PRP Records

Probable Primes Top 10000

(172213 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 ?
47512^263448-51950979306Paul Bourdelais03/2013
475221^59971-20^5997179295Robert Price05/2012
47532^263372+12379283Lelio R Paula05/2012
475417^64429+8479277Lelio R Paula03/2015
475511^76124-1143079275Enzo Doria12/2012
475613^71157+1879265Lelio R Paula03/2015
47572^263297+6583579261Lelio R Paula07/2013
475819^61980-1879258Theodore Burton12/2005
47592*10^79242+9379243Robert Price07/2016
4760(103*29^54179-39)/479233Curtis Bright05/2015
476117^64382-2679219Lelio R Paula03/2015
47627^93733-7479214Lelio R Paula02/2015
476315^67352+3879213Lelio R Paula02/2015
47642^263135-11023579212Enzo Doria05/2014
47652^263044+425779185Lelio R Paula07/2013
47672^263032+8751779181Yves Minet11/2010
47666^101755+9579181Lelio R Paula03/2015
47684^131497-3^13149779170Jean-Louis Charton05/2004
47695*7^93674+879165Lelio R Paula10/2014
4770lucasU(486,25,29457)-5*lucasU(486,25,29456)79137Mike Oakes05/2009
477111^75978-4279123Lelio R Paula02/2015
47728*5^113180+979111Lelio R Paula10/2014
4773(6883*2^262741-1)/483579094Lelio R Paula04/2015
4774(9*2^262745+1)/13779093Lelio R Paula10/2012
477512^73285+8579088Lelio R Paula02/2015
477619^61840+5279079Lelio R Paula03/2015
4777(10^79067+77)/379067Robert Price01/2017
4778(1017*2^262640-1)/1155779062Lelio R Paula04/2015
477910^79040+13794979041Patrick De Geest02/2016
478110^79040-100729779040Robert Price02/2015
478010^79040-7742779040Patrick De Geest02/2016
47822^262551-1729579036Lelio R Paula07/2013
47833^165597+34079010Lelio R Paula02/2015
4784(23*2^262435+1)/5579001Lelio R Paula10/2012
478511^75860-210079001Enzo Doria12/2012
47868*7^93463+978987Lelio R Paula10/2014
478767^43240-278960Lelio R Paula09/2013
47881000001^13159-1000000^1315978953Jean-Louis Charton10/2003
47892^262199-11028778930Enzo Doria05/2014
4790(19*2^262180-1)/17778924Lelio R Paula02/2014
4791(3^165403+4)/778917Lelio R Paula10/2012
47932^21068*(2^241076+1)-178914Makoto Morimoto03/2014
47942^29258*(2^232886+1)-178914Makoto Morimoto03/2014
47922^262144+1853178914Makoto Morimoto12/2015
479514^68837+7578897Lelio R Paula02/2015
4796106^38949+10578884Norbert Schneider12/2016
4797(25*2^261917-1)/2092778842Lelio R Paula02/2014
47982^261881-185971378835Enzo Doria03/2016
47992^261874+191578832Lelio R Paula07/2013
48002^261856+9876533178827Jason Earls01/2009
4801(5*2^261857-1)/2050127778821Lelio R Paula02/2014
48022^261724+9269178787Tony Prest / Never Odd Or Even03/2014
48032^261724+28511178787Tony Prest / Never Odd Or Even04/2014
48042^261724+29371378787Tony Prest / Never Odd Or Even04/2014
4805(2^261724+381949)/578787Tony Prest / Never Odd Or Even04/2014
48062^261724+57297178787Tony Prest / Never Odd Or Even05/2014
4807(2^261724+392705)/3/778786Tony Prest / Never Odd Or Even04/2014
4808(2^261724+629709)/5/578786Tony Prest / Never Odd Or Even05/2014
4809(2^261724+67397)/3/10378785Tony Prest / Never Odd Or Even04/2014
4810(2^261724+323043)/11/10378784Tony Prest / Never Odd Or Even04/2014
4811(2^261724+370143)/128978784Tony Prest / Never Odd Or Even04/2014
4812(2^261724+560259)/5/5/7378784Tony Prest / Never Odd Or Even05/2014
4813(2^261724+64109)/3/3/3/5/5/1978783Tony Prest / Never Odd Or Even04/2014
4814(2^261724+394491)/5578778783Tony Prest / Never Odd Or Even04/2014
4815(2^261724+625897)/23/88378783Tony Prest / Never Odd Or Even05/2014
