PRP Records

Probable Primes Top 10000

(173006 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 ?
30012^331938+7114999924Enzo Doria04/2016
30022^331932-7879599922Lelio R Paula09/2016
30032^331921+77199919Lelio R Paula01/2013
3004(3^209419-2)/513275599912Lelio R Paula09/2013
30052^331860-11498999900Enzo Doria05/2015
30062^331746-1165599866Lelio R Paula09/2016
300711^95891-2899861Lelio R Paula08/2016
3008(2^331694-5)/1199849Lelio R Paula10/2013
3009(3^209246+7)/6499834Lelio R Paula09/2013
301015^84866-5299811Lelio R Paula08/2016
301113^89600+3099810Lelio R Paula08/2016
30125^142772-3899794Lelio R Paula08/2016
3013(23*2^331459+1)/47599778Lelio R Paula11/2013
30142^331416-331416+199767Robert Price10/2014
30152^331256-5799718Lelio R Paula12/2012
30162^331185+73799697Lelio R Paula01/2013
3017(4*10^99693+149)/999693Robert Price03/2017
30182^331154+188052799688Enzo Doria10/2016
3019(19^77951+1)/2099679Paul Bourdelais03/2010
30202^331110+187045999675Enzo Doria05/2016
30215*2^331075+799665Lelio R Paula08/2014
3022(16*10^99656-31)/399657Robert Price03/2016
30232^330968+34599632Lelio R Paula09/2016
30252*5^142528-799624Lelio R Paula11/2014
30242^330942+7732999624Enzo Doria05/2016
302614^86914-9999615Lelio R Paula08/2016
3027(19*2^330902+1)/7799611Lelio R Paula11/2013
30282^330845+7168799595Enzo Doria04/2016
3029(23*2^330770+1)/399573Lelio R Paula11/2013
30302^330735+841599562Lelio R Paula09/2016
30312^330720+7407199557Enzo Doria04/2016
303231^66738-299531Lelio R Paula09/2013
30337*3^208567+499513Lelio R Paula08/2014
3034(13*10^99508+47)/399509Robert Price01/2017
30352^330553+77999507Lelio R Paula01/2013
303615^84606-9499505Lelio R Paula08/2016
30376^127858+4799493Lelio R Paula08/2016
30385^142337+4899490Lelio R Paula08/2016
30397^117724-2099489Lelio R Paula08/2016
3040(29*10^99474-17)/399475Erik Branger09/2014
3041(9*2^330407-1)/799463Lelio R Paula03/2014
3042(68*10^99441+7)/399443Robert Price03/2016
304346^59791-45^5979199418Jean-Louis Charton01/2013
3044(2*10^99408+529)/999408Robert Price01/2017
304553^57646-299398Lelio R Paula09/2013
30462^330165+187002599390Enzo Doria05/2016
30472^330142-15599383Lelio R Paula12/2012
30482^330088-11525999367Enzo Doria06/2015
3049(746*10^99303+1)/999305Robert Price02/2017
30503^208107+4099293Lelio R Paula08/2016
3051(5*2^329833-1)/36999288Lelio R Paula02/2014
30528*3^208093+599287Lelio R Paula08/2014
30535^142043+5699284Lelio R Paula08/2016
305422*10^99275+799277Robert Price04/2016
30552^329778+187618999274Enzo Doria07/2016
3056(10^99239-13)/399239Robert Price02/2017
30573^207987+6299236Lelio R Paula08/2016
30582^329638+4999231Lelio R Paula12/2012
30597^117413-1899226Lelio R Paula08/2016
30602^329586-45890399216Enzo Doria04/2015
30612^329553+10199206Lelio R Paula12/2012
30622^329551-11289799205Enzo Doria06/2014
3063(3^207925+7)/5099204Lelio R Paula09/2013
30646^127458-1799399182Enzo Doria03/2013
3065(46*10^99143-1)/999144Robert Price12/2014
306618^78968-306599127Enzo Doria03/2013
30672^329259+18999117Lelio R Paula12/2012
30688*10^99113+3999114Robert Price01/2017
30696^127364+7799109Lelio R Paula08/2016
30706^127285+1399047Lelio R Paula08/2016
30712^329007+7328399041Enzo Doria04/2016
30725*3^207543-899024Lelio R Paula08/2014
30732^328885+14999005Lelio R Paula12/2012
3074(2^328879-9)/11999001Lelio R Paula10/2013
30755^141618+5498987Lelio R Paula08/2016
30768*10^98982+5198983Robert Price05/2017
3077(21*2^328809-1)/770998979Lelio R Paula03/2014
30782^328794-279760198977Enzo Doria04/2016
30796^127176+598963Lelio R Paula11/2014
30802^328700-10970998949Enzo Doria04/2014
308146711!2-2^4671198916Robert Price09/2015
30829*7^117037+498909Lelio R Paula11/2014
3083(10^98890+149)/398890Serge Batalov12/2014
30842^328497-21693398888Enzo Doria05/2014
