PRP Records

Probable Primes Top 10000

(180278 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 ?
5001(2^261724+629709)/5/578786Tony Prest / Never Odd Or Even05/2014
5002(2^261724+67397)/3/10378785Tony Prest / Never Odd Or Even04/2014
5003(2^261724+323043)/11/10378784Tony Prest / Never Odd Or Even04/2014
5004(2^261724+370143)/128978784Tony Prest / Never Odd Or Even04/2014
5005(2^261724+560259)/5/5/7378784Tony Prest / Never Odd Or Even05/2014
5006(2^261724+64109)/3/3/3/5/5/1978783Tony Prest / Never Odd Or Even04/2014
5007(2^261724+394491)/5578778783Tony Prest / Never Odd Or Even04/2014
5008(2^261724+625897)/23/88378783Tony Prest / Never Odd Or Even05/2014
5009(2^261724+292471)/13/97/15178782Tony Prest / Never Odd Or Even04/2014
5010(2^261724+154303)/11/67/12778782Tony Prest / Never Odd Or Even04/2014
5011(2^261724+313319)/3/3/3/3/5/11/11378782Tony Prest / Never Odd Or Even04/2014
5012(2^261724+383949)/5/41/43/8378781Tony Prest / Never Odd Or Even04/2014
5013(2^261724+626567)/3/331/63178781Tony Prest / Never Odd Or Even05/2014
5014(2^261724+32987)/3/3/19/223/103178780Tony Prest / Never Odd Or Even04/2014
5015(2^261724+5813)/3/599139778780Tony Prest / Never Odd Or Even04/2014
5016(2^261724+13481)/3/11/239/208778780Tony Prest / Never Odd Or Even04/2014
5017(2^261724+103399)/5/13/37/1060778780Tony Prest / Never Odd Or Even04/2014
5018(2^261724+18477)/367/6511178780Tony Prest / Never Odd Or Even04/2014
5019(2^261724+121285)/167/227/121778780Tony Prest / Never Odd Or Even04/2014
5020(2^261724+262037)/3/3/11/23/1851778780Tony Prest / Never Odd Or Even04/2014
5021(2^261724+586157)/3/7/457/125978780Tony Prest / Never Odd Or Even05/2014
5022(2^261724+315287)/3/4582254178779Tony Prest / Never Odd Or Even04/2014
5023(2^261724+605675)/3/3/3/103/20748178779Tony Prest / Never Odd Or Even05/2014
5024(2^261724+60031)/13/31/702487778778Tony Prest / Never Odd Or Even04/2014
5025(2^261724+121879)/5/78943321778778Tony Prest / Never Odd Or Even04/2014
5026(2^261724+290135)/3/3/8467/905978778Tony Prest / Never Odd Or Even04/2014
5027(2^261724+79857)/59/3847/16533178777Tony Prest / Never Odd Or Even04/2014
5028(2^261724+22883)/3/17/23/2351/1007978777Tony Prest / Never Odd Or Even04/2014
5029(2^261724+154799)/3/5/365565371978777Tony Prest / Never Odd Or Even04/2014
5030(2^261724+391001)/3/11/17/41/43/2407178777Tony Prest / Never Odd Or Even04/2014
5031(2^261724+622383)/34843/55071778777Tony Prest / Never Odd Or Even05/2014
5032(2^261724+302829)/5/37/37/3707814778776Tony Prest / Never Odd Or Even04/2014
5033(2^261724+315837)/43/217613624378776Tony Prest / Never Odd Or Even04/2014
5034(2^261724+582373)/53/307/311/3211778776Tony Prest / Never Odd Or Even05/2014
5035(2^261724+295283)/3/3/3/29/43/1781227378775Tony Prest / Never Odd Or Even04/2014
5036(2^261724+27491)/3/22787/10597844978774Tony Prest / Never Odd Or Even04/2014
5037(2^261724+392751)/193813/28782668978774Tony Prest / Never Odd Or Even04/2014
5038(2^261724+328501)/7/1091/3149561051978773Tony Prest / Never Odd Or Even04/2014
5039(2^261724+111267)/19/4637/1514056042778772Tony Prest / Never Odd Or Even04/2014
5040(2^261724+572133)/127/131/7378775233378772Tony Prest / Never Odd Or Even05/2014
5041(2^261724+608733)/59/7079/18451/90915178771Tony Prest / Never Odd Or Even05/2014
5042(2^261724+255449)/3/3/5/7/1759/10177/3315886978770Tony Prest / Never Odd Or Even04/2014