4816(2^261724+292471)/13/97/15178782Tony Prest / Never Odd Or Even04/2014
4817(2^261724+154303)/11/67/12778782Tony Prest / Never Odd Or Even04/2014
4818(2^261724+313319)/3/3/3/3/5/11/11378782Tony Prest / Never Odd Or Even04/2014
4819(2^261724+383949)/5/41/43/8378781Tony Prest / Never Odd Or Even04/2014
4820(2^261724+626567)/3/331/63178781Tony Prest / Never Odd Or Even05/2014
4821(2^261724+32987)/3/3/19/223/103178780Tony Prest / Never Odd Or Even04/2014
4822(2^261724+5813)/3/599139778780Tony Prest / Never Odd Or Even04/2014
4823(2^261724+13481)/3/11/239/208778780Tony Prest / Never Odd Or Even04/2014
4824(2^261724+103399)/5/13/37/1060778780Tony Prest / Never Odd Or Even04/2014
4825(2^261724+18477)/367/6511178780Tony Prest / Never Odd Or Even04/2014
4826(2^261724+121285)/167/227/121778780Tony Prest / Never Odd Or Even04/2014
4827(2^261724+262037)/3/3/11/23/1851778780Tony Prest / Never Odd Or Even04/2014
4828(2^261724+586157)/3/7/457/125978780Tony Prest / Never Odd Or Even05/2014
4829(2^261724+315287)/3/4582254178779Tony Prest / Never Odd Or Even04/2014
4830(2^261724+605675)/3/3/3/103/20748178779Tony Prest / Never Odd Or Even05/2014
4831(2^261724+60031)/13/31/702487778778Tony Prest / Never Odd Or Even04/2014
4832(2^261724+121879)/5/78943321778778Tony Prest / Never Odd Or Even04/2014
4833(2^261724+290135)/3/3/8467/905978778Tony Prest / Never Odd Or Even04/2014
4834(2^261724+79857)/59/3847/16533178777Tony Prest / Never Odd Or Even04/2014
4835(2^261724+22883)/3/17/23/2351/1007978777Tony Prest / Never Odd Or Even04/2014
4836(2^261724+154799)/3/5/365565371978777Tony Prest / Never Odd Or Even04/2014
4837(2^261724+391001)/3/11/17/41/43/2407178777Tony Prest / Never Odd Or Even04/2014
4838(2^261724+622383)/34843/55071778777Tony Prest / Never Odd Or Even05/2014
4839(2^261724+302829)/5/37/37/3707814778776Tony Prest / Never Odd Or Even04/2014
4840(2^261724+315837)/43/217613624378776Tony Prest / Never Odd Or Even04/2014
4841(2^261724+582373)/53/307/311/3211778776Tony Prest / Never Odd Or Even05/2014
4842(2^261724+295283)/3/3/3/29/43/1781227378775Tony Prest / Never Odd Or Even04/2014
4843(2^261724+27491)/3/22787/10597844978774Tony Prest / Never Odd Or Even04/2014
4844(2^261724+392751)/193813/28782668978774Tony Prest / Never Odd Or Even04/2014
4845(2^261724+328501)/7/1091/3149561051978773Tony Prest / Never Odd Or Even04/2014
4846(2^261724+111267)/19/4637/1514056042778772Tony Prest / Never Odd Or Even04/2014
4847(2^261724+572133)/127/131/7378775233378772Tony Prest / Never Odd Or Even05/2014
4848(2^261724+608733)/59/7079/18451/90915178771Tony Prest / Never Odd Or Even05/2014
4849(2^261724+255449)/3/3/5/7/1759/10177/3315886978770Tony Prest / Never Odd Or Even04/2014
4850(2^261724+99509)/3/5/5/6507271/674965928978769Tony Prest / Never Odd Or Even04/2014
4851(2^261724+52501)/563/53939/2794283139178769Tony Prest / Never Odd Or Even04/2014
4852(2^261724+117089)/3/5/37/149/967/2027/416374178769Tony Prest / Never Odd Or Even04/2014
4853(2^261724+372571)/1487/9209/21559/226324978769Tony Prest / Never Odd Or Even04/2014
4854(2^261724+184549)/5/8699/44053/140932299778769Tony Prest / Never Odd Or Even04/2014
4855(2^261724+363351)/937/159683/5952320022778768Tony Prest / Never Odd Or Even04/2014
4856(2^261724+326501)/3/43/193/263/19403/25350140378768Tony Prest / Never Odd Or Even04/2014
4857(2^261724+629477)/3/17/17/137/263/1993/16187/5734778768Tony Prest / Never Odd Or Even05/2014
