PRP Records

Probable Primes Top 10000

(255244 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 (> 50000) Who ? When ?
65012^260678-11106578472Enzo Doria05/2014
650218^62501-9778456Lelio R Paula02/2015
650353^45498-278452Lelio R Paula08/2013
65042^260513-11112178423Enzo Doria05/2014
650537845!2-6478412Robert Price06/2015
65062^260469-11069578409Enzo Doria05/2014
6507(11*10^78408-113)/378409Robert Price01/2017
65082^260447+841578403Lelio R Paula07/2013
650937837!2-6478394Robert Price06/2015
6510(19*2^260379-1)/5378382Lelio R Paula02/2014
65112^260377-11323378382Enzo Doria07/2014
65139^82138+6^82138-2^8213878380Mike Oakes08/2010
651269^42624+278380Lelio R Paula05/2013
65142^260369-185971378379Enzo Doria03/2016
651514*10^78362+108978364Jens K. Andersen11/2007
65165^112070-5478334Lelio R Paula02/2015
6517(10^(2*39165+1)+54*10^39165-1)/978331Robert Price04/2017
65182^260182-11345378323Enzo Doria07/2014
6519f(16405)78319Robert Price09/2017
6520(78557*2^260084+1)/51978296Lelio R Paula06/2014
652210^78288+9^(78288+1)78289Robert Price08/2016
652110^78288+3910978289Patrick De Geest12/2016
652310^78288-21629978288Patrick De Geest12/2016
65245^111997+3678283Lelio R Paula02/2015
6525(21^59183+1)/2278252Paul Bourdelais03/2010
6526(88*10^78242-7)/978243Robert Price11/2014
65272*6^100547+778242Lelio R Paula10/2014
65282^259860-11108978226Enzo Doria05/2014
652937^49875-278215Lelio R Paula09/2013
6530(13*10^78213+401)/978214Robert Price10/2017
65317*5^111893-478211Lelio R Paula10/2014
6532(11*2^259809-1)/143778209Lelio R Paula02/2014
65337^92511-678181Theodore Burton11/2005
6534(3^163859-4)/25378179Lelio R Paula10/2012
6535(27*2^259666-1)/62569178163Lelio R Paula02/2014
65363*10^78146+1778147Robert Price03/2017
6537(576^28307+1)/57778137Richard Fischer01/2018
65382^259503+7433378119Enzo Doria04/2016
6539(31*2^259504-1)/1336578116Lelio R Paula02/2014
6541(58547^16384+1)/278111Lelio R Paula11/2011
65406^100379+1378111Lelio R Paula03/2015
65422^259469-10990978108Enzo Doria04/2014
654315^66413-2678108Lelio R Paula02/2015
65447^92410-926678096Mike Oakes02/2010
65452^259398+7579978087Enzo Doria04/2016
65462^259394+187618978086Enzo Doria07/2016
6547PIPrime(78073)78073Eric W. Weisstein07/2006
65485*2^259344-778072Lelio R Paula06/2014
654914^68097-8778048Lelio R Paula02/2015
65502^259233-47557378037Paul Bourdelais03/2013
6551181^34554-278012Lelio R Paula10/2017
65523^163500-2878010Robert Price12/2013
6553(65*10^77992+691)/977993Robert Price08/2016
65542^259013-11259177971Enzo Doria06/2014
65557*10^77969-1177970Robert Price10/2017
65566^100193-100193^677966Norbert Schneider04/2017
65572^258863-11023577926Enzo Doria05/2014
65582^258852+160577923Lelio R Paula06/2013
6559(11*10^77909+49)/377910Robert Price05/2016
65602*7^92187-977908Lelio R Paula10/2014
65612^258763-11015577896Enzo Doria04/2014
65622^258694-11038777875Enzo Doria05/2014
656311^74773-9477869Lelio R Paula02/2015
65646^100067+12577868Lelio R Paula03/2015
656515^66205+877864Lelio R Paula07/2014
65665^111373-1813677847Enzo Doria05/2014
65672^258524-10987777824Enzo Doria04/2014
65686^100002-1664377817Enzo Doria02/2013
6569(13*10^77811+347)/977812Robert Price10/2017
657065^42916+2877803Lelio R Paula01/2016
6571(89*10^77781-17)/977782Robert Price11/2015
65722^258382-11040577781Enzo Doria05/2014
65735^111278-1499677780Enzo Doria02/2013
657414^67862+6177779Lelio R Paula02/2015
657510^77777+4848377778Patrick De Geest11/2010
657610^77777-18324377777Patrick De Geest11/2010
6577(27*2^258352+1)/4377772Lelio R Paula08/2012
6578337^30756-1000277740Enzo Doria07/2012
657910^77726+9977727Robert Price03/2011
658010^77726-8594777726Patrick De Geest06/2013
658189^39870-277723Lelio R Paula08/2013
65827^91966-3277721Lelio R Paula02/2015
658335^50327+277709Lelio R Paula05/2013
658424^56298+2377704Norbert Schneider12/2016
