PRP Records

Probable Primes Top 10000

(191107 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 ?
5251(2^261724+326501)/3/43/193/263/19403/25350140378768Tony Prest / Never Odd Or Even04/2014
5252(2^261724+629477)/3/17/17/137/263/1993/16187/5734778768Tony Prest / Never Odd Or Even05/2014
5253(2^261724+94871)/3/3/13/6734017/167342524578778766Tony Prest / Never Odd Or Even04/2014
5254(2^261724+25981)/577/1181/3643/51778633474378766Tony Prest / Never Odd Or Even04/2014
5256(23*2^261642+1)/9378762Lelio R Paula10/2012
5255(2^261724+351227)/3/3/3/3/71/13997/9595373/819397800778762Tony Prest / Never Odd Or Even04/2014
5257(2^261724+22571)/3/7243/7321/18046081/4573074121178761Tony Prest / Never Odd Or Even04/2014
5258(2^261724+56495)/3/3/3/7/7/13/9041/512818459/2370858911978760Tony Prest / Never Odd Or Even04/2014
5259(2^261724+604119)/5/7/7/41/14107/19681/211777/90145981/103602083412778750Tony Prest / Never Odd Or Even05/2014
52602^261507-228778722Yves Minet04/2009
52618*10^78717+3978718Robert Price01/2017
5262(78557*2^261440+1)/378706Lelio R Paula06/2014
52636^101128-1643378693Enzo Doria02/2013
526420^60482+9978689Lelio R Paula03/2015
52652^261348-11063378674Enzo Doria05/2014
5266191^34487+278666Lelio R Paula05/2013
52672^261305-11013978661Enzo Doria04/2014
5268(82*10^78635-1)/978636Robert Price12/2014
526910^78632+8178633Robert Price03/2011
527010^78632-40269378632Patrick De Geest07/2013
52713*10^78631+1778632Robert Price03/2017
52722^261174-391178622Yves Minet04/2017
52732^261167+7484378620Enzo Doria04/2016
5274L(376121)+F(376122)78605Henri Lifchitz01/2007
527514^68580-2978602Lelio R Paula02/2015
5276(73*10^78576-1)/978577Robert Price01/2015
5277(17*2^261026-1)/4045178574Lelio R Paula02/2014
52782^261001-19578570Lelio R Paula05/2012
52795*2^260950+978555Lelio R Paula06/2014
52802^260931-760578549Lelio R Paula07/2013
528115^66778-3278538Lelio R Paula02/2015
5282(11*2^260896-1)/24578537Lelio R Paula02/2014
528330^53166+2978533Norbert Schneider03/2017
5284lucasU(2403,1,23229)-lucasU(2403,1,23228)78529Mike Oakes05/2009
52857*3^164574-278523Lelio R Paula06/2014
52862^260830-11213378518Enzo Doria06/2014
528713^70486+4278518Lelio R Paula03/2015
528811^75386-708078507Enzo Doria01/2013
5289(86^40583-1)/8578506Paul Bourdelais08/2017
52902^260711-5869578482Lelio R Paula07/2013
52912^260678-11106578472Enzo Doria05/2014
529218^62501-9778456Lelio R Paula02/2015
529353^45498-278452Lelio R Paula08/2013
52942^260513-11112178423Enzo Doria05/2014
529537845!2-6478412Robert Price06/2015
52962^260469-11069578409Enzo Doria05/2014
5297(11*10^78408-113)/378409Robert Price01/2017
52982^260447+841578403Lelio R Paula07/2013
529937837!2-6478394Robert Price06/2015
5300(19*2^260379-1)/5378382Lelio R Paula02/2014
53012^260377-11323378382Enzo Doria07/2014
53039^82138+6^82138-2^8213878380Mike Oakes08/2010
530269^42624+278380Lelio R Paula05/2013
53042^260369-185971378379Enzo Doria03/2016
530514*10^78362+108978364Jens K. Andersen11/2007
