294439^37228+37228^43998374Norbert Schneider08/2018
42962^326782-186067198372Enzo Doria03/2016
429517^79948+5898372Lelio R Paula08/2016
42973^206143-9898356Lelio R Paula08/2016
42988*5^140705+798350Lelio R Paula11/2014
42992^326585+1198312Lelio R Paula12/2012
43002^326582-45916198311Enzo Doria05/2015
4302(2^326548+9)/598301Lelio R Paula10/2013
4301(2^326549+18)/1098301Stefano Morozzi03/2020
43032^326538+7165998298Enzo Doria04/2016
430415^83575-5898292Lelio R Paula08/2016
430510^98288+398289Robert Price03/2011
430610^98288-11701798288Patrick De Geest11/2011
4307(44*10^98284-719)/998285Robert Price12/2017
430823466^15419+15419^2346698277Hans Havermann02/2020
43092^326421-279757398263Enzo Doria04/2016
43102^326401+1609598257Lelio R Paula07/2016
43117^116240-116240^798235Norbert Schneider05/2017
431217^79826-7898222Lelio R Paula08/2016
43132^326268-80998217Yves Minet04/2011
431422659^21590+21590^2265998210Hans Havermann10/2019
4315(418*10^98199+23)/998201Robert Price08/2017
431612*10^98198-798200Robert Price11/2017
431715^83496-7698199Lelio R Paula08/2016
4318(10223*2^326179+1)/612598190Lelio R Paula07/2014
43199*5^140471-498186Lelio R Paula11/2014
43202^326069-238398157Yves Minet10/2013
43212^325973+118598128Lelio R Paula07/2016
4322(25*2^325949-1)/1798121Lelio R Paula02/2014
43232^325945-184726998120Enzo Doria07/2015
43248*10^98111-6798112Robert Price10/2017
43252^325866+1598096Lelio R Paula12/2012
432622591^21952+21952^2259198079Hans Havermann02/2020
43272^325765+197430598066Enzo Doria06/2016
43282^325733-5869598056Lelio R Paula07/2016
43292^325717-364598051Lelio R Paula07/2016
433023968^12293+12293^2396898021Hans Havermann11/2019
4331(23*2^325583-1)/2198011Lelio R Paula02/2014
4332(7*10^98007-13)/398008Robert Price06/2016
43332^325512-45995997989Enzo Doria05/2015
4334(3^205354-8)/1797978Lelio R Paula09/2013
43352^325433+7681797966Enzo Doria05/2016
43365*10^97963+8197964Robert Price08/2017
43372^325390-10906197953Enzo Doria04/2014
433813^87921+2497940Lelio R Paula08/2016
4339961^32831-960^3283197926Jean-Louis Charton02/2011
43402^325215+1290997900Lelio R Paula07/2016
43417*10^97874-6997875Robert Price01/2017
4343(17^79537+5^79537)/2297865Robert Price06/2013
434215^83212+2297865Lelio R Paula08/2016
43442^325087-10905797861Enzo Doria04/2014
43452^325074+187065797858Enzo Doria05/2016
43472^325066-211197855Yves Minet08/2013
4346CopelandErdos(97855)97855Eric W. Weisstein10/2015
434826660^4677+4677^2666097842Hans Havermann12/2019
434918^77944-8997841Lelio R Paula07/2016
4350119^47136+11897833Norbert Schneider09/2018
43516^125720-1766397830Enzo Doria02/2013
43522^324972-206997827Yves Minet05/2013
43532^324958-469197823Yves Minet05/2019
43542^324944-278831997818Enzo Doria03/2016
435522845^19112+19112^2284597807Hans Havermann10/2019
43574*10^97799-997800Erik Branger11/2013
43562^324882+57729457597800Lelio R Paula09/2016
43582^324863-186792197794Enzo Doria04/2016
43596^125662-1847397785Enzo Doria03/2013
436012^90604+1197779Lelio R Paula07/2016
43615^139830+2497737Lelio R Paula04/2016
43622^324612+115597718Lelio R Paula07/2016
436319^76404-4497702Lelio R Paula07/2016
43642^324505-298397686Yves Minet04/2011