5043(2^261724+99509)/3/5/5/6507271/674965928978769Tony Prest / Never Odd Or Even04/2014
5044(2^261724+52501)/563/53939/2794283139178769Tony Prest / Never Odd Or Even04/2014
5045(2^261724+117089)/3/5/37/149/967/2027/416374178769Tony Prest / Never Odd Or Even04/2014
5046(2^261724+372571)/1487/9209/21559/226324978769Tony Prest / Never Odd Or Even04/2014
5047(2^261724+184549)/5/8699/44053/140932299778769Tony Prest / Never Odd Or Even04/2014
5048(2^261724+363351)/937/159683/5952320022778768Tony Prest / Never Odd Or Even04/2014
5049(2^261724+326501)/3/43/193/263/19403/25350140378768Tony Prest / Never Odd Or Even04/2014
5050(2^261724+629477)/3/17/17/137/263/1993/16187/5734778768Tony Prest / Never Odd Or Even05/2014
5051(2^261724+94871)/3/3/13/6734017/167342524578778766Tony Prest / Never Odd Or Even04/2014
5052(2^261724+25981)/577/1181/3643/51778633474378766Tony Prest / Never Odd Or Even04/2014
5054(23*2^261642+1)/9378762Lelio R Paula10/2012
5053(2^261724+351227)/3/3/3/3/71/13997/9595373/819397800778762Tony Prest / Never Odd Or Even04/2014
5055(2^261724+22571)/3/7243/7321/18046081/4573074121178761Tony Prest / Never Odd Or Even04/2014
5056(2^261724+56495)/3/3/3/7/7/13/9041/512818459/2370858911978760Tony Prest / Never Odd Or Even04/2014
5057(2^261724+604119)/5/7/7/41/14107/19681/211777/90145981/103602083412778750Tony Prest / Never Odd Or Even05/2014
50582^261507-228778722Yves Minet04/2009
50598*10^78717+3978718Robert Price01/2017
5060(78557*2^261440+1)/378706Lelio R Paula06/2014
50616^101128-1643378693Enzo Doria02/2013
506220^60482+9978689Lelio R Paula03/2015
50632^261348-11063378674Enzo Doria05/2014
5064191^34487+278666Lelio R Paula05/2013
50652^261305-11013978661Enzo Doria04/2014
5066(82*10^78635-1)/978636Robert Price12/2014
506710^78632+8178633Robert Price03/2011
506810^78632-40269378632Patrick De Geest07/2013
50693*10^78631+1778632Robert Price03/2017
50702^261174-391178622Yves Minet04/2017
50712^261167+7484378620Enzo Doria04/2016
5072L(376121)+F(376122)78605Henri Lifchitz01/2007
507314^68580-2978602Lelio R Paula02/2015
5074(73*10^78576-1)/978577Robert Price01/2015
5075(17*2^261026-1)/4045178574Lelio R Paula02/2014
50762^261001-19578570Lelio R Paula05/2012
50775*2^260950+978555Lelio R Paula06/2014
50782^260931-760578549Lelio R Paula07/2013
507915^66778-3278538Lelio R Paula02/2015
5080(11*2^260896-1)/24578537Lelio R Paula02/2014
508130^53166+2978533Norbert Schneider03/2017
5082lucasU(2403,1,23229)-lucasU(2403,1,23228)78529Mike Oakes05/2009
50837*3^164574-278523Lelio R Paula06/2014
50842^260830-11213378518Enzo Doria06/2014
508513^70486+4278518Lelio R Paula03/2015
508611^75386-708078507Enzo Doria01/2013
50872^260711-5869578482Lelio R Paula07/2013
50882^260678-11106578472Enzo Doria05/2014
508918^62501-9778456Lelio R Paula02/2015
509053^45498-278452Lelio R Paula08/2013
50912^260513-11112178423Enzo Doria05/2014
509237845!2-6478412Robert Price06/2015
50932^260469-11069578409Enzo Doria05/2014
5094(11*10^78408-113)/378409Robert Price01/2017
50952^260447+841578403Lelio R Paula07/2013
509637837!2-6478394Robert Price06/2015
5097(19*2^260379-1)/5378382Lelio R Paula02/2014
50982^260377-11323378382Enzo Doria07/2014
50999^82138+6^82138-2^8213878380Mike Oakes08/2010
510069^42624+278380Lelio R Paula05/2013
51012^260369-185971378379Enzo Doria03/2016
510214*10^78362+108978364Jens K. Andersen11/2007
