PRP Records

Probable Primes Top 10000

(224926 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
5751(78557*2^260084+1)/51978296Lelio R Paula06/2014
575210^78288+9^(78288+1)78289Robert Price08/2016
575310^78288+3910978289Patrick De Geest12/2016
575410^78288-21629978288Patrick De Geest12/2016
57555^111997+3678283Lelio R Paula02/2015
5756(21^59183+1)/2278252Paul Bourdelais03/2010
5757(88*10^78242-7)/978243Robert Price11/2014
57582*6^100547+778242Lelio R Paula10/2014
57592^259860-11108978226Enzo Doria05/2014
576037^49875-278215Lelio R Paula09/2013
5761(13*10^78213+401)/978214Robert Price10/2017
57627*5^111893-478211Lelio R Paula10/2014
5763(11*2^259809-1)/143778209Lelio R Paula02/2014
57647^92511-678181Theodore Burton11/2005
5765(3^163859-4)/25378179Lelio R Paula10/2012
5766(27*2^259666-1)/62569178163Lelio R Paula02/2014
57673*10^78146+1778147Robert Price03/2017
5768(576^28307+1)/57778137Richard Fischer01/2018
57692^259503+7433378119Enzo Doria04/2016
5770(31*2^259504-1)/1336578116Lelio R Paula02/2014
5772(58547^16384+1)/278111Lelio R Paula11/2011
57716^100379+1378111Lelio R Paula03/2015
57732^259469-10990978108Enzo Doria04/2014
577415^66413-2678108Lelio R Paula02/2015
57757^92410-926678096Mike Oakes02/2010
57762^259398+7579978087Enzo Doria04/2016
57772^259394+187618978086Enzo Doria07/2016
5778PIPrime(78073)78073Eric W. Weisstein07/2006
57795*2^259344-778072Lelio R Paula06/2014
578014^68097-8778048Lelio R Paula02/2015
57812^259233-47557378037Paul Bourdelais03/2013
5782181^34554-278012Lelio R Paula10/2017
57833^163500-2878010Robert Price12/2013
5784(65*10^77992+691)/977993Robert Price08/2016
57852^259013-11259177971Enzo Doria06/2014
57867*10^77969-1177970Robert Price10/2017
57876^100193-100193^677966Norbert Schneider04/2017
57882^258863-11023577926Enzo Doria05/2014
57892^258852+160577923Lelio R Paula06/2013
5790(11*10^77909+49)/377910Robert Price05/2016
57912*7^92187-977908Lelio R Paula10/2014
57922^258763-11015577896Enzo Doria04/2014
57932^258694-11038777875Enzo Doria05/2014
579411^74773-9477869Lelio R Paula02/2015
57956^100067+12577868Lelio R Paula03/2015
579615^66205+877864Lelio R Paula07/2014
57975^111373-1813677847Enzo Doria05/2014
57982^258524-10987777824Enzo Doria04/2014
57996^100002-1664377817Enzo Doria02/2013
5800(13*10^77811+347)/977812Robert Price10/2017
580165^42916+2877803Lelio R Paula01/2016
5802(89*10^77781-17)/977782Robert Price11/2015
58032^258382-11040577781Enzo Doria05/2014
58045^111278-1499677780Enzo Doria02/2013
580514^67862+6177779Lelio R Paula02/2015
580610^77777+4848377778Patrick De Geest11/2010
580710^77777-18324377777Patrick De Geest11/2010
5808(27*2^258352+1)/4377772Lelio R Paula08/2012
5809337^30756-1000277740Enzo Doria07/2012
581010^77726+9977727Robert Price03/2011
581110^77726-8594777726Patrick De Geest06/2013
581289^39870-277723Lelio R Paula08/2013
58137^91966-3277721Lelio R Paula02/2015
581435^50327+277709Lelio R Paula05/2013
581524^56298+2377704Norbert Schneider12/2016
5816(2^258105+78557)/1977697Lelio R Paula10/2012
58172^258079+17977690Lelio R Paula03/2012
58182^258062-11311177685Enzo Doria07/2014
581980^40807-7977660Norbert Schneider03/2015
5820(10^77637+359)/977637Serge Batalov12/2014
58212^257862-16577625Lelio R Paula03/2012
5822(25*2^257853+1)/377623Lelio R Paula07/2012
5823(2^257869+1)/(3*18645362967379)77613Henri Lifchitz04/2005
58246^99728+7177604Lelio R Paula01/2015
58252^257778-11276777599Enzo Doria06/2014
5826(31*2^257771+1)/53777596Lelio R Paula07/2012
58272^257729-7377585Lelio R Paula03/2012
58282^257689-6377573Lelio R Paula03/2012
5829(47*10^77572+493)/977573Robert Price11/2017
5830(78557*2^257665+1)/610872577564Lelio R Paula06/2014
5831(3^162563+8)/288577559Lelio R Paula10/2012
58322^257636-11023577557Enzo Doria05/2014
5833(23*10^77556+97)/377557Robert Price02/2017
