PRP Records

Probable Primes Top 10000

(174961 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 ?
301010^100000+346579100001Robert Price04/2012
301110^100000+829767100001Robert Price05/2012
301210^100000+871899100001Robert Price05/2012
301310^100000+1475997100001Robert Price07/2012
300310^100000+1751769100001Robert Price08/2012
300410^100000+2155489100001Robert Price10/2012
300510^100000+2483527100001Robert Price12/2012
300610^100000+2503087100001Robert Price12/2012
300710^100000+2686179100001Robert Price12/2012
300810^100000+2688933100001Robert Price12/2012
300910^100000+3667159100001Robert Price08/2013
300110^100000+9528747100001Robert Smith05/2017
300210^100000+9548071100001Robert Price06/2017
301510^99999+309403100000Daniel Heuer01/2004
301410^100000-260199100000Patrick De Geest01/2010
301610^99999-5951199999Patrick De Geest07/2009
30172^332141-11307399985Enzo Doria07/2014
3018(3^209561+2)/72810125599978Lelio R Paula09/2013
30192^332085+186589799968Enzo Doria03/2016
3020(9787*2^332070-1)/93640236999959Lelio R Paula05/2015
30212^332023+19199949Lelio R Paula02/2011
30222^331938+7114999924Enzo Doria04/2016
30232^331932-7879599922Lelio R Paula09/2016
30242^331921+77199919Lelio R Paula01/2013
3025(3^209419-2)/513275599912Lelio R Paula09/2013
30262^331860-11498999900Enzo Doria05/2015
30272^331746-1165599866Lelio R Paula09/2016
302811^95891-2899861Lelio R Paula08/2016
3029(2^331694-5)/1199849Lelio R Paula10/2013
3030(3^209246+7)/6499834Lelio R Paula09/2013
303115^84866-5299811Lelio R Paula08/2016
303213^89600+3099810Lelio R Paula08/2016
30335^142772-3899794Lelio R Paula08/2016
3034(23*2^331459+1)/47599778Lelio R Paula11/2013
30352^331416-331416+199767Robert Price10/2014
30362^331256-5799718Lelio R Paula12/2012
30372^331185+73799697Lelio R Paula01/2013
3038(4*10^99693+149)/999693Robert Price03/2017
30392^331154+188052799688Enzo Doria10/2016
3040(19^77951+1)/2099679Paul Bourdelais03/2010
30412^331110+187045999675Enzo Doria05/2016
30425*2^331075+799665Lelio R Paula08/2014
3043(16*10^99656-31)/399657Robert Price03/2016
30442^330968+34599632Lelio R Paula09/2016
30462*5^142528-799624Lelio R Paula11/2014
30452^330942+7732999624Enzo Doria05/2016
304714^86914-9999615Lelio R Paula08/2016
3048(19*2^330902+1)/7799611Lelio R Paula11/2013
30492^330845+7168799595Enzo Doria04/2016
3050(23*2^330770+1)/399573Lelio R Paula11/2013
30512^330735+841599562Lelio R Paula09/2016
30522^330720+7407199557Enzo Doria04/2016
305331^66738-299531Lelio R Paula09/2013
30547*3^208567+499513Lelio R Paula08/2014
3055(13*10^99508+47)/399509Robert Price01/2017
30562^330553+77999507Lelio R Paula01/2013
305715^84606-9499505Lelio R Paula08/2016
30586^127858+4799493Lelio R Paula08/2016
30595^142337+4899490Lelio R Paula08/2016
30607^117724-2099489Lelio R Paula08/2016
3061(29*10^99474-17)/399475Erik Branger09/2014
3062(9*2^330407-1)/799463Lelio R Paula03/2014
3063(68*10^99441+7)/399443Robert Price03/2016
306446^59791-45^5979199418Jean-Louis Charton01/2013
3065(2*10^99408+529)/999408Robert Price01/2017
306653^57646-299398Lelio R Paula09/2013
30672^330165+187002599390Enzo Doria05/2016
30682^330142-15599383Lelio R Paula12/2012
30692^330088-11525999367Enzo Doria06/2015
3070(746*10^99303+1)/999305Robert Price02/2017
30713^208107+4099293Lelio R Paula08/2016
3072(5*2^329833-1)/36999288Lelio R Paula02/2014
30738*3^208093+599287Lelio R Paula08/2014
30745^142043+5699284Lelio R Paula08/2016
307522*10^99275+799277Robert Price04/2016
30762^329778+187618999274Enzo Doria07/2016
3077(10^99239-13)/399239Robert Price02/2017
30783^207987+6299236Lelio R Paula08/2016
30792^329638+4999231Lelio R Paula12/2012
30807^117413-1899226Lelio R Paula08/2016
30812^329586-45890399216Enzo Doria04/2015
30822^329553+10199206Lelio R Paula12/2012