53065^112070-5478334Lelio R Paula02/2015
5307(10^(2*39165+1)+54*10^39165-1)/978331Robert Price04/2017
53082^260182-11345378323Enzo Doria07/2014
5309f(16405)78319Robert Price09/2017
5310(78557*2^260084+1)/51978296Lelio R Paula06/2014
531110^78288+9^(78288+1)78289Robert Price08/2016
531210^78288+3910978289Patrick De Geest12/2016
531310^78288-21629978288Patrick De Geest12/2016
53145^111997+3678283Lelio R Paula02/2015
5315(21^59183+1)/2278252Paul Bourdelais03/2010
5316(88*10^78242-7)/978243Robert Price11/2014
53172*6^100547+778242Lelio R Paula10/2014
53182^259860-11108978226Enzo Doria05/2014
531937^49875-278215Lelio R Paula09/2013
5320(13*10^78213+401)/978214Robert Price10/2017
53217*5^111893-478211Lelio R Paula10/2014
5322(11*2^259809-1)/143778209Lelio R Paula02/2014
53237^92511-678181Theodore Burton11/2005
5324(3^163859-4)/25378179Lelio R Paula10/2012
5325(27*2^259666-1)/62569178163Lelio R Paula02/2014
53263*10^78146+1778147Robert Price03/2017
53272^259503+7433378119Enzo Doria04/2016
5328(31*2^259504-1)/1336578116Lelio R Paula02/2014
5330(58547^16384+1)/278111Lelio R Paula11/2011
53296^100379+1378111Lelio R Paula03/2015
53312^259469-10990978108Enzo Doria04/2014
533215^66413-2678108Lelio R Paula02/2015
53337^92410-926678096Mike Oakes02/2010
53342^259398+7579978087Enzo Doria04/2016
53352^259394+187618978086Enzo Doria07/2016
5336PIPrime(78073)78073Eric W. Weisstein07/2006
53375*2^259344-778072Lelio R Paula06/2014
533814^68097-8778048Lelio R Paula02/2015
53392^259233-47557378037Paul Bourdelais03/2013
5340181^34554-278012Lelio R Paula10/2017
53413^163500-2878010Robert Price12/2013
5342(65*10^77992+691)/977993Robert Price08/2016
53432^259013-11259177971Enzo Doria06/2014
53447*10^77969-1177970Robert Price10/2017
53456^100193-100193^677966Norbert Schneider04/2017
53462^258863-11023577926Enzo Doria05/2014
53472^258852+160577923Lelio R Paula06/2013
5348(11*10^77909+49)/377910Robert Price05/2016
53492*7^92187-977908Lelio R Paula10/2014
53502^258763-11015577896Enzo Doria04/2014
53512^258694-11038777875Enzo Doria05/2014
535211^74773-9477869Lelio R Paula02/2015
53536^100067+12577868Lelio R Paula03/2015
535415^66205+877864Lelio R Paula07/2014
53555^111373-1813677847Enzo Doria05/2014
53562^258524-10987777824Enzo Doria04/2014
53576^100002-1664377817Enzo Doria02/2013
5358(13*10^77811+347)/977812Robert Price10/2017
535965^42916+2877803Lelio R Paula01/2016
5360(89*10^77781-17)/977782Robert Price11/2015
53612^258382-11040577781Enzo Doria05/2014
53625^111278-1499677780Enzo Doria02/2013
536314^67862+6177779Lelio R Paula02/2015
536410^77777+4848377778Patrick De Geest11/2010
536510^77777-18324377777Patrick De Geest11/2010
5366(27*2^258352+1)/4377772Lelio R Paula08/2012
5367337^30756-1000277740Enzo Doria07/2012
536810^77726+9977727Robert Price03/2011
536910^77726-8594777726Patrick De Geest06/2013
537089^39870-277723Lelio R Paula08/2013
53717^91966-3277721Lelio R Paula02/2015
