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 ?
6751(86*10^76128+121)/976129Robert Price03/2017
675222154*29^52050+976123Curtis Bright05/2015
67533^159530-11235876116Enzo Doria06/2014
675411^73089-4876115Lelio R Paula02/2015
675586^39337-8576098Norbert Schneider10/2015
6756(3^159505-7)/31329731676095Lelio R Paula06/2012
67576^97783+7776090Lelio R Paula01/2015
67582^252712-10576074Lelio R Paula03/2012
6759(10^76069-19)/976069Robert Price10/2017
6761131^35927+276068Lelio R Paula05/2013
6760(41*10^76067+373)/976068Robert Price04/2017
67622^252683-13976066Lelio R Paula03/2012
6763137^35597-13676061Norbert Schneider05/2015
67643^159413+10676060Lelio R Paula01/2015
67659^79677+3*8^79677-2*4^79677-3*2^7967776032Mike Oakes12/2010
6766(2^252557-9)/7176026Lelio R Paula07/2012
6767(85*10^76021-103)/976022Robert Price10/2017
676811^72989+8076011Lelio R Paula02/2015
676999877!6-3675996Robert Price11/2018
67702^252449-45952375995Enzo Doria05/2015
677120^58408+7375991Lelio R Paula01/2015
67722^252418-142175986Yves Minet01/2013
6773(11*2^252396-1)/575980Lelio R Paula02/2014
67742^252365-11068975970Enzo Doria05/2014
677511^72949-102075969Enzo Doria11/2012
6776(2^252294+47)/654975945Lelio R Paula07/2012
67772^252261-11059575939Enzo Doria05/2014
67787^89853+7675935Lelio R Paula01/2015
67793^159132+5675926Lelio R Paula01/2015
6780730^26513+26513^73075916Norbert Schneider11/2016
6781(27*2^252163-1)/194575907Lelio R Paula01/2014
67825^108596-1484675906Enzo Doria02/2013
67835^108560-1484675881Enzo Doria02/2013
67842^252051-11035975875Enzo Doria05/2014
67852^251971-11050975851Enzo Doria05/2014
6786(42457^16384+1)/32768275819Lelio R Paula11/2011
67872^251842-471575812Yves Minet05/2019
678899655!6-275811Robert Price07/2017
678914*10^75798+108975800Jens K. Andersen11/2007
67902^251784-45575795Yves Minet03/2012
67912^251780-128975794Yves Minet01/2013
67922^251760-21560975788Paul Bourdelais03/2013
679399^37973+275781Lelio R Paula05/2013
6794(185*10^75777+7)/375779Robert Price02/2017
67955*2^251690+375767Lelio R Paula06/2014
67966^97366+9575766Lelio R Paula01/2015
6797s(23010)75760Hans Havermann11/2017
67988*6^97337-775744Lelio R Paula10/2014
67992^251588-11167775736Enzo Doria05/2014
68005^108346-1325675731Enzo Doria02/2013
6801(31^50777+1)/3275726Robert Price07/2013
6802(10^75707+77)/375707Robert Price01/2017
6803(174907#+1673)/(7*239*15467899)75700Makoto Morimoto10/2017
68042^251466+19375699Lelio R Paula03/2012
6805(5*2^251464+1)/942375695Lelio R Paula07/2012
68062^251422-10999175686Enzo Doria04/2014
680791*(10^23+1)*(10^1721+1)*(10^118749+1)/(10^69+1)/(10^5163+1)/(10^39583+1)75680Makoto Kamada03/2019
68084*5^108245-375661Lelio R Paula10/2014
680912^70067-11^7006775615Jean-Louis Charton11/2006
681012^70066+9575614Lelio R Paula02/2015
6811-E20534/206375607Thomas Ritschel02/2017
681219^59120-5075600Lelio R Paula01/2015
681318^60222-469775596Enzo Doria03/2013
681418^60211-435575582Enzo Doria03/2013
68157*2^251014-975564Lelio R Paula06/2014
68166^97101-2575560Lelio R Paula01/2015
68178^83663-7^8366375556Jean-Louis Charton01/2004
68183^158331-14075544Lelio R Paula01/2015
6821(37^48157-1)/3675519Robert Price03/2012
6820(19*10^75518-43)/375519Robert Price10/2017
68192^250868-422975519Yves Minet08/2018
682210^75516+3146775517Patrick De Geest03/2016
682410^75516-10^2256-175516Serge Batalov01/2011
682310^75516-6659175516Patrick De Geest03/2016
68252^250851-18775514Lelio R Paula03/2012
6826(43*10^75498-7)/975499Robert Price12/2014
6827(3^158244-5)/24791675497Lelio R Paula06/2012
68284*5^107971-375470Lelio R Paula10/2014
6829(25*10^75465+71)/375466Robert Price01/2017
6830(5*2^250681-1)/99975461Lelio R Paula01/2014
6831(182*10^75456+1)/375458Robert Price02/2017
6832(2^250669-9)/9889772975451Lelio R Paula07/2012
683310^75441+1375442Robert Price01/2011
683410^75441-992375441Patrick De Geest05/2013
