PRP Records

Probable Primes Top 10000

(259919 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 ?
7501(2^252335+2394)/275961Stefano Morozzi01/2020
7502(2^252294+47)/654975945Lelio R Paula07/2012
75032^252261-11059575939Enzo Doria05/2014
75047^89853+7675935Lelio R Paula01/2015
75053^159132+5675926Lelio R Paula01/2015
7506730^26513+26513^73075916Norbert Schneider11/2016
7507(27*2^252163-1)/194575907Lelio R Paula01/2014
75085^108596-1484675906Enzo Doria02/2013
7509(2^252082+2734)/275884Stefano Morozzi01/2020
75105^108560-1484675881Enzo Doria02/2013
75112^252051-11035975875Enzo Doria05/2014
75122^251971-11050975851Enzo Doria05/2014
7513(42457^16384+1)/32768275819Lelio R Paula11/2011
75142^251842-471575812Yves Minet05/2019
751599655!6-275811Robert Price07/2017
7516(2^251823+3290)/275806Stefano Morozzi01/2020
751714*10^75798+108975800Jens K. Andersen11/2007
75182^251784-45575795Yves Minet03/2012
75192^251780-128975794Yves Minet01/2013
75202^251760-21560975788Paul Bourdelais03/2013
752121947^2838+2838^2194775784Hans Havermann01/2020
752299^37973+275781Lelio R Paula05/2013
7523(185*10^75777+7)/375779Robert Price02/2017
75245*2^251690+375767Lelio R Paula06/2014
75256^97366+9575766Lelio R Paula01/2015
7526s(23010)75760Hans Havermann11/2017
7527(2^251666+1882)/275759Stefano Morozzi01/2020
75288*6^97337-775744Lelio R Paula10/2014
752924045^1412+1412^2404575738Hans Havermann01/2020
75302^251588-11167775736Enzo Doria05/2014
7531(2^251580+2086)/275733Stefano Morozzi01/2020
75325^108346-1325675731Enzo Doria02/2013
7533(2^251570+1182)/275730Stefano Morozzi01/2020
7534(31^50777+1)/3275726Robert Price07/2013
7535(10^75707+77)/375707Robert Price01/2017
7536(174907#+1673)/(7*239*15467899)75700Makoto Morimoto10/2017
75372^251466+19375699Lelio R Paula03/2012
7538(2^251463+1338)/275698Stefano Morozzi01/2020
7539(5*2^251464+1)/942375695Lelio R Paula07/2012
75402^251422-10999175686Enzo Doria04/2014
754191*(10^23+1)*(10^1721+1)*(10^118749+1)/(10^69+1)/(10^5163+1)/(10^39583+1)75680Makoto Kamada03/2019
7542(2^251355+3806)/275666Stefano Morozzi01/2020
7543(2^251347+1278)/275663Stefano Morozzi01/2020
75444*5^108245-375661Lelio R Paula10/2014
7545(2^251261+846)/275637Stefano Morozzi01/2020
7546(2^251195+3770)/275617Stefano Morozzi01/2020
754712^70067-11^7006775615Jean-Louis Charton11/2006
754812^70066+9575614Lelio R Paula02/2015
7549(2^251181+1130)/275613Stefano Morozzi01/2020
7550-E20534/206375607Thomas Ritschel02/2017
755119^59120-5075600Lelio R Paula01/2015
755218^60222-469775596Enzo Doria03/2013
755318^60211-435575582Enzo Doria03/2013
75547*2^251014-975564Lelio R Paula06/2014
75556^97101-2575560Lelio R Paula01/2015
75568^83663-7^8366375556Jean-Louis Charton01/2004
7557(2^250974+3838)/275551Stefano Morozzi01/2020
75583^158331-14075544Lelio R Paula01/2015
7561(37^48157-1)/3675519Robert Price03/2012
7559(19*10^75518-43)/375519Robert Price10/2017
75602^250868-422975519Yves Minet08/2018
756210^75516+3146775517Patrick De Geest03/2016