6585(2^258105+78557)/1977697Lelio R Paula10/2012
65862^258079+17977690Lelio R Paula03/2012
65872^258062-11311177685Enzo Doria07/2014
658810^77669+12345678977670Robert Price10/2019
658980^40807-7977660Norbert Schneider03/2015
659070385!4-477658Robert Price11/2019
6591(10^77637+359)/977637Serge Batalov12/2014
65922^257862-16577625Lelio R Paula03/2012
6593(25*2^257853+1)/377623Lelio R Paula07/2012
6594(2^257869+1)/(3*18645362967379)77613Henri Lifchitz04/2005
65956^99728+7177604Lelio R Paula01/2015
65962^257778-11276777599Enzo Doria06/2014
6597(31*2^257771+1)/53777596Lelio R Paula07/2012
65982^257729-7377585Lelio R Paula03/2012
65992^257689-6377573Lelio R Paula03/2012
6600(47*10^77572+493)/977573Robert Price11/2017
6601(78557*2^257665+1)/610872577564Lelio R Paula06/2014
6602(3^162563+8)/288577559Lelio R Paula10/2012
66032^257636-11023577557Enzo Doria05/2014
6604(23*10^77556+97)/377557Robert Price02/2017
66052^257621-11007177552Enzo Doria04/2014
66062^257567-6487577536Lelio R Paula06/2013
66072*7^91674+977474Lelio R Paula10/2014
6608(17*10^77427-47)/377428Robert Price05/2017
660910^77418+84168377419Patrick De Geest06/2013
661010^77418-3377418Robert Price05/2011
661119^60539-3677415Lelio R Paula03/2015
661237401!!-102477397Robert Price11/2015
661311^74313-1875077390Enzo Doria12/2012
66142^257044-11288377378Enzo Doria06/2014
66158*10^77377+5177378Robert Price05/2017
66162*7^91553+977372Lelio R Paula10/2014
6617713^27118+27118^71377371Norbert Schneider12/2016
66182^256920-11115577341Enzo Doria05/2014
66192^256896-655577334Lelio R Paula06/2013
6620(52*10^77322-7)/977323Robert Price12/2014
66212^256849-11293977320Enzo Doria06/2014
6622(4*10^77309-31)/977309Erik Branger05/2011
6623(3^161988+7)/4186477284Lelio R Paula10/2012
6624(14^67421-1)/1377272Paul Bourdelais09/2008
66255*3^161923-477258Lelio R Paula06/2014
66262^256552-149977230Yves Minet05/2013
66272^256460-11275777203Enzo Doria06/2014
66282^256398+2329977184Yves Minet02/2011
66292^256391-1155*25639177182Henri Lifchitz03/2005
6630(2^256391-9)/5659377177Lelio R Paula10/2012
6631(2^256308+9)/1058577153Lelio R Paula10/2012
663221^58348-277149Lelio R Paula08/2013
6633(17*2^256291-1)/478577149Lelio R Paula02/2014
6634(5*2^256274-1)/214177144Lelio R Paula02/2014
663519^60321+8277136Lelio R Paula03/2015
66365*2^256233-377135Lelio R Paula06/2014
66373*2^256149+777110Lelio R Paula06/2014
66383^161594-10677100Lelio R Paula02/2015
66392^256114-18577098Lelio R Paula03/2012
66408^85349-85349^877078Norbert Schneider05/2017
66412^256043-278637777077Enzo Doria03/2016
66422^255973+186994777056Enzo Doria05/2016
664312^71393-4377046Lelio R Paula02/2015
664415^65490+4477023Lelio R Paula02/2015
6645(3^161411-7)/94077010Lelio R Paula10/2012
6646lucasU(1107,1,25297)-lucasU(1107,1,25296)77005Mike Oakes05/2009
6647(570^27943-1)/56977005Serge Batalov12/2016
66482^255750-7576989Lelio R Paula03/2012
66493*6^98926-576980Lelio R Paula10/2014
665018^61320-143376974Enzo Doria03/2013
66516^98916-1709376972Enzo Doria02/2013
66522^255659-11013176962Enzo Doria04/2014
665369805!4-12876956Robert Price11/2019
665412^71303+9176949Lelio R Paula02/2015
665518^61298+5976946Lelio R Paula02/2015
6656(223^32768+1)/13107476945Lelio R Paula02/2009
6657(2^255613-5)/28151776942Lelio R Paula10/2012
665818^61290-1176936Lelio R Paula02/2015
666063^42752-276926Lelio R Paula08/2013
6659(11*2^255545-1)/11776926Lelio R Paula02/2014
66612^255517+5638776919Yves Minet02/2011
66622^255499-11256776913Enzo Doria06/2014
66632^255492+34576911Lelio R Paula06/2013
666410^76875+21759176876Patrick De Geest05/2013
666610^76875-5376875Robert Price05/2011
666511^73819-588076875Enzo Doria01/2013
66672^255313+1891576857Lelio R Paula06/2013
6668(2^255320-1017)/144666776853Lelio R Paula10/2012
66692^255296+577576852Lelio R Paula06/2013
