PRP Records

Probable Primes Top 10000

(173006 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 ?
50012^260830-11213378518Enzo Doria06/2014
500213^70486+4278518Lelio R Paula03/2015
500311^75386-708078507Enzo Doria01/2013
50042^260711-5869578482Lelio R Paula07/2013
50052^260678-11106578472Enzo Doria05/2014
500618^62501-9778456Lelio R Paula02/2015
500753^45498-278452Lelio R Paula08/2013
50082^260513-11112178423Enzo Doria05/2014
500937845!2-6478412Robert Price06/2015
50102^260469-11069578409Enzo Doria05/2014
5011(11*10^78408-113)/378409Robert Price01/2017
50122^260447+841578403Lelio R Paula07/2013
501337837!2-6478394Robert Price06/2015
5014(19*2^260379-1)/5378382Lelio R Paula02/2014
50152^260377-11323378382Enzo Doria07/2014
50169^82138+6^82138-2^8213878380Mike Oakes08/2010
501769^42624+278380Lelio R Paula05/2013
50182^260369-185971378379Enzo Doria03/2016
501914*10^78362+108978364Jens K. Andersen11/2007
50205^112070-5478334Lelio R Paula02/2015
5021(10^(2*39165+1)+54*10^39165-1)/978331Robert Price04/2017
50222^260182-11345378323Enzo Doria07/2014
5023(78557*2^260084+1)/51978296Lelio R Paula06/2014
502510^78288+9^(78288+1)78289Robert Price08/2016
502410^78288+3910978289Patrick De Geest12/2016
502610^78288-21629978288Patrick De Geest12/2016
50275^111997+3678283Lelio R Paula02/2015
5028(21^59183+1)/2278252Paul Bourdelais03/2010
5029(88*10^78242-7)/978243Robert Price11/2014
50302*6^100547+778242Lelio R Paula10/2014
50312^259860-11108978226Enzo Doria05/2014
503237^49875-278215Lelio R Paula09/2013
50337*5^111893-478211Lelio R Paula10/2014
5034(11*2^259809-1)/143778209Lelio R Paula02/2014
50357^92511-678181Theodore Burton11/2005
5036(3^163859-4)/25378179Lelio R Paula10/2012
5037(27*2^259666-1)/62569178163Lelio R Paula02/2014
50383*10^78146+1778147Robert Price03/2017
50392^259503+7433378119Enzo Doria04/2016
5040(31*2^259504-1)/1336578116Lelio R Paula02/2014
5042(58547^16384+1)/278111Lelio R Paula11/2011
50416^100379+1378111Lelio R Paula03/2015
50432^259469-10990978108Enzo Doria04/2014
504415^66413-2678108Lelio R Paula02/2015
50457^92410-926678096Mike Oakes02/2010
50462^259398+7579978087Enzo Doria04/2016
50472^259394+187618978086Enzo Doria07/2016
5048PIPrime(78073)78073Eric W. Weisstein07/2006
50495*2^259344-778072Lelio R Paula06/2014
505014^68097-8778048Lelio R Paula02/2015
50512^259233-47557378037Paul Bourdelais03/2013
50523^163500-2878010Robert Price12/2013
5053(65*10^77992+691)/977993Robert Price08/2016
50542^259013-11259177971Enzo Doria06/2014
50556^100193-100193^677966Norbert Schneider04/2017
50562^258863-11023577926Enzo Doria05/2014
50572^258852+160577923Lelio R Paula06/2013
5058(11*10^77909+49)/377910Robert Price05/2016
50592*7^92187-977908Lelio R Paula10/2014
50602^258763-11015577896Enzo Doria04/2014
50612^258694-11038777875Enzo Doria05/2014
506211^74773-9477869Lelio R Paula02/2015
50636^100067+12577868Lelio R Paula03/2015
506415^66205+877864Lelio R Paula07/2014
50655^111373-1813677847Enzo Doria05/2014
50662^258524-10987777824Enzo Doria04/2014
50676^100002-1664377817Enzo Doria02/2013
506865^42916+2877803Lelio R Paula01/2016
5069(89*10^77781-17)/977782Robert Price11/2015
50702^258382-11040577781Enzo Doria05/2014
50715^111278-1499677780Enzo Doria02/2013
507214^67862+6177779Lelio R Paula02/2015
507310^77777+4848377778Patrick De Geest11/2010
507410^77777-18324377777Patrick De Geest11/2010
5075(27*2^258352+1)/4377772Lelio R Paula08/2012
5076337^30756-1000277740Enzo Doria07/2012
507710^77726+9977727Robert Price03/2011
507810^77726-8594777726Patrick De Geest06/2013
507989^39870-277723Lelio R Paula08/2013
50807^91966-3277721Lelio R Paula02/2015
508135^50327+277709Lelio R Paula05/2013
508224^56298+2377704Norbert Schneider12/2016
5083(2^258105+78557)/1977697Lelio R Paula10/2012
50842^258079+17977690Lelio R Paula03/2012