51035^112070-5478334Lelio R Paula02/2015
5104(10^(2*39165+1)+54*10^39165-1)/978331Robert Price04/2017
51052^260182-11345378323Enzo Doria07/2014
5106(78557*2^260084+1)/51978296Lelio R Paula06/2014
510810^78288+9^(78288+1)78289Robert Price08/2016
510710^78288+3910978289Patrick De Geest12/2016
510910^78288-21629978288Patrick De Geest12/2016
51105^111997+3678283Lelio R Paula02/2015
5111(21^59183+1)/2278252Paul Bourdelais03/2010
5112(88*10^78242-7)/978243Robert Price11/2014
51132*6^100547+778242Lelio R Paula10/2014
51142^259860-11108978226Enzo Doria05/2014
511537^49875-278215Lelio R Paula09/2013
51167*5^111893-478211Lelio R Paula10/2014
5117(11*2^259809-1)/143778209Lelio R Paula02/2014
51187^92511-678181Theodore Burton11/2005
5119(3^163859-4)/25378179Lelio R Paula10/2012
5120(27*2^259666-1)/62569178163Lelio R Paula02/2014
51213*10^78146+1778147Robert Price03/2017
51222^259503+7433378119Enzo Doria04/2016
5123(31*2^259504-1)/1336578116Lelio R Paula02/2014
5125(58547^16384+1)/278111Lelio R Paula11/2011
51246^100379+1378111Lelio R Paula03/2015
51262^259469-10990978108Enzo Doria04/2014
512715^66413-2678108Lelio R Paula02/2015
51287^92410-926678096Mike Oakes02/2010
51292^259398+7579978087Enzo Doria04/2016
51302^259394+187618978086Enzo Doria07/2016
5131PIPrime(78073)78073Eric W. Weisstein07/2006
51325*2^259344-778072Lelio R Paula06/2014
513314^68097-8778048Lelio R Paula02/2015
51342^259233-47557378037Paul Bourdelais03/2013
51353^163500-2878010Robert Price12/2013
5136(65*10^77992+691)/977993Robert Price08/2016
51372^259013-11259177971Enzo Doria06/2014
51386^100193-100193^677966Norbert Schneider04/2017
51392^258863-11023577926Enzo Doria05/2014
51402^258852+160577923Lelio R Paula06/2013
5141(11*10^77909+49)/377910Robert Price05/2016
51422*7^92187-977908Lelio R Paula10/2014
51432^258763-11015577896Enzo Doria04/2014
51442^258694-11038777875Enzo Doria05/2014
514511^74773-9477869Lelio R Paula02/2015
51466^100067+12577868Lelio R Paula03/2015
514715^66205+877864Lelio R Paula07/2014
51485^111373-1813677847Enzo Doria05/2014
51492^258524-10987777824Enzo Doria04/2014
51506^100002-1664377817Enzo Doria02/2013
515165^42916+2877803Lelio R Paula01/2016
5152(89*10^77781-17)/977782Robert Price11/2015
51532^258382-11040577781Enzo Doria05/2014
51545^111278-1499677780Enzo Doria02/2013
515514^67862+6177779Lelio R Paula02/2015
515610^77777+4848377778Patrick De Geest11/2010
515710^77777-18324377777Patrick De Geest11/2010
5158(27*2^258352+1)/4377772Lelio R Paula08/2012
5159337^30756-1000277740Enzo Doria07/2012
516010^77726+9977727Robert Price03/2011
516110^77726-8594777726Patrick De Geest06/2013
516289^39870-277723Lelio R Paula08/2013
51637^91966-3277721Lelio R Paula02/2015
516435^50327+277709Lelio R Paula05/2013
516524^56298+2377704Norbert Schneider12/2016
5166(2^258105+78557)/1977697Lelio R Paula10/2012
51672^258079+17977690Lelio R Paula03/2012
51682^258062-11311177685Enzo Doria07/2014
516980^40807-7977660Norbert Schneider03/2015
5170(10^77637+359)/977637Serge Batalov12/2014
51712^257862-16577625Lelio R Paula03/2012
5172(25*2^257853+1)/377623Lelio R Paula07/2012
5173(2^257869+1)/(3*18645362967379)77613Henri Lifchitz04/2005
51746^99728+7177604Lelio R Paula01/2015
51752^257778-11276777599Enzo Doria06/2014
5176(31*2^257771+1)/53777596Lelio R Paula07/2012
51772^257729-7377585Lelio R Paula03/2012
51782^257689-6377573Lelio R Paula03/2012
