PRP Records

Probable Primes Top 10000

(205869 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 ?
57516^97366+9575766Lelio R Paula01/2015
5752s(23010)75760Hans Havermann11/2017
57538*6^97337-775744Lelio R Paula10/2014
57542^251588-11167775736Enzo Doria05/2014
57555^108346-1325675731Enzo Doria02/2013
5756(31^50777+1)/3275726Robert Price07/2013
5757(10^75707+77)/375707Robert Price01/2017
5758(174907#+1673)/(7*239*15467899)75700Makoto Morimoto10/2017
57592^251466+19375699Lelio R Paula03/2012
5760(5*2^251464+1)/942375695Lelio R Paula07/2012
57612^251422-10999175686Enzo Doria04/2014
57624*5^108245-375661Lelio R Paula10/2014
576312^70067-11^7006775615Jean-Louis Charton11/2006
576412^70066+9575614Lelio R Paula02/2015
5765-E20534/206375607Thomas Ritschel02/2017
576619^59120-5075600Lelio R Paula01/2015
576718^60222-469775596Enzo Doria03/2013
576818^60211-435575582Enzo Doria03/2013
57697*2^251014-975564Lelio R Paula06/2014
57706^97101-2575560Lelio R Paula01/2015
57718^83663-7^8366375556Jean-Louis Charton01/2004
57723^158331-14075544Lelio R Paula01/2015
5773(37^48157-1)/3675519Robert Price03/2012
5774(19*10^75518-43)/375519Robert Price10/2017
577510^75516+3146775517Patrick De Geest03/2016
577710^75516-10^2256-175516Serge Batalov01/2011
577610^75516-6659175516Patrick De Geest03/2016
57782^250851-18775514Lelio R Paula03/2012
5779(43*10^75498-7)/975499Robert Price12/2014
5780(3^158244-5)/24791675497Lelio R Paula06/2012
57814*5^107971-375470Lelio R Paula10/2014
5782(25*10^75465+71)/375466Robert Price01/2017
5783(5*2^250681-1)/99975461Lelio R Paula01/2014
5784(182*10^75456+1)/375458Robert Price02/2017
5785(2^250669-9)/9889772975451Lelio R Paula07/2012
578610^75441+1375442Robert Price01/2011
578710^75441-992375441Patrick De Geest05/2013
5788(27*2^250546-1)/645775420Lelio R Paula01/2014
57895*7^89231-675410Lelio R Paula10/2014
57912^250503-1699575409Lelio R Paula05/2013
579011^72411-2875409Lelio R Paula02/2015
57923*5^107860-875392Lelio R Paula10/2014
5793(34*10^75387-403)/975388Robert Price10/2017
57952^250426+2983575386Lelio R Paula05/2013
57948*3^157999-775386Lelio R Paula05/2014
5796(88*10^75381-43)/975382Robert Price11/2015
57972^250382-11175575373Enzo Doria05/2014
57982^250374-279805175371Eric Chen03/2016
5799(22*10^75368-1)/375369Robert Price12/2014
5800(19*10^75338+119)/375339Robert Price02/2017
58012^250223-185916775325Enzo Doria03/2016
5802(3^157854-7)/6602528275308Lelio R Paula06/2012
58033^157831-9875305Lelio R Paula01/2015
5804(46^45281+11^45281)/5775290Serge Batalov12/2016
580592^38335-9175282Norbert Schneider01/2016
58062^250020+1891575264Lelio R Paula05/2013
58072^250002+819375259Lelio R Paula05/2013
5808(11*2^249977-7)/1575251Renaud Lifchitz02/2011
5809(2^249968+78557)/6375247Lelio R Paula07/2012
5810(5*10^75244+91)/375245Robert Price11/2016
5811(10489!)^2+Prime(10489)75242Robert Price08/2014
581214^65644+6775237Lelio R Paula01/2015
5813(2^249928-5)/1185905975229Lelio R Paula06/2012
5814129^35638+275218Lelio R Paula05/2013
58152^249853-11047575214Enzo Doria05/2014
58162^249762+7540975186Enzo Doria04/2016
5817565^27318+27318^56575181Norbert Schneider12/2016
5818(2^249741-7)/68575177Lelio R Paula06/2012
58192^249726-11218175176Enzo Doria06/2014
58202^249721+1171575174Lelio R Paula05/2013
5821(38661^16384+1)/275158Lelio R Paula11/2011
58222^249658-4735575155Lelio R Paula05/2013
5823155^34311+275153Lelio R Paula05/2013
5824(10^87682+1)/(10^12526+1)/99009900990175145Maksym Voznyy06/2015
5825(23*2^249602+1)/9375138Lelio R Paula08/2012
58262^249522+841575114Lelio R Paula05/2013
58272^249489-11091175104Enzo Doria05/2014
5828(28*10^75078+131)/375079Robert Price02/2017
5829(206*10^75073-17)/975075Robert Price03/2017
58302^249368-11057375068Enzo Doria05/2014
5831NaturalLogarithmOf10(75067)75067Eric W. Weisstein10/2015
5832(2^249375+78557)/4505612575062Lelio R Paula07/2012