4365(144^45259+1)/14597684Paul Bourdelais08/2019
4366(31*2^324496-1)/4597683Lelio R Paula02/2014
43676^125488-1784397649Enzo Doria02/2013
43687^115515-297622Lelio R Paula09/2013
4369(89^50069-1)/8897603Paul Bourdelais08/2017
43706^125418-597595Lelio R Paula11/2014
43712^324076+115597557Lelio R Paula07/2016
4372(2^324074+9)/1397555Lelio R Paula10/2013
4373(55459*2^323993+1)/2197536Lelio R Paula07/2014
437413^87557-12^8755797534Jean-Louis Charton12/2008
43752^323946+7393997518Enzo Doria04/2016
43762^323937+186694797515Enzo Doria03/2016
43776^125290-1853397495Enzo Doria03/2013
43782^323845+10197488Lelio R Paula12/2012
437918^77662+6597487Lelio R Paula07/2016
43802^323772+7677197466Enzo Doria05/2016
43812^323765-11221397463Enzo Doria06/2014
438222730^19389+19389^2273097457Hans Havermann02/2020
43832^323720-655597450Lelio R Paula07/2016
43842^323694-186040197442Enzo Doria03/2016
438520^74886+397429Lelio R Paula06/2016
438624476^9561+9561^2447697427Hans Havermann01/2020
43883*10^97399+7397400Robert Price04/2016
43877^115252-5097400Lelio R Paula07/2016
4389224737#+39358197389Nicolas PALAU12/2016
4390(26*10^97353+31)/397354Robert Price07/2016
439161^54517-60^5451797331Jean-Louis Charton09/2005
4392(38*10^97329+187)/997330Robert Price11/2017
439386455!4+897319Robert Price09/2019
4394p(19982)#/2-102497293Robert Price09/2017
43956^125021-8597286Lelio R Paula08/2016
43962^323164-4735597283Lelio R Paula07/2016
4397(3^203902+4)/3605101515797276Lelio R Paula09/2013
43982^323054-655597249Lelio R Paula07/2016
439922822^18247+18247^2282297249Hans Havermann02/2020
44009*10^97247-2997248Robert Price05/2017
440124382^9735+9735^2438297244Hans Havermann02/2020
4402(31*10^97242+41)/997243Robert Price04/2015
4403GoldenRatioPrime[97241]97241Eric W. Weisstein06/2009
440412^90098-4197233Lelio R Paula07/2016
44052^322928-21692997212Enzo Doria05/2014
4406(7*2^322896-1)/5797201Lelio R Paula02/2014
4407(2^322897+5)/314610748997193Lelio R Paula10/2013
44082^322725+7576197150Enzo Doria04/2016
4409(13*2^322686+1)/11997138Lelio R Paula11/2013
4410(41*10^97085+373)/997086Robert Price04/2017
44112^322413+7797056Lelio R Paula12/2012
44122^322406+17797054Lelio R Paula12/2012
4413(14*10^97044+31)/997045Robert Price02/2015
44142^322302+25525597023Lelio R Paula07/2016
44152^322196-11309396991Enzo Doria07/2014
44162^322000-186146996932Enzo Doria03/2016
44172^321971-11274796923Enzo Doria06/2014
441811^93062-9296915Lelio R Paula06/2016
4419(11*2^321841-7)/1596884Renaud Lifchitz03/2011
44203^203051+3496880Lelio R Paula05/2016
44212*10^96867-5196868Robert Price11/2017
4422(64*10^96863-1)/2796864Serge Batalov05/2010
44232^321716-278693996847Enzo Doria03/2016
442422496^20181+20181^2249696844Hans Havermann03/2020
44262^321701-11305396842Enzo Doria07/2014
44252^321700-2863596842Lelio R Paula06/2016
4427(5*2^321691-1)/2796838Lelio R Paula02/2014
44286^124433-12443396828Robert Price01/2014
44292^321631+6996821Lelio R Paula12/2012
4430(13*2^321606+1)/11996813Lelio R Paula11/2013
4431(46*10^96798-1)/996799Serge Batalov10/2014
4432(59*10^96798+31)/996799Robert Price09/2015
4433223319#+23122396790Makoto Morimoto02/2016
44342^321519-2863596787Lelio R Paula06/2016