756410^75516-10^2256-175516Serge Batalov01/2011
756310^75516-6659175516Patrick De Geest03/2016
75652^250851-18775514Lelio R Paula03/2012
7566(2^250836+466)/275509Stefano Morozzi01/2020
756722273^2454+2454^2227375503Hans Havermann01/2020
7568(43*10^75498-7)/975499Robert Price12/2014
7569(3^158244-5)/24791675497Lelio R Paula06/2012
75704*5^107971-375470Lelio R Paula10/2014
7571(25*10^75465+71)/375466Robert Price01/2017
7572(2^250690+1222)/275465Stefano Morozzi01/2020
7574(5*2^250681-1)/99975461Lelio R Paula01/2014
7573(2^250674+1354)/275461Stefano Morozzi01/2020
7575(2^250670+1878)/275459Stefano Morozzi01/2020
7576(182*10^75456+1)/375458Robert Price02/2017
7577(2^250669-9)/9889772975451Lelio R Paula07/2012
757810^75441+1375442Robert Price01/2011
757910^75441-992375441Patrick De Geest05/2013
7580(27*2^250546-1)/645775420Lelio R Paula01/2014
75815*7^89231-675410Lelio R Paula10/2014
75832^250503-1699575409Lelio R Paula05/2013
758211^72411-2875409Lelio R Paula02/2015
75843*5^107860-875392Lelio R Paula10/2014
7585(34*10^75387-403)/975388Robert Price10/2017
75872^250426+2983575386Lelio R Paula05/2013
75868*3^157999-775386Lelio R Paula05/2014
7588(2^250417+2642)/275383Stefano Morozzi01/2020
7589(88*10^75381-43)/975382Robert Price11/2015
7590(2^250394+2902)/275376Stefano Morozzi01/2020
75912^250382-11175575373Enzo Doria05/2014
75922^250374-279805175371Eric Chen03/2016
7594(22*10^75368-1)/375369Robert Price12/2014
75932^250369-454375369Yves Minet03/2019
759520078^5667+5667^2007875360Hans Havermann02/2020
7596(2^250318+2242)/275353Stefano Morozzi01/2020
7598(19*10^75338+119)/375339Robert Price02/2017
759721517^3172+3172^2151775339Hans Havermann01/2020
75992^250223-185916775325Enzo Doria03/2016
7600(3^157854-7)/6602528275308Lelio R Paula06/2012
7601(2^250164+1578)/275307Stefano Morozzi01/2020
76023^157831-9875305Lelio R Paula01/2015
7603(46^45281+11^45281)/5775290Serge Batalov12/2016
760492^38335-9175282Norbert Schneider01/2016
7605(2^250026+2398)/275266Stefano Morozzi01/2020
76062^250020+1891575264Lelio R Paula05/2013
76072^250002+819375259Lelio R Paula05/2013
7608(2^249996+1678)/275256Stefano Morozzi01/2020
7609(11*2^249977-7)/1575251Renaud Lifchitz02/2011
7610(2^249968+78557)/6375247Lelio R Paula07/2012
7611(5*10^75244+91)/375245Robert Price11/2016
7612(10489!)^2+Prime(10489)75242Robert Price08/2014
761314^65644+6775237Lelio R Paula01/2015
761468383!4+3275236Robert Price09/2019
7615(2^249928-5)/1185905975229Lelio R Paula06/2012
7616129^35638+275218Lelio R Paula05/2013
76172^249853-11047575214Enzo Doria05/2014
761820574^4517+4517^2057475195Hans Havermann01/2020
76192^249762+7540975186Enzo Doria04/2016
7620565^27318+27318^56575181Norbert Schneider12/2016
7621(2^249741-7)/68575177Lelio R Paula06/2012
76222^249726-11218175176Enzo Doria06/2014
76232^249721+1171575174Lelio R Paula05/2013
7624(2^249705+654)/275169Stefano Morozzi01/2020
7625(38661^16384+1)/275158Lelio R Paula11/2011
76262^249658-4735575155Lelio R Paula05/2013