5833(26*10^75055-173)/375056Robert Price10/2017
58342^249272+19375039Lelio R Paula03/2012
583514^65468+4375035Lelio R Paula01/2015
583637^47844+3675030Norbert Schneider05/2014
5837(52*10^75027-7)/975028Robert Price12/2014
583820^57653+8975009Lelio R Paula01/2015
58392^249061-186835374975Enzo Doria04/2016
58407^88713+2*3^8871374972Mike Oakes07/2010
58412*6^96313+574947Lelio R Paula10/2014
5842(8*10^74944+49)/374945Robert Price03/2016
5843300^30247+30247^30074926Norbert Schneider11/2014
58442^248866-17174917Lelio R Paula03/2012
58456*5^107168-774908Lelio R Paula10/2014
584611^71926+7874904Lelio R Paula02/2015
58472^248824+186939174904Enzo Doria05/2016
58482^248816+111174902Lelio R Paula01/2011
5849V(388219)74890Serge Batalov03/2015
58502*F(358297)-174880Henri Lifchitz12/2009
5851(22*10^74874-31)/974875Robert Price04/2015
585211^71892-7680000074868Enzo Doria01/2013
58539*5^107107-474866Lelio R Paula10/2014
58542^248678-71011174860Paul Bourdelais03/2013
5855(14*10^74858+211)/974859Robert Price11/2017
585613^67194+1274851Lelio R Paula01/2015
5857(7*2^248634+1)/7174846Lelio R Paula08/2012
585811^71867-309074842Enzo Doria12/2012
58592^248609+26214574839Lelio R Paula05/2013
58603^156852+5074838Lelio R Paula01/2015
586118^59607-1174824Lelio R Paula01/2015
58622^248556-11050774823Enzo Doria05/2014
58637^88531-3674818Lelio R Paula01/2015
5864p(15738)#/2+102474814Robert Price07/2017
58654*3^156740-574785Lelio R Paula05/2014
5866(32*10^74773-41)/974774Robert Price05/2015
5867(29*2^248384-1)/1374772Lelio R Paula01/2014
586819401!+19401#+174765D. Gazzoni Filho & Lucas Teixeira06/2005
58692^248357-1279741374763Enzo Doria03/2016
587042^46057+4174762Lelio R Paula07/2012
587111^71784-300074756Enzo Doria12/2012
587219^58458+1874754Lelio R Paula01/2015
587312^69265-3574750Lelio R Paula02/2015
587411^71771-4800074742Enzo Doria12/2012
5875(7*10^74741+197)/374742Robert Price07/2017
5876(2^248282-5)/5012974736Lelio R Paula06/2012
58772^248252-11010574732Enzo Doria04/2014
5878(7*10^74729+71)/374730Robert Price03/2016
58793^156614-5074724Lelio R Paula01/2015
5880(7*2^248213+1)/13574719Lelio R Paula07/2012
5881(2^248173+78557)/76774705Lelio R Paula07/2012
5882125^35622+12474697Norbert Schneider02/2015
5883(19*2^248099-1)/2974686Lelio R Paula01/2014
5884(86*10^74676-41)/974677Robert Price11/2015
5885(p(15711)#-4)/274672Robert Price09/2017
588610^74670+3174671Robert Price01/2011
588710^74670-12246374670Patrick De Geest05/2013
58882^248036-6974667Lelio R Paula03/2012
588911^71698-600074666Enzo Doria12/2012
589058*(10^(3*24887)-1)/111-174661Robert Price10/2014
589114^65139-4574658Lelio R Paula01/2015
58926^95921-13374642Lelio R Paula01/2015
589311^71675+7874642Lelio R Paula02/2015
589418^59449-9174625Lelio R Paula01/2015
58956^95864-1604374597Enzo Doria02/2013
58965*7^88261+674590Lelio R Paula10/2014
58979*5^106710+474589Lelio R Paula10/2014
5898(777*2^247788+1)/(11*754121)74588Jens K. Andersen09/2007
5899(265*10^74579+17)/374581Robert Price05/2016
5900(2^247759-1017)/331831171774574Lelio R Paula07/2012
59015^106682-2474568Lelio R Paula08/2014
5902474^27863+27863^47474556Norbert Schneider01/2017
5903(14*10^74540+79)/374541Robert Price11/2017
5904(35365^16384+1)/274524Lelio R Paula11/2011
59053^156161+266074508Lelio R Paula01/2015
59062^247474-5869574498Lelio R Paula05/2013
590711^71519-9074480Enzo Doria07/2012
5908(19*2^247419-1)/2320298374475Lelio R Paula01/2014
5910(2^247394-7)/374473Lelio R Paula06/2012
590918^59328+1774473Lelio R Paula01/2015
59112^247379-18174469Lelio R Paula03/2012
5912(15*2^247370-1)/47974465Lelio R Paula01/2014
59132^247344+204774458Lelio R Paula05/2013
59142^247311-101774449Lelio R Paula05/2013
59152^247280+774439Lelio R Paula03/2012
5916(68*10^74434+13)/974435Ray Chandler11/2010
59173^156004-6274433Lelio R Paula01/2015