4858(2^261724+94871)/3/3/13/6734017/167342524578778766Tony Prest / Never Odd Or Even04/2014
4859(2^261724+25981)/577/1181/3643/51778633474378766Tony Prest / Never Odd Or Even04/2014
4861(23*2^261642+1)/9378762Lelio R Paula10/2012
4860(2^261724+351227)/3/3/3/3/71/13997/9595373/819397800778762Tony Prest / Never Odd Or Even04/2014
4862(2^261724+22571)/3/7243/7321/18046081/4573074121178761Tony Prest / Never Odd Or Even04/2014
4863(2^261724+56495)/3/3/3/7/7/13/9041/512818459/2370858911978760Tony Prest / Never Odd Or Even04/2014
4864(2^261724+604119)/5/7/7/41/14107/19681/211777/90145981/103602083412778750Tony Prest / Never Odd Or Even05/2014
48652^261507-228778722Yves Minet04/2009
48668*10^78717+3978718Robert Price01/2017
4867(78557*2^261440+1)/378706Lelio R Paula06/2014
48686^101128-1643378693Enzo Doria02/2013
486920^60482+9978689Lelio R Paula03/2015
48702^261348-11063378674Enzo Doria05/2014
4871191^34487+278666Lelio R Paula05/2013
48722^261305-11013978661Enzo Doria04/2014
4873(82*10^78635-1)/978636Robert Price12/2014
487410^78632+8178633Robert Price03/2011
487510^78632-40269378632Patrick De Geest07/2013
48763*10^78631+1778632Robert Price03/2017
48772^261167+7484378620Enzo Doria04/2016
4878L(376121)+F(376122)78605Henri Lifchitz01/2007
487914^68580-2978602Lelio R Paula02/2015
4880(73*10^78576-1)/978577Robert Price01/2015
4881(17*2^261026-1)/4045178574Lelio R Paula02/2014
48822^261001-19578570Lelio R Paula05/2012
48835*2^260950+978555Lelio R Paula06/2014
48842^260931-760578549Lelio R Paula07/2013
488515^66778-3278538Lelio R Paula02/2015
4886(11*2^260896-1)/24578537Lelio R Paula02/2014
4887lucasU(2403,1,23229)-lucasU(2403,1,23228)78529Mike Oakes05/2009
48887*3^164574-278523Lelio R Paula06/2014
48892^260830-11213378518Enzo Doria06/2014
489013^70486+4278518Lelio R Paula03/2015
489111^75386-708078507Enzo Doria01/2013
48922^260711-5869578482Lelio R Paula07/2013
48932^260678-11106578472Enzo Doria05/2014
489418^62501-9778456Lelio R Paula02/2015
489553^45498-278452Lelio R Paula08/2013
48962^260513-11112178423Enzo Doria05/2014
489737845!2-6478412Robert Price06/2015
48982^260469-11069578409Enzo Doria05/2014
4899(11*10^78408-113)/378409Robert Price01/2017
49002^260447+841578403Lelio R Paula07/2013
490137837!2-6478394Robert Price06/2015
4902(19*2^260379-1)/5378382Lelio R Paula02/2014
49032^260377-11323378382Enzo Doria07/2014
49059^82138+6^82138-2^8213878380Mike Oakes08/2010
490469^42624+278380Lelio R Paula05/2013
49062^260369-185971378379Enzo Doria03/2016
490714*10^78362+108978364Jens K. Andersen11/2007
49085^112070-5478334Lelio R Paula02/2015
49092^260182-11345378323Enzo Doria07/2014
4910(78557*2^260084+1)/51978296Lelio R Paula06/2014
491210^78288+9^(78288+1)78289Robert Price08/2016
491110^78288+3910978289Patrick De Geest12/2016
491310^78288-21629978288Patrick De Geest12/2016
49145^111997+3678283Lelio R Paula02/2015
4915(21^59183+1)/2278252Paul Bourdelais03/2010
4916(88*10^78242-7)/978243Robert Price11/2014
49172*6^100547+778242Lelio R Paula10/2014
49182^259860-11108978226Enzo Doria05/2014
491937^49875-278215Lelio R Paula09/2013
49207*5^111893-478211Lelio R Paula10/2014
4921(11*2^259809-1)/143778209Lelio R Paula02/2014
49227^92511-678181Theodore Burton11/2005
4923(3^163859-4)/25378179Lelio R Paula10/2012
4924(27*2^259666-1)/62569178163Lelio R Paula02/2014
49253*10^78146+1778147Robert Price03/2017
49262^259503+7433378119Enzo Doria04/2016
