PRP Records

Probable Primes Top 10000

(218736 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 (> 30000) Who ? When ?
3501(10^99239-13)/399239Robert Price02/2017
35023^207987+6299236Lelio R Paula08/2016
35032^329638+4999231Lelio R Paula12/2012
35047^117413-1899226Lelio R Paula08/2016
35052^329586-45890399216Enzo Doria04/2015
35062^329553+10199206Lelio R Paula12/2012
35072^329551-11289799205Enzo Doria06/2014
3508(3^207925+7)/5099204Lelio R Paula09/2013
35096^127458-1799399182Enzo Doria03/2013
351027197^4428+4428^2719799166Hans Havermann10/2017
3511(46*10^99143-1)/999144Robert Price12/2014
35127*10^99133+6999134Robert Price10/2017
351318^78968-306599127Enzo Doria03/2013
351425927^6654+6654^2592799122Hans Havermann10/2017
35152^329259+18999117Lelio R Paula12/2012
35168*10^99113+3999114Robert Price01/2017
35176^127364+7799109Lelio R Paula08/2016
35186^127285+1399047Lelio R Paula08/2016
3519(228581#+235862)/(2^3*11*71*151)99044Makoto Morimoto10/2017
35202^329007+7328399041Enzo Doria04/2016
35215*3^207543-899024Lelio R Paula08/2014
35222^328885+14999005Lelio R Paula12/2012
352323392^17075+17075^2339299004Hans Havermann09/2017
3524(2^328879-9)/11999001Lelio R Paula10/2013
35255^141618+5498987Lelio R Paula08/2016
35268*10^98982+5198983Robert Price05/2017
3527(21*2^328809-1)/770998979Lelio R Paula03/2014
35282^328794-279760198977Enzo Doria04/2016
35296^127176+598963Lelio R Paula11/2014
353024262^11989+11989^2426298960Hans Havermann09/2017
35312^328700-10970998949Enzo Doria04/2014
353246711!2-2^4671198916Robert Price09/2015
35339*7^117037+498909Lelio R Paula11/2014
3534(10^98890+149)/398890Serge Batalov12/2014
353522775^21978+21978^2277598889Hans Havermann08/2017
35362^328497-21693398888Enzo Doria05/2014
35372^328487+3276998885Lelio R Paula08/2016
35383^207250-11235898884Enzo Doria06/2014
353913^88754-9098867Lelio R Paula08/2016
35402^328406+70998861Lelio R Paula02/2013
3541(17*2^328413-1)/1617398860Lelio R Paula03/2014
35427^116976+7698857Lelio R Paula08/2016
35432^328335+115598839Lelio R Paula08/2016
3544(3*2^328311+1)/598832Lelio R Paula11/2013
3545287^40210+40210^28798832Norbert Schneider11/2014
3546(2^328284+9)/132598821Lelio R Paula10/2013
3547(21*2^328258+1)/212598814Lelio R Paula11/2013
354865^54491+4898788Lelio R Paula04/2016
35493^207042+9898785Lelio R Paula08/2016
35503^206977-11275698754Enzo Doria07/2014
35517^116846-5098747Lelio R Paula08/2016
35522^327967-2863598728Lelio R Paula08/2016
3553707^34642+34642^70798710Norbert Schneider12/2017
35546^126850-4798709Lelio R Paula08/2016
35558*6^126830-798694Lelio R Paula11/2014
355611^94770-27098693Enzo Doria08/2012
35572^327832+4398688Lelio R Paula12/2012
35582^327795+76198677Lelio R Paula02/2013
355910^98669+14741198670Patrick De Geest11/2016
356110^98669-9^(98669-1)98669Robert Price05/2016
356010^98669-10524998669Patrick De Geest11/2016
35622^327671-10980198639Enzo Doria04/2014
35635^141090-1498618Lelio R Paula08/2016
356420^75799+4798617Lelio R Paula08/2016
35652^327515-101798592Lelio R Paula08/2016
35666^126692+9768198586Mike Oakes04/2011
35672^327467-74198578Lelio R Paula08/2016
3568(2^327329+9)/1998535Lelio R Paula10/2013
35697^116577-6698519Lelio R Paula08/2016
3570(3*2^327250+1)/798512Lelio R Paula11/2013
3571(19*2^327192+1)/27598494Lelio R Paula11/2013
35722^327162-6694598486Lelio R Paula08/2016
35734*10^98472-398473Erik Branger11/2013
3574(6883*2^327047-1)/7798453Lelio R Paula05/2015
3575(71*10^98446+1)/998447Serge Batalov11/2010
357613^88363+9498432Lelio R Paula08/2016
357748^58543-47^5854398425Jean-Louis Charton11/2005
35786^126481+4198422Lelio R Paula08/2016
357978*10^98413-798415Robert Price05/2017
35807^116416+4698383Lelio R Paula08/2016
35817^116407-2498376Lelio R Paula07/2016
35832^326782-186067198372Enzo Doria03/2016