30832^329551-11289799205Enzo Doria06/2014
3084(3^207925+7)/5099204Lelio R Paula09/2013
30856^127458-1799399182Enzo Doria03/2013
3086(46*10^99143-1)/999144Robert Price12/2014
308718^78968-306599127Enzo Doria03/2013
30882^329259+18999117Lelio R Paula12/2012
30898*10^99113+3999114Robert Price01/2017
30906^127364+7799109Lelio R Paula08/2016
30916^127285+1399047Lelio R Paula08/2016
30922^329007+7328399041Enzo Doria04/2016
30935*3^207543-899024Lelio R Paula08/2014
30942^328885+14999005Lelio R Paula12/2012
3095(2^328879-9)/11999001Lelio R Paula10/2013
30965^141618+5498987Lelio R Paula08/2016
30978*10^98982+5198983Robert Price05/2017
3098(21*2^328809-1)/770998979Lelio R Paula03/2014
30992^328794-279760198977Enzo Doria04/2016
31006^127176+598963Lelio R Paula11/2014
31012^328700-10970998949Enzo Doria04/2014
310246711!2-2^4671198916Robert Price09/2015
31039*7^117037+498909Lelio R Paula11/2014
3104(10^98890+149)/398890Serge Batalov12/2014
31052^328497-21693398888Enzo Doria05/2014
31062^328487+3276998885Lelio R Paula08/2016
31073^207250-11235898884Enzo Doria06/2014
310813^88754-9098867Lelio R Paula08/2016
31092^328406+70998861Lelio R Paula02/2013
3110(17*2^328413-1)/1617398860Lelio R Paula03/2014
31117^116976+7698857Lelio R Paula08/2016
31122^328335+115598839Lelio R Paula08/2016
3113(3*2^328311+1)/598832Lelio R Paula11/2013
3114287^40210+40210^28798832Norbert Schneider11/2014
3115(2^328284+9)/132598821Lelio R Paula10/2013
3116(21*2^328258+1)/212598814Lelio R Paula11/2013
311765^54491+4898788Lelio R Paula04/2016
31183^207042+9898785Lelio R Paula08/2016
31193^206977-11275698754Enzo Doria07/2014
31207^116846-5098747Lelio R Paula08/2016
31212^327967-2863598728Lelio R Paula08/2016
31226^126850-4798709Lelio R Paula08/2016
31238*6^126830-798694Lelio R Paula11/2014
312411^94770-27098693Enzo Doria08/2012
31252^327832+4398688Lelio R Paula12/2012
31262^327795+76198677Lelio R Paula02/2013
312710^98669+14741198670Patrick De Geest11/2016
312910^98669-9^(98669-1)98669Robert Price05/2016
312810^98669-10524998669Patrick De Geest11/2016
31302^327671-10980198639Enzo Doria04/2014
31315^141090-1498618Lelio R Paula08/2016
313220^75799+4798617Lelio R Paula08/2016
31332^327515-101798592Lelio R Paula08/2016
31346^126692+9768198586Mike Oakes04/2011
31352^327467-74198578Lelio R Paula08/2016
3136(2^327329+9)/1998535Lelio R Paula10/2013
31377^116577-6698519Lelio R Paula08/2016
3138(3*2^327250+1)/798512Lelio R Paula11/2013
3139(19*2^327192+1)/27598494Lelio R Paula11/2013
31402^327162-6694598486Lelio R Paula08/2016
31414*10^98472-398473Erik Branger11/2013
3142(6883*2^327047-1)/7798453Lelio R Paula05/2015
3143(71*10^98446+1)/998447Serge Batalov11/2010
314413^88363+9498432Lelio R Paula08/2016
314548^58543-47^5854398425Jean-Louis Charton11/2005
31466^126481+4198422Lelio R Paula08/2016
314778*10^98413-798415Robert Price05/2017
31487^116416+4698383Lelio R Paula08/2016
31497^116407-2498376Lelio R Paula07/2016
31512^326782-186067198372Enzo Doria03/2016
315017^79948+5898372Lelio R Paula08/2016
31523^206143-9898356Lelio R Paula08/2016
31538*5^140705+798350Lelio R Paula11/2014
31542^326585+1198312Lelio R Paula12/2012
31552^326582-45916198311Enzo Doria05/2015
3156(2^326548+9)/598301Lelio R Paula10/2013
31572^326538+7165998298Enzo Doria04/2016
315815^83575-5898292Lelio R Paula08/2016
315910^98288+398289Robert Price03/2011
316010^98288-11701798288Patrick De Geest11/2011
31612^326421-279757398263Enzo Doria04/2016
31622^326401+1609598257Lelio R Paula07/2016
31637^116240-116240^798235Norbert Schneider05/2017
316417^79826-7898222Lelio R Paula08/2016
31652^326268-80998217Yves Minet04/2011
316615^83496-7698199Lelio R Paula08/2016
3167(10223*2^326179+1)/612598190Lelio R Paula07/2014
31689*5^140471-498186Lelio R Paula11/2014