667014^67052-2976851Lelio R Paula02/2015
6671(8*10^76840+43)/376841Robert Price10/2017
6672(7*10^76818-313)/976818Robert Price11/2016
667310^76801+6976802Robert Price03/2011
667410^76801-8094376801Patrick De Geest06/2013
66752^255105+5776795Lelio R Paula03/2012
6676(lucasV(1,2,510187)+2)/(3*5*11)76789Mike Oakes04/2017
6677(2^255097-7)/2002005576785Lelio R Paula10/2012
66782^255055+186935376780Enzo Doria05/2016
667917^62396-9076776Lelio R Paula03/2015
66807^90833-6076763Lelio R Paula02/2015
668113^68901-5676752Lelio R Paula03/2015
66822^254961+186991776751Enzo Doria05/2016
66839*5^109791-876742Lelio R Paula10/2014
668482^40089+40089^8276723Serge Batalov02/2012
66852^254861-279001376721Enzo Doria03/2016
6686(10^278+1)*(10^115926+1)/(10^834+1)/(10^38642+1)/2045977974176718Makoto Kamada03/2019
668710^76705+1376706Robert Price01/2011
668810^76705-9407776705Patrick De Geest06/2013
6689(5*2^254785-1)/99976696Lelio R Paula02/2014
66902^254758-11040576690Enzo Doria05/2014
66912^254716-377976678Yves Minet04/2017
66922^254708-11050776675Enzo Doria05/2014
6693(47*10^76672+133)/976673Robert Price04/2017
66942^254670-11290176664Enzo Doria06/2014
6695(3^160665+7)/98135076651Lelio R Paula10/2012
66962^254598-11318376642Enzo Doria07/2014
669719^59932+2276639Lelio R Paula01/2015
66982^254569-11221376633Enzo Doria06/2014
66992*5^109626+976626Lelio R Paula10/2014
67002^254521+187252776619Enzo Doria05/2016
6701(76*10^76615+167)/976616Robert Price08/2016
670225^54799-24^5479976606Robert Price07/2012
6703(24737*2^254464+1)/976605Lelio R Paula06/2014
670412^70961-8576580Lelio R Paula02/2015
67057^90590-3876558Lelio R Paula02/2015
67062^254304+522776554Lelio R Paula06/2013
6707(76*10^76547-211)/976548Robert Price10/2017
670818^60979-536376546Enzo Doria03/2013
6709(21181*2^254264+1)/5531437976538Lelio R Paula06/2014
6711(34*10^76547-7)/9/61/94529/21480776536Makoto Morimoto05/2016
6710(7*10^76536-313)/976536Robert Price11/2016
67132^254239-2776534Lelio R Paula03/2012
67122^254238-184176534Yves Minet03/2013
6714(10^76537-1)/9/6612796976529Jens K. Andersen04/2009
67152^254189-11222576519Enzo Doria06/2014
671618^60938-139776494Enzo Doria03/2013
67172^254075-278841776485Enzo Doria03/2016
67187*10^76483-2376484Robert Price04/2016
67192^254042-11291376475Enzo Doria06/2014
672014^66723-3776474Lelio R Paula02/2015
67212^254037-11030576473Enzo Doria05/2014
67222^253931-11110976441Enzo Doria05/2014
67232^253926-116776440Lelio R Paula05/2013
6724(49*10^76438-13)/976439Robert Price07/2015
6725(21*2^253845-1)/14376415Lelio R Paula02/2014
672610^76374+3176375Robert Price03/2011
672710^76374-22215976374Patrick De Geest05/2013
67282^253561-11053376330Enzo Doria05/2014
6729gcd(V(917285),5*F(183457)*(F(183457)+1)+1)76321Serge Batalov04/2015
67309*5^109182+276316Lelio R Paula10/2014
673111^73279-369076313Enzo Doria12/2012
6732(598*10^76309-31)/976311Robert Price02/2017
673311^73274-2400076308Enzo Doria12/2012
67347^90291-676305Theodore Burton11/2005
6735(21181*2^253432+1)/2143776291Lelio R Paula06/2014
673669247!4+476280Robert Price09/2019
67376^98025+14576279Lelio R Paula01/2015
67382^253355+115576268Lelio R Paula05/2013
6739(73*10^76262+413)/976263Robert Price10/2017
67402^253292-7121976249Enzo Doria04/2016
67417^90221-3676246Lelio R Paula02/2015
674218^60727-347376229Enzo Doria03/2013
6743(78557*2^253184+1)/376221Lelio R Paula06/2014
6744(8*10^76220-83)/376221Robert Price10/2017
6745(44791^20480+1)/(44791^4096+1)76206Serge Batalov01/2017
674611^73163-201076192Enzo Doria12/2012
67472^253060+5461576179Lelio R Paula05/2013
67482^253029+186976176170Enzo Doria05/2016
67492^252955-11100776148Enzo Doria05/2014
67502*5^108931+776140Lelio R Paula10/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: November, 10 2019 12:07 (Time in France)

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