50852^258062-11311177685Enzo Doria07/2014
508680^40807-7977660Norbert Schneider03/2015
5087(10^77637+359)/977637Serge Batalov12/2014
50882^257862-16577625Lelio R Paula03/2012
5089(25*2^257853+1)/377623Lelio R Paula07/2012
5090(2^257869+1)/(3*18645362967379)77613Henri Lifchitz04/2005
50916^99728+7177604Lelio R Paula01/2015
50922^257778-11276777599Enzo Doria06/2014
5093(31*2^257771+1)/53777596Lelio R Paula07/2012
50942^257729-7377585Lelio R Paula03/2012
50952^257689-6377573Lelio R Paula03/2012
5096(78557*2^257665+1)/610872577564Lelio R Paula06/2014
5097(3^162563+8)/288577559Lelio R Paula10/2012
50982^257636-11023577557Enzo Doria05/2014
5099(23*10^77556+97)/377557Robert Price02/2017
51002^257621-11007177552Enzo Doria04/2014
51012^257567-6487577536Lelio R Paula06/2013
51022*7^91674+977474Lelio R Paula10/2014
5103(17*10^77427-47)/377428Robert Price05/2017
510410^77418+84168377419Patrick De Geest06/2013
510510^77418-3377418Robert Price05/2011
510619^60539-3677415Lelio R Paula03/2015
510737401!!-102477397Robert Price11/2015
510811^74313-1875077390Enzo Doria12/2012
51092^257044-11288377378Enzo Doria06/2014
51108*10^77377+5177378Robert Price05/2017
51112*7^91553+977372Lelio R Paula10/2014
5112713^27118+27118^71377371Norbert Schneider12/2016
51132^256920-11115577341Enzo Doria05/2014
51142^256896-655577334Lelio R Paula06/2013
5115(52*10^77322-7)/977323Robert Price12/2014
51162^256849-11293977320Enzo Doria06/2014
5117(4*10^77309-31)/977309Erik Branger05/2011
5118(3^161988+7)/4186477284Lelio R Paula10/2012
5119(14^67421-1)/1377272Paul Bourdelais09/2008
51205*3^161923-477258Lelio R Paula06/2014
51212^256552-149977230Yves Minet05/2013
51222^256460-11275777203Enzo Doria06/2014
51232^256398+2329977184Yves Minet02/2011
51242^256391-1155*25639177182Henri Lifchitz03/2005
5125(2^256391-9)/5659377177Lelio R Paula10/2012
5126(2^256308+9)/1058577153Lelio R Paula10/2012
512821^58348-277149Lelio R Paula08/2013
5127(17*2^256291-1)/478577149Lelio R Paula02/2014
5129(5*2^256274-1)/214177144Lelio R Paula02/2014
513019^60321+8277136Lelio R Paula03/2015
51315*2^256233-377135Lelio R Paula06/2014
51323*2^256149+777110Lelio R Paula06/2014
51333^161594-10677100Lelio R Paula02/2015
51342^256114-18577098Lelio R Paula03/2012
51352^256043-278637777077Enzo Doria03/2016
51362^255973+186994777056Enzo Doria05/2016
513712^71393-4377046Lelio R Paula02/2015
513815^65490+4477023Lelio R Paula02/2015
5139(3^161411-7)/94077010Lelio R Paula10/2012
5141lucasU(1107,1,25297)-lucasU(1107,1,25296)77005Mike Oakes05/2009
5140(570^27943-1)/56977005Serge Batalov12/2016
51422^255750-7576989Lelio R Paula03/2012
51433*6^98926-576980Lelio R Paula10/2014
514418^61320-143376974Enzo Doria03/2013
51456^98916-1709376972Enzo Doria02/2013
51462^255659-11013176962Enzo Doria04/2014
514712^71303+9176949Lelio R Paula02/2015
514818^61298+5976946Lelio R Paula02/2015
5149(223^32768+1)/13107476945Lelio R Paula02/2009
5150(2^255613-5)/28151776942Lelio R Paula10/2012
515118^61290-1176936Lelio R Paula02/2015
515363^42752-276926Lelio R Paula08/2013
5152(11*2^255545-1)/11776926Lelio R Paula02/2014
51542^255517+5638776919Yves Minet02/2011
51552^255499-11256776913Enzo Doria06/2014
51562^255492+34576911Lelio R Paula06/2013
515710^76875+21759176876Patrick De Geest05/2013
515910^76875-5376875Robert Price05/2011
515811^73819-588076875Enzo Doria01/2013
51602^255313+1891576857Lelio R Paula06/2013
5161(2^255320-1017)/144666776853Lelio R Paula10/2012
51622^255296+577576852Lelio R Paula06/2013
516314^67052-2976851Lelio R Paula02/2015
5164(7*10^76818-313)/976818Robert Price11/2016
516510^76801+6976802Robert Price03/2011
516610^76801-8094376801Patrick De Geest06/2013
51672^255105+5776795Lelio R Paula03/2012
5168(lucasV(1,2,510187)+2)/(3*5*11)76789Mike Oakes04/2017