7627155^34311+275153Lelio R Paula05/2013
7628(10^87682+1)/(10^12526+1)/99009900990175145Maksym Voznyy06/2015
7629(23*2^249602+1)/9375138Lelio R Paula08/2012
76302^249522+841575114Lelio R Paula05/2013
76312^249489-11091175104Enzo Doria05/2014
7632(28*10^75078+131)/375079Robert Price02/2017
7633(206*10^75073-17)/975075Robert Price03/2017
7634(2^249384+3330)/275072Stefano Morozzi01/2020
76352^249368-11057375068Enzo Doria05/2014
7636NaturalLogarithmOf10(75067)75067Eric W. Weisstein10/2015
763719167^8248+8248^1916775065Hans Havermann02/2020
7638(2^249375+78557)/4505612575062Lelio R Paula07/2012
7639(26*10^75055-173)/375056Robert Price10/2017
76412^249272+19375039Lelio R Paula03/2012
764017433^17692-17692^1743375039Norbert Schneider11/2019
764214^65468+4375035Lelio R Paula01/2015
764337^47844+3675030Norbert Schneider05/2014
7644(52*10^75027-7)/975028Robert Price12/2014
764517943^15178+15178^1794375024Hans Havermann02/2020
7646(2^249219+494)/275023Stefano Morozzi01/2020
764720^57653+8975009Lelio R Paula01/2015
7648(2^249084+2682)/274982Stefano Morozzi01/2020
76492^249061-186835374975Enzo Doria04/2016
7650(2^249056+1006)/274974Stefano Morozzi01/2020
76517^88713+2*3^8871374972Mike Oakes07/2010
765218325^12334+12334^1832574970Hans Havermann02/2020
76532*6^96313+574947Lelio R Paula10/2014
7654(8*10^74944+49)/374945Robert Price03/2016
7655300^30247+30247^30074926Norbert Schneider11/2014
76562^248866-17174917Lelio R Paula03/2012
76576*5^107168-774908Lelio R Paula10/2014
765811^71926+7874904Lelio R Paula02/2015
76592^248824+186939174904Enzo Doria05/2016
76602^248816+111174902Lelio R Paula01/2011
7661V(388219)74890Serge Batalov03/2015
7662159^34017+15874885Norbert Schneider12/2018
76632*F(358297)-174880Henri Lifchitz12/2009
7664(22*10^74874-31)/974875Robert Price04/2015
766511^71892-7680000074868Enzo Doria01/2013
76669*5^107107-474866Lelio R Paula10/2014
76672^248678-71011174860Paul Bourdelais03/2013
7668(14*10^74858+211)/974859Robert Price11/2017
766913^67194+1274851Lelio R Paula01/2015
7670(7*2^248634+1)/7174846Lelio R Paula08/2012
767111^71867-309074842Enzo Doria12/2012
767268057!4-1674841Robert Price11/2019
76732^248609+26214574839Lelio R Paula05/2013
76743^156852+5074838Lelio R Paula01/2015
767518^59607-1174824Lelio R Paula01/2015
76762^248556-11050774823Enzo Doria05/2014
76777^88531-3674818Lelio R Paula01/2015
7678p(15738)#/2+102474814Robert Price07/2017
7679(2^248505+422)/274808Stefano Morozzi01/2020
7680(2^248507+1938)/274808Stefano Morozzi01/2020
768121137^3454+3454^2113774790Hans Havermann11/2019
76824*3^156740-574785Lelio R Paula05/2014
768317918^14907+14907^1791874779Hans Havermann12/2019
7684(32*10^74773-41)/974774Robert Price05/2015
7685(29*2^248384-1)/1374772Lelio R Paula01/2014
768619401!+19401#+174765D. Gazzoni Filho & Lucas Teixeira06/2005
76872^248357-1279741374763Enzo Doria03/2016
768842^46057+4174762Lelio R Paula07/2012
7689(2^248339+1686)/274758Stefano Morozzi01/2020