537235^50327+277709Lelio R Paula05/2013
537324^56298+2377704Norbert Schneider12/2016
5374(2^258105+78557)/1977697Lelio R Paula10/2012
53752^258079+17977690Lelio R Paula03/2012
53762^258062-11311177685Enzo Doria07/2014
537780^40807-7977660Norbert Schneider03/2015
5378(10^77637+359)/977637Serge Batalov12/2014
53792^257862-16577625Lelio R Paula03/2012
5380(25*2^257853+1)/377623Lelio R Paula07/2012
5381(2^257869+1)/(3*18645362967379)77613Henri Lifchitz04/2005
53826^99728+7177604Lelio R Paula01/2015
53832^257778-11276777599Enzo Doria06/2014
5384(31*2^257771+1)/53777596Lelio R Paula07/2012
53852^257729-7377585Lelio R Paula03/2012
53862^257689-6377573Lelio R Paula03/2012
5387(78557*2^257665+1)/610872577564Lelio R Paula06/2014
5388(3^162563+8)/288577559Lelio R Paula10/2012
53892^257636-11023577557Enzo Doria05/2014
5390(23*10^77556+97)/377557Robert Price02/2017
53912^257621-11007177552Enzo Doria04/2014
53922^257567-6487577536Lelio R Paula06/2013
53932*7^91674+977474Lelio R Paula10/2014
5394(17*10^77427-47)/377428Robert Price05/2017
539510^77418+84168377419Patrick De Geest06/2013
539610^77418-3377418Robert Price05/2011
539719^60539-3677415Lelio R Paula03/2015
539837401!!-102477397Robert Price11/2015
539911^74313-1875077390Enzo Doria12/2012
54002^257044-11288377378Enzo Doria06/2014
54018*10^77377+5177378Robert Price05/2017
54022*7^91553+977372Lelio R Paula10/2014
5403713^27118+27118^71377371Norbert Schneider12/2016
54042^256920-11115577341Enzo Doria05/2014
54052^256896-655577334Lelio R Paula06/2013
5406(52*10^77322-7)/977323Robert Price12/2014
54072^256849-11293977320Enzo Doria06/2014
5408(4*10^77309-31)/977309Erik Branger05/2011
5409(3^161988+7)/4186477284Lelio R Paula10/2012
5410(14^67421-1)/1377272Paul Bourdelais09/2008
54115*3^161923-477258Lelio R Paula06/2014
54122^256552-149977230Yves Minet05/2013
54132^256460-11275777203Enzo Doria06/2014
54142^256398+2329977184Yves Minet02/2011
54152^256391-1155*25639177182Henri Lifchitz03/2005
5416(2^256391-9)/5659377177Lelio R Paula10/2012
5417(2^256308+9)/1058577153Lelio R Paula10/2012
541921^58348-277149Lelio R Paula08/2013
5418(17*2^256291-1)/478577149Lelio R Paula02/2014
5420(5*2^256274-1)/214177144Lelio R Paula02/2014
542119^60321+8277136Lelio R Paula03/2015
54225*2^256233-377135Lelio R Paula06/2014
54233*2^256149+777110Lelio R Paula06/2014
54243^161594-10677100Lelio R Paula02/2015
54252^256114-18577098Lelio R Paula03/2012
54268^85349-85349^877078Norbert Schneider05/2017
54272^256043-278637777077Enzo Doria03/2016
54282^255973+186994777056Enzo Doria05/2016
542912^71393-4377046Lelio R Paula02/2015
543015^65490+4477023Lelio R Paula02/2015
5431(3^161411-7)/94077010Lelio R Paula10/2012
5433lucasU(1107,1,25297)-lucasU(1107,1,25296)77005Mike Oakes05/2009
5432(570^27943-1)/56977005Serge Batalov12/2016
54342^255750-7576989Lelio R Paula03/2012
54353*6^98926-576980Lelio R Paula10/2014
543618^61320-143376974Enzo Doria03/2013
54376^98916-1709376972Enzo Doria02/2013