6835(27*2^250546-1)/645775420Lelio R Paula01/2014
68365*7^89231-675410Lelio R Paula10/2014
68382^250503-1699575409Lelio R Paula05/2013
683711^72411-2875409Lelio R Paula02/2015
68393*5^107860-875392Lelio R Paula10/2014
6840(34*10^75387-403)/975388Robert Price10/2017
68422^250426+2983575386Lelio R Paula05/2013
68418*3^157999-775386Lelio R Paula05/2014
6843(88*10^75381-43)/975382Robert Price11/2015
68442^250382-11175575373Enzo Doria05/2014
68452^250374-279805175371Eric Chen03/2016
6846(22*10^75368-1)/375369Robert Price12/2014
68472^250369-454375369Yves Minet03/2019
6848(19*10^75338+119)/375339Robert Price02/2017
68492^250223-185916775325Enzo Doria03/2016
6850(3^157854-7)/6602528275308Lelio R Paula06/2012
68513^157831-9875305Lelio R Paula01/2015
6852(46^45281+11^45281)/5775290Serge Batalov12/2016
685392^38335-9175282Norbert Schneider01/2016
68542^250020+1891575264Lelio R Paula05/2013
68552^250002+819375259Lelio R Paula05/2013
6856(11*2^249977-7)/1575251Renaud Lifchitz02/2011
6857(2^249968+78557)/6375247Lelio R Paula07/2012
6858(5*10^75244+91)/375245Robert Price11/2016
6859(10489!)^2+Prime(10489)75242Robert Price08/2014
686014^65644+6775237Lelio R Paula01/2015
686168383!4+3275236Robert Price09/2019
6862(2^249928-5)/1185905975229Lelio R Paula06/2012
6863129^35638+275218Lelio R Paula05/2013
68642^249853-11047575214Enzo Doria05/2014
68652^249762+7540975186Enzo Doria04/2016
6866565^27318+27318^56575181Norbert Schneider12/2016
6867(2^249741-7)/68575177Lelio R Paula06/2012
68682^249726-11218175176Enzo Doria06/2014
68692^249721+1171575174Lelio R Paula05/2013
6870(38661^16384+1)/275158Lelio R Paula11/2011
68712^249658-4735575155Lelio R Paula05/2013
6872155^34311+275153Lelio R Paula05/2013
6873(10^87682+1)/(10^12526+1)/99009900990175145Maksym Voznyy06/2015
6874(23*2^249602+1)/9375138Lelio R Paula08/2012
68752^249522+841575114Lelio R Paula05/2013
68762^249489-11091175104Enzo Doria05/2014
6877(28*10^75078+131)/375079Robert Price02/2017
6878(206*10^75073-17)/975075Robert Price03/2017
68792^249368-11057375068Enzo Doria05/2014
6880NaturalLogarithmOf10(75067)75067Eric W. Weisstein10/2015
6881(2^249375+78557)/4505612575062Lelio R Paula07/2012
6882(26*10^75055-173)/375056Robert Price10/2017
68832^249272+19375039Lelio R Paula03/2012
688414^65468+4375035Lelio R Paula01/2015
688537^47844+3675030Norbert Schneider05/2014
6886(52*10^75027-7)/975028Robert Price12/2014
688720^57653+8975009Lelio R Paula01/2015
68882^249061-186835374975Enzo Doria04/2016
68897^88713+2*3^8871374972Mike Oakes07/2010
68902*6^96313+574947Lelio R Paula10/2014
6891(8*10^74944+49)/374945Robert Price03/2016
6892300^30247+30247^30074926Norbert Schneider11/2014
68932^248866-17174917Lelio R Paula03/2012
68946*5^107168-774908Lelio R Paula10/2014
689511^71926+7874904Lelio R Paula02/2015
68962^248824+186939174904Enzo Doria05/2016
68972^248816+111174902Lelio R Paula01/2011
6898V(388219)74890Serge Batalov03/2015
6899159^34017+15874885Norbert Schneider12/2018
69002*F(358297)-174880Henri Lifchitz12/2009
6901(22*10^74874-31)/974875Robert Price04/2015
690211^71892-7680000074868Enzo Doria01/2013
69039*5^107107-474866Lelio R Paula10/2014
69042^248678-71011174860Paul Bourdelais03/2013
6905(14*10^74858+211)/974859Robert Price11/2017
690613^67194+1274851Lelio R Paula01/2015
6907(7*2^248634+1)/7174846Lelio R Paula08/2012
690811^71867-309074842Enzo Doria12/2012
690968057!4-1674841Robert Price11/2019
69102^248609+26214574839Lelio R Paula05/2013
69113^156852+5074838Lelio R Paula01/2015
691218^59607-1174824Lelio R Paula01/2015
69132^248556-11050774823Enzo Doria05/2014
69147^88531-3674818Lelio R Paula01/2015
6915p(15738)#/2+102474814Robert Price07/2017
69164*3^156740-574785Lelio R Paula05/2014
6917(32*10^74773-41)/974774Robert Price05/2015
6918(29*2^248384-1)/1374772Lelio R Paula01/2014