4927(31*2^259504-1)/1336578116Lelio R Paula02/2014
4929(58547^16384+1)/278111Lelio R Paula11/2011
49286^100379+1378111Lelio R Paula03/2015
49302^259469-10990978108Enzo Doria04/2014
493115^66413-2678108Lelio R Paula02/2015
49327^92410-926678096Mike Oakes02/2010
49332^259398+7579978087Enzo Doria04/2016
49342^259394+187618978086Enzo Doria07/2016
4935PIPrime(78073)78073Eric W. Weisstein07/2006
49365*2^259344-778072Lelio R Paula06/2014
493714^68097-8778048Lelio R Paula02/2015
49382^259233-47557378037Paul Bourdelais03/2013
49393^163500-2878010Robert Price12/2013
4940(65*10^77992+691)/977993Robert Price08/2016
49412^259013-11259177971Enzo Doria06/2014
49422^258863-11023577926Enzo Doria05/2014
49432^258852+160577923Lelio R Paula06/2013
4944(11*10^77909+49)/377910Robert Price05/2016
49452*7^92187-977908Lelio R Paula10/2014
49462^258763-11015577896Enzo Doria04/2014
49472^258694-11038777875Enzo Doria05/2014
494811^74773-9477869Lelio R Paula02/2015
49496^100067+12577868Lelio R Paula03/2015
495015^66205+877864Lelio R Paula07/2014
49515^111373-1813677847Enzo Doria05/2014
49522^258524-10987777824Enzo Doria04/2014
49536^100002-1664377817Enzo Doria02/2013
495465^42916+2877803Lelio R Paula01/2016
4955(89*10^77781-17)/977782Robert Price11/2015
49562^258382-11040577781Enzo Doria05/2014
49575^111278-1499677780Enzo Doria02/2013
495814^67862+6177779Lelio R Paula02/2015
495910^77777+4848377778Patrick De Geest11/2010
496010^77777-18324377777Patrick De Geest11/2010
4961(27*2^258352+1)/4377772Lelio R Paula08/2012
4962337^30756-1000277740Enzo Doria07/2012
496310^77726+9977727Robert Price03/2011
496410^77726-8594777726Patrick De Geest06/2013
496589^39870-277723Lelio R Paula08/2013
49667^91966-3277721Lelio R Paula02/2015
496735^50327+277709Lelio R Paula05/2013
496824^56298+2377704Norbert Schneider12/2016
4969(2^258105+78557)/1977697Lelio R Paula10/2012
49702^258079+17977690Lelio R Paula03/2012
49712^258062-11311177685Enzo Doria07/2014
497280^40807-7977660Norbert Schneider03/2015
4973(10^77637+359)/977637Serge Batalov12/2014
49742^257862-16577625Lelio R Paula03/2012
4975(25*2^257853+1)/377623Lelio R Paula07/2012
4976(2^257869+1)/(3*18645362967379)77613Henri Lifchitz04/2005
49776^99728+7177604Lelio R Paula01/2015
49782^257778-11276777599Enzo Doria06/2014
4979(31*2^257771+1)/53777596Lelio R Paula07/2012
49802^257729-7377585Lelio R Paula03/2012
49812^257689-6377573Lelio R Paula03/2012
4982(78557*2^257665+1)/610872577564Lelio R Paula06/2014
4983(3^162563+8)/288577559Lelio R Paula10/2012
49842^257636-11023577557Enzo Doria05/2014
4985(23*10^77556+97)/377557Robert Price02/2017
49862^257621-11007177552Enzo Doria04/2014
49872^257567-6487577536Lelio R Paula06/2013
49882*7^91674+977474Lelio R Paula10/2014
498910^77418+84168377419Patrick De Geest06/2013
499010^77418-3377418Robert Price05/2011
499119^60539-3677415Lelio R Paula03/2015
499237401!!-102477397Robert Price11/2015
499311^74313-1875077390Enzo Doria12/2012
49942^257044-11288377378Enzo Doria06/2014
49952*7^91553+977372Lelio R Paula10/2014
4996713^27118+27118^71377371Norbert Schneider12/2016
49972^256920-11115577341Enzo Doria05/2014
49982^256896-655577334Lelio R Paula06/2013
4999(52*10^77322-7)/977323Robert Price12/2014
50002^256849-11293977320Enzo Doria06/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 26 2017 17:51 (Time in France)

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