769011^71784-300074756Enzo Doria12/2012
769119^58458+1874754Lelio R Paula01/2015
769212^69265-3574750Lelio R Paula02/2015
7693(2^248291+830)/274743Stefano Morozzi01/2020
769511^71771-4800074742Enzo Doria12/2012
7694(7*10^74741+197)/374742Robert Price07/2017
7696(2^248282-5)/5012974736Lelio R Paula06/2012
76972^248252-11010574732Enzo Doria04/2014
7698(7*10^74729+71)/374730Robert Price03/2016
76993^156614-5074724Lelio R Paula01/2015
7700(7*2^248213+1)/13574719Lelio R Paula07/2012
7701(2^248193+870)/274714Stefano Morozzi01/2020
7702(2^248167+1178)/274706Stefano Morozzi01/2020
7703(2^248173+78557)/76774705Lelio R Paula07/2012
7704(2^248145+3866)/274699Stefano Morozzi01/2020
7705125^35622+12474697Norbert Schneider02/2015
7706(2^248114+994)/274690Stefano Morozzi01/2020
7707(19*2^248099-1)/2974686Lelio R Paula01/2014
770820780^3927+3927^2078074685Hans Havermann12/2019
7709(86*10^74676-41)/974677Robert Price11/2015
7710(2^248065+3650)/274675Stefano Morozzi01/2020
7711(p(15711)#-4)/274672Robert Price09/2017
771210^74670+3174671Robert Price01/2011
771310^74670-12246374670Patrick De Geest05/2013
77142^248036-6974667Lelio R Paula03/2012
771511^71698-600074666Enzo Doria12/2012
7716(2^248032+406)/274665Stefano Morozzi01/2020
771758*(10^(3*24887)-1)/111-174661Robert Price10/2014
771814^65139-4574658Lelio R Paula01/2015
771917967^14288+14288^1796774653Hans Havermann11/2019
77206^95921-13374642Lelio R Paula01/2015
772111^71675+7874642Lelio R Paula02/2015
772217875^14986+14986^1787574641Hans Havermann12/2019
7723(2^247931+1458)/274635Stefano Morozzi01/2020
772418^59449-9174625Lelio R Paula01/2015
77256^95864-1604374597Enzo Doria02/2013
77265*7^88261+674590Lelio R Paula10/2014
77279*5^106710+474589Lelio R Paula10/2014
7728(777*2^247788+1)/(11*754121)74588Jens K. Andersen09/2007
772921157^3352+3352^2115774585Hans Havermann12/2019
7730(265*10^74579+17)/374581Robert Price05/2016
773117798^15489+15489^1779874575Hans Havermann11/2019
7732(2^247759-1017)/331831171774574Lelio R Paula07/2012
77335^106682-2474568Lelio R Paula08/2014
7734(2^247686+1450)/274561Stefano Morozzi01/2020
7735474^27863+27863^47474556Norbert Schneider01/2017
7736(14*10^74540+79)/374541Robert Price11/2017
7737(2^247582+1630)/274530Stefano Morozzi01/2020
7738(35365^16384+1)/274524Lelio R Paula11/2011
77393^156161+266074508Lelio R Paula01/2015
77412^247474-5869574498Lelio R Paula05/2013
7740(2^247476+886)/274498Stefano Morozzi01/2020
774211^71519-9074480Enzo Doria07/2012
7743(19*2^247419-1)/2320298374475Lelio R Paula01/2014
7745(2^247394-7)/374473Lelio R Paula06/2012
774418^59328+1774473Lelio R Paula01/2015
77462^247379-18174469Lelio R Paula03/2012
7747(15*2^247370-1)/47974465Lelio R Paula01/2014
774818860^8877+8877^1886074465Hans Havermann12/2019
774917355^17564-17564^1735574462Norbert Schneider11/2019
77502^247344+204774458Lelio R Paula05/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 29 2020 17:41 (Time in France)

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