58342^257621-11007177552Enzo Doria04/2014
58352^257567-6487577536Lelio R Paula06/2013
58362*7^91674+977474Lelio R Paula10/2014
5837(17*10^77427-47)/377428Robert Price05/2017
583810^77418+84168377419Patrick De Geest06/2013
583910^77418-3377418Robert Price05/2011
584019^60539-3677415Lelio R Paula03/2015
584137401!!-102477397Robert Price11/2015
584211^74313-1875077390Enzo Doria12/2012
58442^257044-11288377378Enzo Doria06/2014
58438*10^77377+5177378Robert Price05/2017
58452*7^91553+977372Lelio R Paula10/2014
5846713^27118+27118^71377371Norbert Schneider12/2016
58472^256920-11115577341Enzo Doria05/2014
58482^256896-655577334Lelio R Paula06/2013
5849(52*10^77322-7)/977323Robert Price12/2014
58502^256849-11293977320Enzo Doria06/2014
5851(4*10^77309-31)/977309Erik Branger05/2011
5852(3^161988+7)/4186477284Lelio R Paula10/2012
5853(14^67421-1)/1377272Paul Bourdelais09/2008
58545*3^161923-477258Lelio R Paula06/2014
58552^256552-149977230Yves Minet05/2013
58562^256460-11275777203Enzo Doria06/2014
58572^256398+2329977184Yves Minet02/2011
58582^256391-1155*25639177182Henri Lifchitz03/2005
5859(2^256391-9)/5659377177Lelio R Paula10/2012
5860(2^256308+9)/1058577153Lelio R Paula10/2012
586221^58348-277149Lelio R Paula08/2013
5861(17*2^256291-1)/478577149Lelio R Paula02/2014
5863(5*2^256274-1)/214177144Lelio R Paula02/2014
586419^60321+8277136Lelio R Paula03/2015
58655*2^256233-377135Lelio R Paula06/2014
58663*2^256149+777110Lelio R Paula06/2014
58673^161594-10677100Lelio R Paula02/2015
58682^256114-18577098Lelio R Paula03/2012
58698^85349-85349^877078Norbert Schneider05/2017
58702^256043-278637777077Enzo Doria03/2016
58712^255973+186994777056Enzo Doria05/2016
587212^71393-4377046Lelio R Paula02/2015
587315^65490+4477023Lelio R Paula02/2015
5874(3^161411-7)/94077010Lelio R Paula10/2012
5875lucasU(1107,1,25297)-lucasU(1107,1,25296)77005Mike Oakes05/2009
5876(570^27943-1)/56977005Serge Batalov12/2016
58772^255750-7576989Lelio R Paula03/2012
58783*6^98926-576980Lelio R Paula10/2014
587918^61320-143376974Enzo Doria03/2013
58806^98916-1709376972Enzo Doria02/2013
58812^255659-11013176962Enzo Doria04/2014
588212^71303+9176949Lelio R Paula02/2015
588318^61298+5976946Lelio R Paula02/2015
5884(223^32768+1)/13107476945Lelio R Paula02/2009
5885(2^255613-5)/28151776942Lelio R Paula10/2012
588618^61290-1176936Lelio R Paula02/2015
588863^42752-276926Lelio R Paula08/2013
5887(11*2^255545-1)/11776926Lelio R Paula02/2014
58892^255517+5638776919Yves Minet02/2011
58902^255499-11256776913Enzo Doria06/2014
58912^255492+34576911Lelio R Paula06/2013
589210^76875+21759176876Patrick De Geest05/2013
589410^76875-5376875Robert Price05/2011
589311^73819-588076875Enzo Doria01/2013
58952^255313+1891576857Lelio R Paula06/2013
5896(2^255320-1017)/144666776853Lelio R Paula10/2012
58972^255296+577576852Lelio R Paula06/2013
589814^67052-2976851Lelio R Paula02/2015
5899(8*10^76840+43)/376841Robert Price10/2017
5900(7*10^76818-313)/976818Robert Price11/2016
590110^76801+6976802Robert Price03/2011
590210^76801-8094376801Patrick De Geest06/2013
59032^255105+5776795Lelio R Paula03/2012
5904(lucasV(1,2,510187)+2)/(3*5*11)76789Mike Oakes04/2017
5905(2^255097-7)/2002005576785Lelio R Paula10/2012
59062^255055+186935376780Enzo Doria05/2016
590717^62396-9076776Lelio R Paula03/2015
59087^90833-6076763Lelio R Paula02/2015
590913^68901-5676752Lelio R Paula03/2015
59102^254961+186991776751Enzo Doria05/2016
59119*5^109791-876742Lelio R Paula10/2014
591282^40089+40089^8276723Serge Batalov02/2012
59132^254861-279001376721Enzo Doria03/2016
591410^76705+1376706Robert Price01/2011
591510^76705-9407776705Patrick De Geest06/2013
5916(5*2^254785-1)/99976696Lelio R Paula02/2014
59172^254758-11040576690Enzo Doria05/2014
59182^254716-377976678Yves Minet04/2017
59192^254708-11050776675Enzo Doria05/2014