358217^79948+5898372Lelio R Paula08/2016
35843^206143-9898356Lelio R Paula08/2016
35858*5^140705+798350Lelio R Paula11/2014
35862^326585+1198312Lelio R Paula12/2012
35872^326582-45916198311Enzo Doria05/2015
3588(2^326548+9)/598301Lelio R Paula10/2013
35892^326538+7165998298Enzo Doria04/2016
359015^83575-5898292Lelio R Paula08/2016
359110^98288+398289Robert Price03/2011
359210^98288-11701798288Patrick De Geest11/2011
3593(44*10^98284-719)/998285Robert Price12/2017
35942^326421-279757398263Enzo Doria04/2016
35952^326401+1609598257Lelio R Paula07/2016
35967^116240-116240^798235Norbert Schneider05/2017
359717^79826-7898222Lelio R Paula08/2016
35982^326268-80998217Yves Minet04/2011
3599(418*10^98199+23)/998201Robert Price08/2017
360012*10^98198-798200Robert Price11/2017
360115^83496-7698199Lelio R Paula08/2016
3602(10223*2^326179+1)/612598190Lelio R Paula07/2014
36039*5^140471-498186Lelio R Paula11/2014
36042^326069-238398157Yves Minet10/2013
36052^325973+118598128Lelio R Paula07/2016
3606(25*2^325949-1)/1798121Lelio R Paula02/2014
36072^325945-184726998120Enzo Doria07/2015
36088*10^98111-6798112Robert Price10/2017
36092^325866+1598096Lelio R Paula12/2012
36102^325765+197430598066Enzo Doria06/2016
36112^325733-5869598056Lelio R Paula07/2016
36122^325717-364598051Lelio R Paula07/2016
3613(23*2^325583-1)/2198011Lelio R Paula02/2014
3614(7*10^98007-13)/398008Robert Price06/2016
36152^325512-45995997989Enzo Doria05/2015
3616(3^205354-8)/1797978Lelio R Paula09/2013
36172^325433+7681797966Enzo Doria05/2016
36185*10^97963+8197964Robert Price08/2017
36192^325390-10906197953Enzo Doria04/2014
362013^87921+2497940Lelio R Paula08/2016
3621961^32831-960^3283197926Jean-Louis Charton02/2011
36222^325215+1290997900Lelio R Paula07/2016
36237*10^97874-6997875Robert Price01/2017
3624(17^79537+5^79537)/2297865Robert Price06/2013
362515^83212+2297865Lelio R Paula08/2016
36262^325087-10905797861Enzo Doria04/2014
36272^325074+187065797858Enzo Doria05/2016
36292^325066-211197855Yves Minet08/2013
3628CopelandErdos(97855)97855Eric W. Weisstein10/2015
363018^77944-8997841Lelio R Paula07/2016
36316^125720-1766397830Enzo Doria02/2013
36322^324972-206997827Yves Minet05/2013
36332^324944-278831997818Enzo Doria03/2016
36354*10^97799-997800Erik Branger11/2013
36342^324882+57729457597800Lelio R Paula09/2016
36362^324863-186792197794Enzo Doria04/2016
36376^125662-1847397785Enzo Doria03/2013
363812^90604+1197779Lelio R Paula07/2016
36395^139830+2497737Lelio R Paula04/2016
36402^324612+115597718Lelio R Paula07/2016
364119^76404-4497702Lelio R Paula07/2016
36422^324505-298397686Yves Minet04/2011
3643(31*2^324496-1)/4597683Lelio R Paula02/2014
36446^125488-1784397649Enzo Doria02/2013
36457^115515-297622Lelio R Paula09/2013
3646(89^50069-1)/8897603Paul Bourdelais08/2017
36476^125418-597595Lelio R Paula11/2014
36482^324076+115597557Lelio R Paula07/2016
3649(2^324074+9)/1397555Lelio R Paula10/2013
3650(55459*2^323993+1)/2197536Lelio R Paula07/2014
365113^87557-12^8755797534Jean-Louis Charton12/2008
36522^323946+7393997518Enzo Doria04/2016
36532^323937+186694797515Enzo Doria03/2016
36546^125290-1853397495Enzo Doria03/2013
36552^323845+10197488Lelio R Paula12/2012
365618^77662+6597487Lelio R Paula07/2016
36572^323772+7677197466Enzo Doria05/2016
36582^323765-11221397463Enzo Doria06/2014
36592^323720-655597450Lelio R Paula07/2016
36602^323694-186040197442Enzo Doria03/2016
366120^74886+397429Lelio R Paula06/2016
36633*10^97399+7397400Robert Price04/2016
36627^115252-5097400Lelio R Paula07/2016
3664224737#+39358197389Nicolas PALAU12/2016
3665(26*10^97353+31)/397354Robert Price07/2016
366661^54517-60^5451797331Jean-Louis Charton09/2005
3667(38*10^97329+187)/997330Robert Price11/2017
3668p(19982)#/2-102497293Robert Price09/2017
36696^125021-8597286Lelio R Paula08/2016