44352^321487-186723796778Enzo Doria03/2016
44362^321461-6396770Lelio R Paula12/2012
44372^321439+12396763Lelio R Paula12/2012
44382^321434+70996762Lelio R Paula02/2013
443914^84413+8996749Lelio R Paula07/2016
4440(28*10^96743+71)/996744Serge Batalov12/2008
444113^86847+9696743Lelio R Paula06/2016
44429*2^321336-796733Lelio R Paula08/2014
4443(209*10^96722-17)/396724Robert Price05/2017
44442^321237-461596702Yves Minet05/2019
44452^321187-115996687Yves Minet11/2012
44462^321182-185008196686Enzo Doria08/2015
44472^321116-11282996666Enzo Doria06/2014
44482^321108-10949996664Enzo Doria04/2014
44492^321098+279385996661Enzo Doria03/2016
44502^321057+409796648Lelio R Paula06/2016
4451(4435*29^66081-4)/796640Curtis Bright05/2015
445222882^16679+16679^2288296612Hans Havermann02/2020
445323452^13163+13163^2345296608Hans Havermann02/2020
4454p(19849)#/2-6496581Robert Price04/2017
44562^320817+18996576Lelio R Paula12/2012
44552^320816-468596576Yves Minet05/2019
4457(361*10^96567-163)/996569Robert Price10/2017
44582^320788-11032796567Enzo Doria05/2014
44592^320764+79396560Lelio R Paula02/2013
4460(9179*2^320652-1)/22196528Lelio R Paula05/2015
44612^320616-7879596516Lelio R Paula03/2016
44622^320612-46193996514Enzo Doria07/2015
446310^96504+98765432196505Robert Price12/2019
446410^96504+7188796505Patrick De Geest02/2020
446510^96504-13927796504Patrick De Geest02/2020
44665*2^320431+796461Lelio R Paula08/2014
446719^75431-9096458Lelio R Paula06/2016
4468(2^320370+3)/6796440Lelio R Paula10/2013
44692^320309+187147796423Enzo Doria05/2016
4470tau(809^6028)96410Nik Lygeros / Olivier Rozier / LR team10/2013
4471(21*2^320252-1)/189596404Lelio R Paula02/2014
44722^320232-17396400Lelio R Paula12/2012
4473175^42975-296395Lelio R Paula10/2017
447410^96377+19991196378Patrick De Geest12/2016
447510^96377-2000196377Robert Price11/2016
44762^320124-279044996367Enzo Doria03/2016
447722488^19255+19255^2248896351Hans Havermann11/2019
447823248^13939+13939^2324896346Hans Havermann11/2019
44802^320043-10877596343Enzo Doria04/2014
447924989^7168+7168^2498996343Hans Havermann11/2019
448110^96338+42493996339Patrick De Geest03/2016
448210^96338-928196338Robert Price09/2015
4483(3*2^320008+1)/796332Lelio R Paula09/2013
44842^319838+425796281Lelio R Paula03/2016
44852^319830-1699596279Lelio R Paula03/2016
44866^123713+14396268Lelio R Paula05/2016
4487(28*10^96265-97)/396266Robert Price07/2016
4488103^47825-10296264Norbert Schneider10/2016
44892^319713-8196244Lelio R Paula11/2012
4490(55459*2^319706+1)/2016796242Lelio R Paula07/2014
449112^89153-4396213Lelio R Paula06/2016
4492(2*10^96195-59)/396195Robert Price05/2017
44932^319545+14796193Lelio R Paula11/2012
449423357^13128+13128^2335796189Hans Havermann02/2020
449525952^5073+5073^2595296160Hans Havermann12/2019
4496(50^56597+1)/5196155Robert Price03/2014
449722313^20374+20374^2231396149Hans Havermann12/2019
449822279^20668+20668^2227996141Hans Havermann11/2019
4499(41*10^96137-59)/996138Robert Price10/2017
45002^319353-11034396135Enzo Doria05/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 29 2020 17:41 (Time in France)

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