5169(2^255097-7)/2002005576785Lelio R Paula10/2012
51702^255055+186935376780Enzo Doria05/2016
517117^62396-9076776Lelio R Paula03/2015
51727^90833-6076763Lelio R Paula02/2015
517313^68901-5676752Lelio R Paula03/2015
51742^254961+186991776751Enzo Doria05/2016
51759*5^109791-876742Lelio R Paula10/2014
517682^40089+40089^8276723Serge Batalov02/2012
51772^254861-279001376721Enzo Doria03/2016
517810^76705+1376706Robert Price01/2011
517910^76705-9407776705Patrick De Geest06/2013
5180(5*2^254785-1)/99976696Lelio R Paula02/2014
51812^254758-11040576690Enzo Doria05/2014
51822^254716-377976678Yves Minet04/2017
51832^254708-11050776675Enzo Doria05/2014
5184(47*10^76672+133)/976673Robert Price04/2017
51852^254670-11290176664Enzo Doria06/2014
5186(3^160665+7)/98135076651Lelio R Paula10/2012
51872^254598-11318376642Enzo Doria07/2014
518819^59932+2276639Lelio R Paula01/2015
51892^254569-11221376633Enzo Doria06/2014
51902*5^109626+976626Lelio R Paula10/2014
51912^254521+187252776619Enzo Doria05/2016
5192(76*10^76615+167)/976616Robert Price08/2016
519325^54799-24^5479976606Robert Price07/2012
5194(24737*2^254464+1)/976605Lelio R Paula06/2014
519512^70961-8576580Lelio R Paula02/2015
51967^90590-3876558Lelio R Paula02/2015
51972^254304+522776554Lelio R Paula06/2013
519818^60979-536376546Enzo Doria03/2013
5199(21181*2^254264+1)/5531437976538Lelio R Paula06/2014
5200(34*10^76547-7)/9/61/94529/21480776536Makoto Morimoto05/2016
5201(7*10^76536-313)/976536Robert Price11/2016
52032^254239-2776534Lelio R Paula03/2012
52022^254238-184176534Yves Minet03/2013
5204(10^76537-1)/9/6612796976529Jens K. Andersen04/2009
52052^254189-11222576519Enzo Doria06/2014
520618^60938-139776494Enzo Doria03/2013
52072^254075-278841776485Enzo Doria03/2016
52087*10^76483-2376484Robert Price04/2016
52092^254042-11291376475Enzo Doria06/2014
521014^66723-3776474Lelio R Paula02/2015
52112^254037-11030576473Enzo Doria05/2014
52122^253931-11110976441Enzo Doria05/2014
52132^253926-116776440Lelio R Paula05/2013
5214(49*10^76438-13)/976439Robert Price07/2015
5215(21*2^253845-1)/14376415Lelio R Paula02/2014
521610^76374+3176375Robert Price03/2011
521710^76374-22215976374Patrick De Geest05/2013
52182^253561-11053376330Enzo Doria05/2014
5219gcd(V(917285),5*F(183457)*(F(183457)+1)+1)76321Serge Batalov04/2015
52209*5^109182+276316Lelio R Paula10/2014
522111^73279-369076313Enzo Doria12/2012
5222(598*10^76309-31)/976311Robert Price02/2017
522311^73274-2400076308Enzo Doria12/2012
52247^90291-676305Theodore Burton11/2005
5225(21181*2^253432+1)/2143776291Lelio R Paula06/2014
52266^98025+14576279Lelio R Paula01/2015
52272^253355+115576268Lelio R Paula05/2013
52282^253292-7121976249Enzo Doria04/2016
52297^90221-3676246Lelio R Paula02/2015
523018^60727-347376229Enzo Doria03/2013
5231(78557*2^253184+1)/376221Lelio R Paula06/2014
5232(44791^20480+1)/(44791^4096+1)76206Serge Batalov01/2017
523311^73163-201076192Enzo Doria12/2012
52342^253060+5461576179Lelio R Paula05/2013
52352^253029+186976176170Enzo Doria05/2016
52362^252955-11100776148Enzo Doria05/2014
52372*5^108931+776140Lelio R Paula10/2014
5238(86*10^76128+121)/976129Robert Price03/2017
523922154*29^52050+976123Curtis Bright05/2015
52403^159530-11235876116Enzo Doria06/2014
524111^73089-4876115Lelio R Paula02/2015
524286^39337-8576098Norbert Schneider10/2015
5243(3^159505-7)/31329731676095Lelio R Paula06/2012
52446^97783+7776090Lelio R Paula01/2015
52452^252712-10576074Lelio R Paula03/2012
5246131^35927+276068Lelio R Paula05/2013
5247(41*10^76067+373)/976068Robert Price04/2017
52482^252683-13976066Lelio R Paula03/2012
5249137^35597-13676061Norbert Schneider05/2015
52503^159413+10676060Lelio R Paula01/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 25 2017 10:58 (Time in France)

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