36702^323164-4735597283Lelio R Paula07/2016
3671(3^203902+4)/3605101515797276Lelio R Paula09/2013
36722^323054-655597249Lelio R Paula07/2016
36739*10^97247-2997248Robert Price05/2017
3674(31*10^97242+41)/997243Robert Price04/2015
3675GoldenRatioPrime[97241]97241Eric W. Weisstein06/2009
367612^90098-4197233Lelio R Paula07/2016
36772^322928-21692997212Enzo Doria05/2014
3678(7*2^322896-1)/5797201Lelio R Paula02/2014
3679(2^322897+5)/314610748997193Lelio R Paula10/2013
36802^322725+7576197150Enzo Doria04/2016
3681(13*2^322686+1)/11997138Lelio R Paula11/2013
3682(41*10^97085+373)/997086Robert Price04/2017
36832^322413+7797056Lelio R Paula12/2012
36842^322406+17797054Lelio R Paula12/2012
3685(14*10^97044+31)/997045Robert Price02/2015
36862^322302+25525597023Lelio R Paula07/2016
36872^322196-11309396991Enzo Doria07/2014
36882^322000-186146996932Enzo Doria03/2016
36892^321971-11274796923Enzo Doria06/2014
369011^93062-9296915Lelio R Paula06/2016
3691(11*2^321841-7)/1596884Renaud Lifchitz03/2011
36923^203051+3496880Lelio R Paula05/2016
36932*10^96867-5196868Robert Price11/2017
3694(64*10^96863-1)/2796864Serge Batalov05/2010
36952^321716-278693996847Enzo Doria03/2016
36972^321701-11305396842Enzo Doria07/2014
36962^321700-2863596842Lelio R Paula06/2016
3698(5*2^321691-1)/2796838Lelio R Paula02/2014
36996^124433-12443396828Robert Price01/2014
37002^321631+6996821Lelio R Paula12/2012
3701(13*2^321606+1)/11996813Lelio R Paula11/2013
3702(46*10^96798-1)/996799Serge Batalov10/2014
3703(59*10^96798+31)/996799Robert Price09/2015
3704223319#+23122396790Makoto Morimoto02/2016
37052^321519-2863596787Lelio R Paula06/2016
37062^321487-186723796778Enzo Doria03/2016
37072^321461-6396770Lelio R Paula12/2012
37082^321439+12396763Lelio R Paula12/2012
37092^321434+70996762Lelio R Paula02/2013
371014^84413+8996749Lelio R Paula07/2016
3711(28*10^96743+71)/996744Serge Batalov12/2008
371213^86847+9696743Lelio R Paula06/2016
37139*2^321336-796733Lelio R Paula08/2014
3714(209*10^96722-17)/396724Robert Price05/2017
37152^321187-115996687Yves Minet11/2012
37162^321182-185008196686Enzo Doria08/2015
37172^321116-11282996666Enzo Doria06/2014
37182^321108-10949996664Enzo Doria04/2014
37192^321098+279385996661Enzo Doria03/2016
37202^321057+409796648Lelio R Paula06/2016
3721(4435*29^66081-4)/796640Curtis Bright05/2015
3722p(19849)#/2-6496581Robert Price04/2017
37232^320817+18996576Lelio R Paula12/2012
3724(361*10^96567-163)/996569Robert Price10/2017
37252^320788-11032796567Enzo Doria05/2014
37262^320764+79396560Lelio R Paula02/2013
3727(9179*2^320652-1)/22196528Lelio R Paula05/2015
37282^320616-7879596516Lelio R Paula03/2016
37292^320612-46193996514Enzo Doria07/2015
37305*2^320431+796461Lelio R Paula08/2014
373119^75431-9096458Lelio R Paula06/2016
3732(2^320370+3)/6796440Lelio R Paula10/2013
37332^320309+187147796423Enzo Doria05/2016
3734tau(809^6028)96410Nik Lygeros / Olivier Rozier / LR team10/2013
3735(21*2^320252-1)/189596404Lelio R Paula02/2014
37362^320232-17396400Lelio R Paula12/2012
3737175^42975-296395Lelio R Paula10/2017
373810^96377+19991196378Patrick De Geest12/2016
373910^96377-2000196377Robert Price11/2016
37402^320124-279044996367Enzo Doria03/2016
37412^320043-10877596343Enzo Doria04/2014
374210^96338+42493996339Patrick De Geest03/2016
374310^96338-928196338Robert Price09/2015
3744(3*2^320008+1)/796332Lelio R Paula09/2013
37452^319838+425796281Lelio R Paula03/2016
37462^319830-1699596279Lelio R Paula03/2016
37476^123713+14396268Lelio R Paula05/2016
3748(28*10^96265-97)/396266Robert Price07/2016
3749103^47825-10296264Norbert Schneider10/2016
37502^319713-8196244Lelio R Paula11/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 14 2018 21:45 (Time in France)

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