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 ?
5001(2^261724+184549)/5/8699/44053/140932299778769Tony Prest / Never Odd Or Even04/2014
5002(2^261724+363351)/937/159683/5952320022778768Tony Prest / Never Odd Or Even04/2014
5003(2^261724+326501)/3/43/193/263/19403/25350140378768Tony Prest / Never Odd Or Even04/2014
5004(2^261724+629477)/3/17/17/137/263/1993/16187/5734778768Tony Prest / Never Odd Or Even05/2014
5005(2^261724+94871)/3/3/13/6734017/167342524578778766Tony Prest / Never Odd Or Even04/2014
5006(2^261724+25981)/577/1181/3643/51778633474378766Tony Prest / Never Odd Or Even04/2014
5008(23*2^261642+1)/9378762Lelio R Paula10/2012
5007(2^261724+351227)/3/3/3/3/71/13997/9595373/819397800778762Tony Prest / Never Odd Or Even04/2014
5009(2^261724+22571)/3/7243/7321/18046081/4573074121178761Tony Prest / Never Odd Or Even04/2014
5010(2^261724+56495)/3/3/3/7/7/13/9041/512818459/2370858911978760Tony Prest / Never Odd Or Even04/2014
5011(2^261724+604119)/5/7/7/41/14107/19681/211777/90145981/103602083412778750Tony Prest / Never Odd Or Even05/2014
50122^261507-228778722Yves Minet04/2009
50138*10^78717+3978718Robert Price01/2017
5014(78557*2^261440+1)/378706Lelio R Paula06/2014
50156^101128-1643378693Enzo Doria02/2013
501620^60482+9978689Lelio R Paula03/2015
50172^261348-11063378674Enzo Doria05/2014
5018191^34487+278666Lelio R Paula05/2013
50192^261305-11013978661Enzo Doria04/2014
5020(82*10^78635-1)/978636Robert Price12/2014
502110^78632+8178633Robert Price03/2011
502210^78632-40269378632Patrick De Geest07/2013
50233*10^78631+1778632Robert Price03/2017
50242^261174-391178622Yves Minet04/2017
50252^261167+7484378620Enzo Doria04/2016
5026L(376121)+F(376122)78605Henri Lifchitz01/2007
502714^68580-2978602Lelio R Paula02/2015
5028(73*10^78576-1)/978577Robert Price01/2015
5029(17*2^261026-1)/4045178574Lelio R Paula02/2014
50302^261001-19578570Lelio R Paula05/2012
50315*2^260950+978555Lelio R Paula06/2014
50322^260931-760578549Lelio R Paula07/2013
503315^66778-3278538Lelio R Paula02/2015
5034(11*2^260896-1)/24578537Lelio R Paula02/2014
503530^53166+2978533Norbert Schneider03/2017
5036lucasU(2403,1,23229)-lucasU(2403,1,23228)78529Mike Oakes05/2009
50377*3^164574-278523Lelio R Paula06/2014
50382^260830-11213378518Enzo Doria06/2014
503913^70486+4278518Lelio R Paula03/2015
504011^75386-708078507Enzo Doria01/2013
50412^260711-5869578482Lelio R Paula07/2013
50422^260678-11106578472Enzo Doria05/2014
504318^62501-9778456Lelio R Paula02/2015
504453^45498-278452Lelio R Paula08/2013
50452^260513-11112178423Enzo Doria05/2014
504637845!2-6478412Robert Price06/2015
50472^260469-11069578409Enzo Doria05/2014
5048(11*10^78408-113)/378409Robert Price01/2017
50492^260447+841578403Lelio R Paula07/2013
505037837!2-6478394Robert Price06/2015
5051(19*2^260379-1)/5378382Lelio R Paula02/2014
50522^260377-11323378382Enzo Doria07/2014
50539^82138+6^82138-2^8213878380Mike Oakes08/2010
505469^42624+278380Lelio R Paula05/2013