30852^328487+3276998885Lelio R Paula08/2016
30863^207250-11235898884Enzo Doria06/2014
308713^88754-9098867Lelio R Paula08/2016
30882^328406+70998861Lelio R Paula02/2013
3089(17*2^328413-1)/1617398860Lelio R Paula03/2014
30907^116976+7698857Lelio R Paula08/2016
30912^328335+115598839Lelio R Paula08/2016
3092(3*2^328311+1)/598832Lelio R Paula11/2013
3093287^40210+40210^28798832Norbert Schneider11/2014
3094(2^328284+9)/132598821Lelio R Paula10/2013
3095(21*2^328258+1)/212598814Lelio R Paula11/2013
309665^54491+4898788Lelio R Paula04/2016
30973^207042+9898785Lelio R Paula08/2016
30983^206977-11275698754Enzo Doria07/2014
30997^116846-5098747Lelio R Paula08/2016
31002^327967-2863598728Lelio R Paula08/2016
31016^126850-4798709Lelio R Paula08/2016
31028*6^126830-798694Lelio R Paula11/2014
310311^94770-27098693Enzo Doria08/2012
31042^327832+4398688Lelio R Paula12/2012
31052^327795+76198677Lelio R Paula02/2013
310610^98669+14741198670Patrick De Geest11/2016
310810^98669-9^(98669-1)98669Robert Price05/2016
310710^98669-10524998669Patrick De Geest11/2016
31092^327671-10980198639Enzo Doria04/2014
31105^141090-1498618Lelio R Paula08/2016
311120^75799+4798617Lelio R Paula08/2016
31122^327515-101798592Lelio R Paula08/2016
31136^126692+9768198586Mike Oakes04/2011
31142^327467-74198578Lelio R Paula08/2016
3115(2^327329+9)/1998535Lelio R Paula10/2013
31167^116577-6698519Lelio R Paula08/2016
3117(3*2^327250+1)/798512Lelio R Paula11/2013
3118(19*2^327192+1)/27598494Lelio R Paula11/2013
31192^327162-6694598486Lelio R Paula08/2016
31204*10^98472-398473Erik Branger11/2013
3121(6883*2^327047-1)/7798453Lelio R Paula05/2015
3122(71*10^98446+1)/998447Serge Batalov11/2010
312313^88363+9498432Lelio R Paula08/2016
312448^58543-47^5854398425Jean-Louis Charton11/2005
31256^126481+4198422Lelio R Paula08/2016
312678*10^98413-798415Robert Price05/2017
31277^116416+4698383Lelio R Paula08/2016
31287^116407-2498376Lelio R Paula07/2016
31302^326782-186067198372Enzo Doria03/2016
312917^79948+5898372Lelio R Paula08/2016
31313^206143-9898356Lelio R Paula08/2016
31328*5^140705+798350Lelio R Paula11/2014
31332^326585+1198312Lelio R Paula12/2012
31342^326582-45916198311Enzo Doria05/2015
3135(2^326548+9)/598301Lelio R Paula10/2013
31362^326538+7165998298Enzo Doria04/2016
313715^83575-5898292Lelio R Paula08/2016
313810^98288+398289Robert Price03/2011
313910^98288-11701798288Patrick De Geest11/2011
31402^326421-279757398263Enzo Doria04/2016
31412^326401+1609598257Lelio R Paula07/2016
314217^79826-7898222Lelio R Paula08/2016
31432^326268-80998217Yves Minet04/2011
314415^83496-7698199Lelio R Paula08/2016
3145(10223*2^326179+1)/612598190Lelio R Paula07/2014
31469*5^140471-498186Lelio R Paula11/2014
31472^326069-238398157Yves Minet10/2013
31482^325973+118598128Lelio R Paula07/2016
3149(25*2^325949-1)/1798121Lelio R Paula02/2014
31502^325945-184726998120Enzo Doria07/2015
31512^325866+1598096Lelio R Paula12/2012
31522^325765+197430598066Enzo Doria06/2016
31532^325733-5869598056Lelio R Paula07/2016
31542^325717-364598051Lelio R Paula07/2016
3155(23*2^325583-1)/2198011Lelio R Paula02/2014
3156(7*10^98007-13)/398008Robert Price06/2016
31572^325512-45995997989Enzo Doria05/2015
3158(3^205354-8)/1797978Lelio R Paula09/2013
31592^325433+7681797966Enzo Doria05/2016
31602^325390-10906197953Enzo Doria04/2014
316113^87921+2497940Lelio R Paula08/2016
3162961^32831-960^3283197926Jean-Louis Charton02/2011
31632^325215+1290997900Lelio R Paula07/2016
31647*10^97874-6997875Robert Price01/2017
3165(17^79537+5^79537)/2297865Robert Price06/2013
316615^83212+2297865Lelio R Paula08/2016
31672^325087-10905797861Enzo Doria04/2014
31682^325074+187065797858Enzo Doria05/2016
31702^325066-211197855Yves Minet08/2013