5179(78557*2^257665+1)/610872577564Lelio R Paula06/2014
5180(3^162563+8)/288577559Lelio R Paula10/2012
51812^257636-11023577557Enzo Doria05/2014
5182(23*10^77556+97)/377557Robert Price02/2017
51832^257621-11007177552Enzo Doria04/2014
51842^257567-6487577536Lelio R Paula06/2013
51852*7^91674+977474Lelio R Paula10/2014
5186(17*10^77427-47)/377428Robert Price05/2017
518710^77418+84168377419Patrick De Geest06/2013
518810^77418-3377418Robert Price05/2011
518919^60539-3677415Lelio R Paula03/2015
519037401!!-102477397Robert Price11/2015
519111^74313-1875077390Enzo Doria12/2012
51922^257044-11288377378Enzo Doria06/2014
51938*10^77377+5177378Robert Price05/2017
51942*7^91553+977372Lelio R Paula10/2014
5195713^27118+27118^71377371Norbert Schneider12/2016
51962^256920-11115577341Enzo Doria05/2014
51972^256896-655577334Lelio R Paula06/2013
5198(52*10^77322-7)/977323Robert Price12/2014
51992^256849-11293977320Enzo Doria06/2014
5200(4*10^77309-31)/977309Erik Branger05/2011
5201(3^161988+7)/4186477284Lelio R Paula10/2012
5202(14^67421-1)/1377272Paul Bourdelais09/2008
52035*3^161923-477258Lelio R Paula06/2014
52042^256552-149977230Yves Minet05/2013
52052^256460-11275777203Enzo Doria06/2014
52062^256398+2329977184Yves Minet02/2011
52072^256391-1155*25639177182Henri Lifchitz03/2005
5208(2^256391-9)/5659377177Lelio R Paula10/2012
5209(2^256308+9)/1058577153Lelio R Paula10/2012
521121^58348-277149Lelio R Paula08/2013
5210(17*2^256291-1)/478577149Lelio R Paula02/2014
5212(5*2^256274-1)/214177144Lelio R Paula02/2014
521319^60321+8277136Lelio R Paula03/2015
52145*2^256233-377135Lelio R Paula06/2014
52153*2^256149+777110Lelio R Paula06/2014
52163^161594-10677100Lelio R Paula02/2015
52172^256114-18577098Lelio R Paula03/2012
52188^85349-85349^877078Norbert Schneider05/2017
52192^256043-278637777077Enzo Doria03/2016
52202^255973+186994777056Enzo Doria05/2016
522112^71393-4377046Lelio R Paula02/2015
522215^65490+4477023Lelio R Paula02/2015
5223(3^161411-7)/94077010Lelio R Paula10/2012
5224lucasU(1107,1,25297)-lucasU(1107,1,25296)77005Mike Oakes05/2009
5225(570^27943-1)/56977005Serge Batalov12/2016
52262^255750-7576989Lelio R Paula03/2012
52273*6^98926-576980Lelio R Paula10/2014
522818^61320-143376974Enzo Doria03/2013
52296^98916-1709376972Enzo Doria02/2013
52302^255659-11013176962Enzo Doria04/2014
523112^71303+9176949Lelio R Paula02/2015
523218^61298+5976946Lelio R Paula02/2015
5233(223^32768+1)/13107476945Lelio R Paula02/2009
5234(2^255613-5)/28151776942Lelio R Paula10/2012
523518^61290-1176936Lelio R Paula02/2015
523763^42752-276926Lelio R Paula08/2013
5236(11*2^255545-1)/11776926Lelio R Paula02/2014
52382^255517+5638776919Yves Minet02/2011
52392^255499-11256776913Enzo Doria06/2014
52402^255492+34576911Lelio R Paula06/2013
524110^76875+21759176876Patrick De Geest05/2013
524310^76875-5376875Robert Price05/2011
524211^73819-588076875Enzo Doria01/2013
52442^255313+1891576857Lelio R Paula06/2013
5245(2^255320-1017)/144666776853Lelio R Paula10/2012
52462^255296+577576852Lelio R Paula06/2013
524714^67052-2976851Lelio R Paula02/2015
5248(7*10^76818-313)/976818Robert Price11/2016
524910^76801+6976802Robert Price03/2011
525010^76801-8094376801Patrick De Geest06/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 20 2017 08:36 (Time in France)

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