50552^260369-185971378379Enzo Doria03/2016
505614*10^78362+108978364Jens K. Andersen11/2007
50575^112070-5478334Lelio R Paula02/2015
5058(10^(2*39165+1)+54*10^39165-1)/978331Robert Price04/2017
50592^260182-11345378323Enzo Doria07/2014
5060(78557*2^260084+1)/51978296Lelio R Paula06/2014
506210^78288+9^(78288+1)78289Robert Price08/2016
506110^78288+3910978289Patrick De Geest12/2016
506310^78288-21629978288Patrick De Geest12/2016
50645^111997+3678283Lelio R Paula02/2015
5065(21^59183+1)/2278252Paul Bourdelais03/2010
5066(88*10^78242-7)/978243Robert Price11/2014
50672*6^100547+778242Lelio R Paula10/2014
50682^259860-11108978226Enzo Doria05/2014
506937^49875-278215Lelio R Paula09/2013
50707*5^111893-478211Lelio R Paula10/2014
5071(11*2^259809-1)/143778209Lelio R Paula02/2014
50727^92511-678181Theodore Burton11/2005
5073(3^163859-4)/25378179Lelio R Paula10/2012
5074(27*2^259666-1)/62569178163Lelio R Paula02/2014
50753*10^78146+1778147Robert Price03/2017
50762^259503+7433378119Enzo Doria04/2016
5077(31*2^259504-1)/1336578116Lelio R Paula02/2014
5079(58547^16384+1)/278111Lelio R Paula11/2011
50786^100379+1378111Lelio R Paula03/2015
50802^259469-10990978108Enzo Doria04/2014
508115^66413-2678108Lelio R Paula02/2015
50827^92410-926678096Mike Oakes02/2010
50832^259398+7579978087Enzo Doria04/2016
50842^259394+187618978086Enzo Doria07/2016
5085PIPrime(78073)78073Eric W. Weisstein07/2006
50865*2^259344-778072Lelio R Paula06/2014
508714^68097-8778048Lelio R Paula02/2015
50882^259233-47557378037Paul Bourdelais03/2013
50893^163500-2878010Robert Price12/2013
5090(65*10^77992+691)/977993Robert Price08/2016
50912^259013-11259177971Enzo Doria06/2014
50926^100193-100193^677966Norbert Schneider04/2017
50932^258863-11023577926Enzo Doria05/2014
50942^258852+160577923Lelio R Paula06/2013
5095(11*10^77909+49)/377910Robert Price05/2016
50962*7^92187-977908Lelio R Paula10/2014
50972^258763-11015577896Enzo Doria04/2014
50982^258694-11038777875Enzo Doria05/2014
509911^74773-9477869Lelio R Paula02/2015
51006^100067+12577868Lelio R Paula03/2015
510115^66205+877864Lelio R Paula07/2014
51025^111373-1813677847Enzo Doria05/2014
51032^258524-10987777824Enzo Doria04/2014
51046^100002-1664377817Enzo Doria02/2013
510565^42916+2877803Lelio R Paula01/2016
5106(89*10^77781-17)/977782Robert Price11/2015
51072^258382-11040577781Enzo Doria05/2014
51085^111278-1499677780Enzo Doria02/2013
510914^67862+6177779Lelio R Paula02/2015
511010^77777+4848377778Patrick De Geest11/2010
511110^77777-18324377777Patrick De Geest11/2010
5112(27*2^258352+1)/4377772Lelio R Paula08/2012
5113337^30756-1000277740Enzo Doria07/2012
511410^77726+9977727Robert Price03/2011
511510^77726-8594777726Patrick De Geest06/2013
511689^39870-277723Lelio R Paula08/2013
51177^91966-3277721Lelio R Paula02/2015
511835^50327+277709Lelio R Paula05/2013
511924^56298+2377704Norbert Schneider12/2016
5120(2^258105+78557)/1977697Lelio R Paula10/2012
51212^258079+17977690Lelio R Paula03/2012