5920(47*10^76672+133)/976673Robert Price04/2017
59212^254670-11290176664Enzo Doria06/2014
5922(3^160665+7)/98135076651Lelio R Paula10/2012
59232^254598-11318376642Enzo Doria07/2014
592419^59932+2276639Lelio R Paula01/2015
59252^254569-11221376633Enzo Doria06/2014
59262*5^109626+976626Lelio R Paula10/2014
59272^254521+187252776619Enzo Doria05/2016
5928(76*10^76615+167)/976616Robert Price08/2016
592925^54799-24^5479976606Robert Price07/2012
5930(24737*2^254464+1)/976605Lelio R Paula06/2014
593112^70961-8576580Lelio R Paula02/2015
59327^90590-3876558Lelio R Paula02/2015
59332^254304+522776554Lelio R Paula06/2013
5934(76*10^76547-211)/976548Robert Price10/2017
593518^60979-536376546Enzo Doria03/2013
5936(21181*2^254264+1)/5531437976538Lelio R Paula06/2014
5938(34*10^76547-7)/9/61/94529/21480776536Makoto Morimoto05/2016
5937(7*10^76536-313)/976536Robert Price11/2016
59402^254239-2776534Lelio R Paula03/2012
59392^254238-184176534Yves Minet03/2013
5941(10^76537-1)/9/6612796976529Jens K. Andersen04/2009
59422^254189-11222576519Enzo Doria06/2014
594318^60938-139776494Enzo Doria03/2013
59442^254075-278841776485Enzo Doria03/2016
59457*10^76483-2376484Robert Price04/2016
59462^254042-11291376475Enzo Doria06/2014
594714^66723-3776474Lelio R Paula02/2015
59482^254037-11030576473Enzo Doria05/2014
59492^253931-11110976441Enzo Doria05/2014
59502^253926-116776440Lelio R Paula05/2013
5951(49*10^76438-13)/976439Robert Price07/2015
5952(21*2^253845-1)/14376415Lelio R Paula02/2014
595310^76374+3176375Robert Price03/2011
595410^76374-22215976374Patrick De Geest05/2013
59552^253561-11053376330Enzo Doria05/2014
5956gcd(V(917285),5*F(183457)*(F(183457)+1)+1)76321Serge Batalov04/2015
59579*5^109182+276316Lelio R Paula10/2014
595811^73279-369076313Enzo Doria12/2012
5959(598*10^76309-31)/976311Robert Price02/2017
596011^73274-2400076308Enzo Doria12/2012
59617^90291-676305Theodore Burton11/2005
5962(21181*2^253432+1)/2143776291Lelio R Paula06/2014
59636^98025+14576279Lelio R Paula01/2015
59642^253355+115576268Lelio R Paula05/2013
5965(73*10^76262+413)/976263Robert Price10/2017
59662^253292-7121976249Enzo Doria04/2016
59677^90221-3676246Lelio R Paula02/2015
596818^60727-347376229Enzo Doria03/2013
5969(78557*2^253184+1)/376221Lelio R Paula06/2014
5970(8*10^76220-83)/376221Robert Price10/2017
5971(44791^20480+1)/(44791^4096+1)76206Serge Batalov01/2017
597211^73163-201076192Enzo Doria12/2012
59732^253060+5461576179Lelio R Paula05/2013
59742^253029+186976176170Enzo Doria05/2016
59752^252955-11100776148Enzo Doria05/2014
59762*5^108931+776140Lelio R Paula10/2014
5977(86*10^76128+121)/976129Robert Price03/2017
597822154*29^52050+976123Curtis Bright05/2015
59793^159530-11235876116Enzo Doria06/2014
598011^73089-4876115Lelio R Paula02/2015
598186^39337-8576098Norbert Schneider10/2015
5982(3^159505-7)/31329731676095Lelio R Paula06/2012
59836^97783+7776090Lelio R Paula01/2015
59842^252712-10576074Lelio R Paula03/2012
5985(10^76069-19)/976069Robert Price10/2017
5987131^35927+276068Lelio R Paula05/2013
5986(41*10^76067+373)/976068Robert Price04/2017
59882^252683-13976066Lelio R Paula03/2012
5989137^35597-13676061Norbert Schneider05/2015
59903^159413+10676060Lelio R Paula01/2015
59919^79677+3*8^79677-2*4^79677-3*2^7967776032Mike Oakes12/2010
5992(2^252557-9)/7176026Lelio R Paula07/2012
5993(85*10^76021-103)/976022Robert Price10/2017
599411^72989+8076011Lelio R Paula02/2015
59952^252449-45952375995Enzo Doria05/2015
599620^58408+7375991Lelio R Paula01/2015
59972^252418-142175986Yves Minet01/2013
5998(11*2^252396-1)/575980Lelio R Paula02/2014
59992^252365-11068975970Enzo Doria05/2014
600011^72949-102075969Enzo Doria11/2012


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 18 2018 22:22 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!