691919401!+19401#+174765D. Gazzoni Filho & Lucas Teixeira06/2005
69202^248357-1279741374763Enzo Doria03/2016
692142^46057+4174762Lelio R Paula07/2012
692211^71784-300074756Enzo Doria12/2012
692319^58458+1874754Lelio R Paula01/2015
692412^69265-3574750Lelio R Paula02/2015
692611^71771-4800074742Enzo Doria12/2012
6925(7*10^74741+197)/374742Robert Price07/2017
6927(2^248282-5)/5012974736Lelio R Paula06/2012
69282^248252-11010574732Enzo Doria04/2014
6929(7*10^74729+71)/374730Robert Price03/2016
69303^156614-5074724Lelio R Paula01/2015
6931(7*2^248213+1)/13574719Lelio R Paula07/2012
6932(2^248173+78557)/76774705Lelio R Paula07/2012
6933125^35622+12474697Norbert Schneider02/2015
6934(19*2^248099-1)/2974686Lelio R Paula01/2014
6935(86*10^74676-41)/974677Robert Price11/2015
6936(p(15711)#-4)/274672Robert Price09/2017
693710^74670+3174671Robert Price01/2011
693810^74670-12246374670Patrick De Geest05/2013
69392^248036-6974667Lelio R Paula03/2012
694011^71698-600074666Enzo Doria12/2012
694158*(10^(3*24887)-1)/111-174661Robert Price10/2014
694214^65139-4574658Lelio R Paula01/2015
69436^95921-13374642Lelio R Paula01/2015
694411^71675+7874642Lelio R Paula02/2015
694518^59449-9174625Lelio R Paula01/2015
69466^95864-1604374597Enzo Doria02/2013
69475*7^88261+674590Lelio R Paula10/2014
69489*5^106710+474589Lelio R Paula10/2014
6949(777*2^247788+1)/(11*754121)74588Jens K. Andersen09/2007
6950(265*10^74579+17)/374581Robert Price05/2016
6951(2^247759-1017)/331831171774574Lelio R Paula07/2012
69525^106682-2474568Lelio R Paula08/2014
6953474^27863+27863^47474556Norbert Schneider01/2017
6954(14*10^74540+79)/374541Robert Price11/2017
6955(35365^16384+1)/274524Lelio R Paula11/2011
69563^156161+266074508Lelio R Paula01/2015
69572^247474-5869574498Lelio R Paula05/2013
695811^71519-9074480Enzo Doria07/2012
6959(19*2^247419-1)/2320298374475Lelio R Paula01/2014
6961(2^247394-7)/374473Lelio R Paula06/2012
696018^59328+1774473Lelio R Paula01/2015
69622^247379-18174469Lelio R Paula03/2012
6963(15*2^247370-1)/47974465Lelio R Paula01/2014
69642^247344+204774458Lelio R Paula05/2013
69652^247311-101774449Lelio R Paula05/2013
69662^247280+774439Lelio R Paula03/2012
6967(68*10^74434+13)/974435Ray Chandler11/2010
69683^156004-6274433Lelio R Paula01/2015
696936095!2-6474416Robert Price06/2015
697067699!4+1674409Robert Price09/2019
69712^247165-374405M. Frind & P. Underwood07/2002
69722^247150+3276974400Lelio R Paula05/2013
697312^68911+7374368Lelio R Paula01/2015
69742^246999+7490374355Enzo Doria04/2016
69752^246989-11064374352Enzo Doria05/2014
697610^74350+27943974351Patrick De Geest07/2017
6979(10^74350+11)/374350Robert Price11/2014
697710^74350-40000000174350Robert Price07/2017
697810^74350-71624174350Patrick De Geest07/2017
698067647!4-51274346Robert Price11/2019
698110^74335+1365974336Patrick De Geest05/2013
698210^74335-5374335Robert Price05/2011
69832^246906-121574327Lelio R Paula05/2013
69842^246848+11174309Lelio R Paula03/2012
69856^95490-1844374306Enzo Doria03/2013
698618^59188-236974298Enzo Doria03/2013
6987(1363*2^246767+1)/(3*5*7*13^2*743)74281Jens K. Andersen09/2007
69882^246744+4075574278Lelio R Paula05/2013
6989(29*10^74276+91)/374277Robert Price03/2016
69906^95441+16374268Lelio R Paula01/2015
6991V(390863)74258Serge Batalov03/2015
699210^74254+9174255Robert Price03/2011
6994(19*10^74253-1)/974254Ray Chandler02/2012
699310^74254-13056974254Patrick De Geest05/2013
6995771^25718+25718^77174250Norbert Schneider10/2016
69962^246618+42774240Henri Lifchitz02/2005
699788*10^74234+374236Robert Price11/2016
69988*10^74234-4974235Robert Price04/2016
69992^246578+1228574228Lelio R Paula05/2013
7000(3^155569-5)/274225Lelio R Paula06/2012


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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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