51222^258062-11311177685Enzo Doria07/2014
512380^40807-7977660Norbert Schneider03/2015
5124(10^77637+359)/977637Serge Batalov12/2014
51252^257862-16577625Lelio R Paula03/2012
5126(25*2^257853+1)/377623Lelio R Paula07/2012
5127(2^257869+1)/(3*18645362967379)77613Henri Lifchitz04/2005
51286^99728+7177604Lelio R Paula01/2015
51292^257778-11276777599Enzo Doria06/2014
5130(31*2^257771+1)/53777596Lelio R Paula07/2012
51312^257729-7377585Lelio R Paula03/2012
51322^257689-6377573Lelio R Paula03/2012
5133(78557*2^257665+1)/610872577564Lelio R Paula06/2014
5134(3^162563+8)/288577559Lelio R Paula10/2012
51362^257636-11023577557Enzo Doria05/2014
5135(23*10^77556+97)/377557Robert Price02/2017
51372^257621-11007177552Enzo Doria04/2014
51382^257567-6487577536Lelio R Paula06/2013
51392*7^91674+977474Lelio R Paula10/2014
5140(17*10^77427-47)/377428Robert Price05/2017
514110^77418+84168377419Patrick De Geest06/2013
514210^77418-3377418Robert Price05/2011
514319^60539-3677415Lelio R Paula03/2015
514437401!!-102477397Robert Price11/2015
514511^74313-1875077390Enzo Doria12/2012
51462^257044-11288377378Enzo Doria06/2014
51478*10^77377+5177378Robert Price05/2017
51482*7^91553+977372Lelio R Paula10/2014
5149713^27118+27118^71377371Norbert Schneider12/2016
51502^256920-11115577341Enzo Doria05/2014
51512^256896-655577334Lelio R Paula06/2013
5152(52*10^77322-7)/977323Robert Price12/2014
51532^256849-11293977320Enzo Doria06/2014
5154(4*10^77309-31)/977309Erik Branger05/2011
5155(3^161988+7)/4186477284Lelio R Paula10/2012
5156(14^67421-1)/1377272Paul Bourdelais09/2008
51575*3^161923-477258Lelio R Paula06/2014
51582^256552-149977230Yves Minet05/2013
51592^256460-11275777203Enzo Doria06/2014
51602^256398+2329977184Yves Minet02/2011
51612^256391-1155*25639177182Henri Lifchitz03/2005
5162(2^256391-9)/5659377177Lelio R Paula10/2012
5163(2^256308+9)/1058577153Lelio R Paula10/2012
516521^58348-277149Lelio R Paula08/2013
5164(17*2^256291-1)/478577149Lelio R Paula02/2014
5166(5*2^256274-1)/214177144Lelio R Paula02/2014
516719^60321+8277136Lelio R Paula03/2015
51685*2^256233-377135Lelio R Paula06/2014
51693*2^256149+777110Lelio R Paula06/2014
51703^161594-10677100Lelio R Paula02/2015
51712^256114-18577098Lelio R Paula03/2012
51728^85349-85349^877078Norbert Schneider05/2017
51732^256043-278637777077Enzo Doria03/2016
51742^255973+186994777056Enzo Doria05/2016
517512^71393-4377046Lelio R Paula02/2015
517615^65490+4477023Lelio R Paula02/2015
5177(3^161411-7)/94077010Lelio R Paula10/2012
5179lucasU(1107,1,25297)-lucasU(1107,1,25296)77005Mike Oakes05/2009
5178(570^27943-1)/56977005Serge Batalov12/2016
51802^255750-7576989Lelio R Paula03/2012
51813*6^98926-576980Lelio R Paula10/2014
518218^61320-143376974Enzo Doria03/2013
51836^98916-1709376972Enzo Doria02/2013
51842^255659-11013176962Enzo Doria04/2014
518512^71303+9176949Lelio R Paula02/2015
518618^61298+5976946Lelio R Paula02/2015
5187(223^32768+1)/13107476945Lelio R Paula02/2009