31692^326069-238398157Yves Minet10/2013
31702^325973+118598128Lelio R Paula07/2016
3171(25*2^325949-1)/1798121Lelio R Paula02/2014
31722^325945-184726998120Enzo Doria07/2015
31732^325866+1598096Lelio R Paula12/2012
31742^325765+197430598066Enzo Doria06/2016
31752^325733-5869598056Lelio R Paula07/2016
31762^325717-364598051Lelio R Paula07/2016
3177(23*2^325583-1)/2198011Lelio R Paula02/2014
3178(7*10^98007-13)/398008Robert Price06/2016
31792^325512-45995997989Enzo Doria05/2015
3180(3^205354-8)/1797978Lelio R Paula09/2013
31812^325433+7681797966Enzo Doria05/2016
31822^325390-10906197953Enzo Doria04/2014
318313^87921+2497940Lelio R Paula08/2016
3184961^32831-960^3283197926Jean-Louis Charton02/2011
31852^325215+1290997900Lelio R Paula07/2016
31867*10^97874-6997875Robert Price01/2017
3187(17^79537+5^79537)/2297865Robert Price06/2013
318815^83212+2297865Lelio R Paula08/2016
31892^325087-10905797861Enzo Doria04/2014
31902^325074+187065797858Enzo Doria05/2016
31922^325066-211197855Yves Minet08/2013
3191CopelandErdos(97855)97855Eric W. Weisstein10/2015
319318^77944-8997841Lelio R Paula07/2016
31946^125720-1766397830Enzo Doria02/2013
31952^324972-206997827Yves Minet05/2013
31962^324944-278831997818Enzo Doria03/2016
31984*10^97799-997800Erik Branger11/2013
31972^324882+57729457597800Lelio R Paula09/2016
31992^324863-186792197794Enzo Doria04/2016
32006^125662-1847397785Enzo Doria03/2013
320112^90604+1197779Lelio R Paula07/2016
32025^139830+2497737Lelio R Paula04/2016
32032^324612+115597718Lelio R Paula07/2016
320419^76404-4497702Lelio R Paula07/2016
32052^324505-298397686Yves Minet04/2011
3206(31*2^324496-1)/4597683Lelio R Paula02/2014
32076^125488-1784397649Enzo Doria02/2013
32087^115515-297622Lelio R Paula09/2013
32096^125418-597595Lelio R Paula11/2014
32102^324076+115597557Lelio R Paula07/2016
3211(2^324074+9)/1397555Lelio R Paula10/2013
3212(55459*2^323993+1)/2197536Lelio R Paula07/2014
321313^87557-12^8755797534Jean-Louis Charton12/2008
32142^323946+7393997518Enzo Doria04/2016
32152^323937+186694797515Enzo Doria03/2016
32166^125290-1853397495Enzo Doria03/2013
32172^323845+10197488Lelio R Paula12/2012
321818^77662+6597487Lelio R Paula07/2016
32192^323772+7677197466Enzo Doria05/2016
32202^323765-11221397463Enzo Doria06/2014
32212^323720-655597450Lelio R Paula07/2016
32222^323694-186040197442Enzo Doria03/2016
322320^74886+397429Lelio R Paula06/2016
32253*10^97399+7397400Robert Price04/2016
32247^115252-5097400Lelio R Paula07/2016
3226224737#+39358197389Nicolas PALAU12/2016
3227(26*10^97353+31)/397354Robert Price07/2016
322861^54517-60^5451797331Jean-Louis Charton09/2005
32296^125021-8597286Lelio R Paula08/2016
32302^323164-4735597283Lelio R Paula07/2016
3231(3^203902+4)/3605101515797276Lelio R Paula09/2013
32322^323054-655597249Lelio R Paula07/2016
32339*10^97247-2997248Robert Price05/2017
3234(31*10^97242+41)/997243Robert Price04/2015
3235GoldenRatioPrime[97241]97241Eric W. Weisstein06/2009
323612^90098-4197233Lelio R Paula07/2016
32372^322928-21692997212Enzo Doria05/2014
3238(7*2^322896-1)/5797201Lelio R Paula02/2014
3239(2^322897+5)/314610748997193Lelio R Paula10/2013
32402^322725+7576197150Enzo Doria04/2016
3241(13*2^322686+1)/11997138Lelio R Paula11/2013
3242(41*10^97085+373)/997086Robert Price04/2017
32432^322413+7797056Lelio R Paula12/2012
32442^322406+17797054Lelio R Paula12/2012
3245(14*10^97044+31)/997045Robert Price02/2015
32462^322302+25525597023Lelio R Paula07/2016
32472^322196-11309396991Enzo Doria07/2014
32482^322000-186146996932Enzo Doria03/2016
32492^321971-11274796923Enzo Doria06/2014
325011^93062-9296915Lelio R Paula06/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 22 2017 08:34 (Time in France)

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