54382^255659-11013176962Enzo Doria04/2014
543912^71303+9176949Lelio R Paula02/2015
544018^61298+5976946Lelio R Paula02/2015
5441(223^32768+1)/13107476945Lelio R Paula02/2009
5442(2^255613-5)/28151776942Lelio R Paula10/2012
544318^61290-1176936Lelio R Paula02/2015
544563^42752-276926Lelio R Paula08/2013
5444(11*2^255545-1)/11776926Lelio R Paula02/2014
54462^255517+5638776919Yves Minet02/2011
54472^255499-11256776913Enzo Doria06/2014
54482^255492+34576911Lelio R Paula06/2013
544910^76875+21759176876Patrick De Geest05/2013
545110^76875-5376875Robert Price05/2011
545011^73819-588076875Enzo Doria01/2013
54522^255313+1891576857Lelio R Paula06/2013
5453(2^255320-1017)/144666776853Lelio R Paula10/2012
54542^255296+577576852Lelio R Paula06/2013
545514^67052-2976851Lelio R Paula02/2015
5456(8*10^76840+43)/376841Robert Price10/2017
5457(7*10^76818-313)/976818Robert Price11/2016
545810^76801+6976802Robert Price03/2011
545910^76801-8094376801Patrick De Geest06/2013
54602^255105+5776795Lelio R Paula03/2012
5461(lucasV(1,2,510187)+2)/(3*5*11)76789Mike Oakes04/2017
5462(2^255097-7)/2002005576785Lelio R Paula10/2012
54632^255055+186935376780Enzo Doria05/2016
546417^62396-9076776Lelio R Paula03/2015
54657^90833-6076763Lelio R Paula02/2015
546613^68901-5676752Lelio R Paula03/2015
54672^254961+186991776751Enzo Doria05/2016
54689*5^109791-876742Lelio R Paula10/2014
546982^40089+40089^8276723Serge Batalov02/2012
54702^254861-279001376721Enzo Doria03/2016
547110^76705+1376706Robert Price01/2011
547210^76705-9407776705Patrick De Geest06/2013
5473(5*2^254785-1)/99976696Lelio R Paula02/2014
54742^254758-11040576690Enzo Doria05/2014
54752^254716-377976678Yves Minet04/2017
54762^254708-11050776675Enzo Doria05/2014
5477(47*10^76672+133)/976673Robert Price04/2017
54782^254670-11290176664Enzo Doria06/2014
5479(3^160665+7)/98135076651Lelio R Paula10/2012
54802^254598-11318376642Enzo Doria07/2014
548119^59932+2276639Lelio R Paula01/2015
54822^254569-11221376633Enzo Doria06/2014
54832*5^109626+976626Lelio R Paula10/2014
54842^254521+187252776619Enzo Doria05/2016
5485(76*10^76615+167)/976616Robert Price08/2016
548625^54799-24^5479976606Robert Price07/2012
5487(24737*2^254464+1)/976605Lelio R Paula06/2014
548812^70961-8576580Lelio R Paula02/2015
54897^90590-3876558Lelio R Paula02/2015
54902^254304+522776554Lelio R Paula06/2013
5491(76*10^76547-211)/976548Robert Price10/2017
549218^60979-536376546Enzo Doria03/2013
5493(21181*2^254264+1)/5531437976538Lelio R Paula06/2014
5495(34*10^76547-7)/9/61/94529/21480776536Makoto Morimoto05/2016
5494(7*10^76536-313)/976536Robert Price11/2016
54972^254239-2776534Lelio R Paula03/2012
54962^254238-184176534Yves Minet03/2013
5498(10^76537-1)/9/6612796976529Jens K. Andersen04/2009
54992^254189-11222576519Enzo Doria06/2014
550018^60938-139776494Enzo Doria03/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: November, 22 2017 23:29 (Time in France)

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