591836095!2-6474416Robert Price06/2015
59192^247165-374405M. Frind & P. Underwood07/2002
59202^247150+3276974400Lelio R Paula05/2013
592112^68911+7374368Lelio R Paula01/2015
59222^246999+7490374355Enzo Doria04/2016
59232^246989-11064374352Enzo Doria05/2014
592410^74350+27943974351Patrick De Geest07/2017
5927(10^74350+11)/374350Robert Price11/2014
592510^74350-40000000174350Robert Price07/2017
592610^74350-71624174350Patrick De Geest07/2017
592810^74335+1365974336Patrick De Geest05/2013
592910^74335-5374335Robert Price05/2011
59302^246906-121574327Lelio R Paula05/2013
59312^246848+11174309Lelio R Paula03/2012
59326^95490-1844374306Enzo Doria03/2013
593318^59188-236974298Enzo Doria03/2013
5934(1363*2^246767+1)/(3*5*7*13^2*743)74281Jens K. Andersen09/2007
59352^246744+4075574278Lelio R Paula05/2013
5936(29*10^74276+91)/374277Robert Price03/2016
59376^95441+16374268Lelio R Paula01/2015
5938V(390863)74258Serge Batalov03/2015
593910^74254+9174255Robert Price03/2011
5940(19*10^74253-1)/974254Ray Chandler02/2012
594110^74254-13056974254Patrick De Geest05/2013
5942771^25718+25718^77174250Norbert Schneider10/2016
59432^246618+42774240Henri Lifchitz02/2005
594488*10^74234+374236Robert Price11/2016
59458*10^74234-4974235Robert Price04/2016
59462^246578+1228574228Lelio R Paula05/2013
5947(3^155569-5)/274225Lelio R Paula06/2012
594813^66628+4674220Lelio R Paula01/2015
59492^246476-1729574197Lelio R Paula05/2013
5950(61*10^74189-1)/374191Robert Price11/2017
5951(15185*2^246432-1)/1374187Lelio R Paula04/2015
59525*2^246413-374179Lelio R Paula05/2014
59532^246386-2863574170Lelio R Paula05/2013
59542^246334-11124574154Enzo Doria05/2014
59553*9^77708+7^77708-2*4^77708-374153Mike Oakes12/2010
595615^63045+8274147Lelio R Paula01/2015
595719255!+19255#+174140D. Gazzoni Filho & Lucas Teixeira06/2005
59582^246268-11050774135Enzo Doria05/2014
59593^155328+266074111Lelio R Paula01/2015
59602^246148-278624974098Enzo Doria03/2016
5961(16*10^74092-19)/374093Robert Price03/2016
59622^246115-11076774088Enzo Doria05/2014
59637^87666-6874087Lelio R Paula08/2014
596410^74079+114514191974080Marisa Kirisame03/2015
596510^74079+621974080Patrick De Geest03/2016
596610^74079-28270774079Patrick De Geest03/2016
5967129^35098+274078Lelio R Paula05/2013
59682^246025-11212374061Enzo Doria06/2014
5969(67*10^74045+17)/374047Robert Price02/2017
59702^245823+6683174001Marek Hubal02/2017
59715^105869+4274000Lelio R Paula08/2014
5972(21*2^245806+1)/63455573991Lelio R Paula08/2012
5973(22699*2^245762+1)/11973985Lelio R Paula06/2014
5974(3^155048-7)/26273975Lelio R Paula06/2012
59759998*2^245696+373966Donovan Johnson10/2004
597613^66400-8073966Lelio R Paula01/2015
5977(2^245704+9)/2573963Lelio R Paula07/2012
597911^71023-717073963Enzo Doria01/2013
59783*10^73962+1373963Robert Price08/2017
5980(31*2^245660-1)/11419573948Lelio R Paula01/2014
59812^245629-279781373942Eric Chen03/2016
59822^245557-15373921Lelio R Paula03/2012
5983(77*10^73917-59)/973918Robert Price11/2017
59842^245525+186988173911Enzo Doria06/2016
59852^245522+15973910Lelio R Paula03/2012
5986(13*10^73891-43)/373892Robert Price08/2017
598719^57783-5673891Lelio R Paula01/2015
59887*10^73888+7973889Robert Price02/2017
59896^94948+17428173884Mike Oakes02/2011
599011^70939-486073876Enzo Doria01/2013
59912^245372+5461573865Lelio R Paula05/2013
59922^245362-14373862Lelio R Paula03/2012
59937^87396+6^(87396-1)73859Robert Price03/2016
5994(22*10^73853-37)/373854Robert Price05/2017
59955^105646-1424673844Enzo Doria02/2013
59972^245290-4173840Lelio R Paula03/2012
59962^245290-9439573840Lelio R Paula05/2013
59988*5^105600-773813Lelio R Paula10/2014
59997*5^105573-473794Lelio R Paula10/2014
600018^58742-480573738Enzo Doria03/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 22 2018 09:48 (Time in France)

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