5188(2^255613-5)/28151776942Lelio R Paula10/2012
518918^61290-1176936Lelio R Paula02/2015
519163^42752-276926Lelio R Paula08/2013
5190(11*2^255545-1)/11776926Lelio R Paula02/2014
51922^255517+5638776919Yves Minet02/2011
51932^255499-11256776913Enzo Doria06/2014
51942^255492+34576911Lelio R Paula06/2013
519510^76875+21759176876Patrick De Geest05/2013
519710^76875-5376875Robert Price05/2011
519611^73819-588076875Enzo Doria01/2013
51982^255313+1891576857Lelio R Paula06/2013
5199(2^255320-1017)/144666776853Lelio R Paula10/2012
52002^255296+577576852Lelio R Paula06/2013
520114^67052-2976851Lelio R Paula02/2015
5202(7*10^76818-313)/976818Robert Price11/2016
520310^76801+6976802Robert Price03/2011
520410^76801-8094376801Patrick De Geest06/2013
52052^255105+5776795Lelio R Paula03/2012
5206(lucasV(1,2,510187)+2)/(3*5*11)76789Mike Oakes04/2017
5207(2^255097-7)/2002005576785Lelio R Paula10/2012
52082^255055+186935376780Enzo Doria05/2016
520917^62396-9076776Lelio R Paula03/2015
52107^90833-6076763Lelio R Paula02/2015
521113^68901-5676752Lelio R Paula03/2015
52122^254961+186991776751Enzo Doria05/2016
52139*5^109791-876742Lelio R Paula10/2014
521482^40089+40089^8276723Serge Batalov02/2012
52152^254861-279001376721Enzo Doria03/2016
521610^76705+1376706Robert Price01/2011
521710^76705-9407776705Patrick De Geest06/2013
5218(5*2^254785-1)/99976696Lelio R Paula02/2014
52192^254758-11040576690Enzo Doria05/2014
52202^254716-377976678Yves Minet04/2017
52212^254708-11050776675Enzo Doria05/2014
5222(47*10^76672+133)/976673Robert Price04/2017
52232^254670-11290176664Enzo Doria06/2014
5224(3^160665+7)/98135076651Lelio R Paula10/2012
52252^254598-11318376642Enzo Doria07/2014
522619^59932+2276639Lelio R Paula01/2015
52272^254569-11221376633Enzo Doria06/2014
52282*5^109626+976626Lelio R Paula10/2014
52292^254521+187252776619Enzo Doria05/2016
5230(76*10^76615+167)/976616Robert Price08/2016
523125^54799-24^5479976606Robert Price07/2012
5232(24737*2^254464+1)/976605Lelio R Paula06/2014
523312^70961-8576580Lelio R Paula02/2015
52347^90590-3876558Lelio R Paula02/2015
52352^254304+522776554Lelio R Paula06/2013
523618^60979-536376546Enzo Doria03/2013
5237(21181*2^254264+1)/5531437976538Lelio R Paula06/2014
5238(34*10^76547-7)/9/61/94529/21480776536Makoto Morimoto05/2016
5239(7*10^76536-313)/976536Robert Price11/2016
52412^254239-2776534Lelio R Paula03/2012
52402^254238-184176534Yves Minet03/2013
5242(10^76537-1)/9/6612796976529Jens K. Andersen04/2009
52432^254189-11222576519Enzo Doria06/2014
524418^60938-139776494Enzo Doria03/2013
52452^254075-278841776485Enzo Doria03/2016
52467*10^76483-2376484Robert Price04/2016
52472^254042-11291376475Enzo Doria06/2014
524814^66723-3776474Lelio R Paula02/2015
52492^254037-11030576473Enzo Doria05/2014
52502^253931-11110976441Enzo Doria05/2014


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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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