3169CopelandErdos(97855)97855Eric W. Weisstein10/2015
317118^77944-8997841Lelio R Paula07/2016
31726^125720-1766397830Enzo Doria02/2013
31732^324972-206997827Yves Minet05/2013
31742^324944-278831997818Enzo Doria03/2016
31764*10^97799-997800Erik Branger11/2013
31752^324882+57729457597800Lelio R Paula09/2016
31772^324863-186792197794Enzo Doria04/2016
31786^125662-1847397785Enzo Doria03/2013
317912^90604+1197779Lelio R Paula07/2016
31805^139830+2497737Lelio R Paula04/2016
31812^324612+115597718Lelio R Paula07/2016
318219^76404-4497702Lelio R Paula07/2016
31832^324505-298397686Yves Minet04/2011
3184(31*2^324496-1)/4597683Lelio R Paula02/2014
31856^125488-1784397649Enzo Doria02/2013
31867^115515-297622Lelio R Paula09/2013
31876^125418-597595Lelio R Paula11/2014
31882^324076+115597557Lelio R Paula07/2016
3189(2^324074+9)/1397555Lelio R Paula10/2013
3190(55459*2^323993+1)/2197536Lelio R Paula07/2014
319113^87557-12^8755797534Jean-Louis Charton12/2008
31922^323946+7393997518Enzo Doria04/2016
31932^323937+186694797515Enzo Doria03/2016
31946^125290-1853397495Enzo Doria03/2013
31952^323845+10197488Lelio R Paula12/2012
319618^77662+6597487Lelio R Paula07/2016
31972^323772+7677197466Enzo Doria05/2016
31982^323765-11221397463Enzo Doria06/2014
31992^323720-655597450Lelio R Paula07/2016
32002^323694-186040197442Enzo Doria03/2016
320120^74886+397429Lelio R Paula06/2016
32033*10^97399+7397400Robert Price04/2016
32027^115252-5097400Lelio R Paula07/2016
3204224737#+39358197389Nicolas PALAU12/2016
3205(26*10^97353+31)/397354Robert Price07/2016
320661^54517-60^5451797331Jean-Louis Charton09/2005
32076^125021-8597286Lelio R Paula08/2016
32082^323164-4735597283Lelio R Paula07/2016
3209(3^203902+4)/3605101515797276Lelio R Paula09/2013
32102^323054-655597249Lelio R Paula07/2016
3211(31*10^97242+41)/997243Robert Price04/2015
3212GoldenRatioPrime[97241]97241Eric W. Weisstein06/2009
321312^90098-4197233Lelio R Paula07/2016
32142^322928-21692997212Enzo Doria05/2014
3215(7*2^322896-1)/5797201Lelio R Paula02/2014
3216(2^322897+5)/314610748997193Lelio R Paula10/2013
32172^322725+7576197150Enzo Doria04/2016
3218(13*2^322686+1)/11997138Lelio R Paula11/2013
3219(41*10^97085+373)/997086Robert Price04/2017
32202^322413+7797056Lelio R Paula12/2012
32212^322406+17797054Lelio R Paula12/2012
3222(14*10^97044+31)/997045Robert Price02/2015
32232^322302+25525597023Lelio R Paula07/2016
32242^322196-11309396991Enzo Doria07/2014
32252^322000-186146996932Enzo Doria03/2016
32262^321971-11274796923Enzo Doria06/2014
322711^93062-9296915Lelio R Paula06/2016
3228(11*2^321841-7)/1596884Renaud Lifchitz03/2011
32293^203051+3496880Lelio R Paula05/2016
3230(64*10^96863-1)/2796864Serge Batalov05/2010
32312^321716-278693996847Enzo Doria03/2016
32322^321701-11305396842Enzo Doria07/2014
32332^321700-2863596842Lelio R Paula06/2016
3234(5*2^321691-1)/2796838Lelio R Paula02/2014
32356^124433-12443396828Robert Price01/2014
32362^321631+6996821Lelio R Paula12/2012
3237(13*2^321606+1)/11996813Lelio R Paula11/2013
3238(46*10^96798-1)/996799Serge Batalov10/2014
3239(59*10^96798+31)/996799Robert Price09/2015
3240223319#+23122396790Makoto Morimoto02/2016
32412^321519-2863596787Lelio R Paula06/2016
32422^321487-186723796778Enzo Doria03/2016
32432^321461-6396770Lelio R Paula12/2012
32442^321439+12396763Lelio R Paula12/2012
32452^321434+70996762Lelio R Paula02/2013
324614^84413+8996749Lelio R Paula07/2016
3247(28*10^96743+71)/996744Serge Batalov12/2008
324813^86847+9696743Lelio R Paula06/2016
32499*2^321336-796733Lelio R Paula08/2014
3250(209*10^96722-17)/396724Robert Price05/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 25 2017 10:58 (Time in France)

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