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 ?
52519^79677+3*8^79677-2*4^79677-3*2^7967776032Mike Oakes12/2010
5252(2^252557-9)/7176026Lelio R Paula07/2012
525311^72989+8076011Lelio R Paula02/2015
52542^252449-45952375995Enzo Doria05/2015
525520^58408+7375991Lelio R Paula01/2015
52562^252418-142175986Yves Minet01/2013
5257(11*2^252396-1)/575980Lelio R Paula02/2014
52582^252365-11068975970Enzo Doria05/2014
525911^72949-102075969Enzo Doria11/2012
5260(2^252294+47)/654975945Lelio R Paula07/2012
52612^252261-11059575939Enzo Doria05/2014
52627^89853+7675935Lelio R Paula01/2015
52633^159132+5675926Lelio R Paula01/2015
5264730^26513+26513^73075916Norbert Schneider11/2016
5265(27*2^252163-1)/194575907Lelio R Paula01/2014
52665^108596-1484675906Enzo Doria02/2013
52675^108560-1484675881Enzo Doria02/2013
52682^252051-11035975875Enzo Doria05/2014
52692^251971-11050975851Enzo Doria05/2014
5270(42457^16384+1)/32768275819Lelio R Paula11/2011
527114*10^75798+108975800Jens K. Andersen11/2007
52722^251784-45575795Yves Minet03/2012
52732^251780-128975794Yves Minet01/2013
52742^251760-21560975788Paul Bourdelais03/2013
527599^37973+275781Lelio R Paula05/2013
5276(185*10^75777+7)/375779Robert Price02/2017
52775*2^251690+375767Lelio R Paula06/2014
52786^97366+9575766Lelio R Paula01/2015
52798*6^97337-775744Lelio R Paula10/2014
52802^251588-11167775736Enzo Doria05/2014
52815^108346-1325675731Enzo Doria02/2013
5282(31^50777+1)/3275726Robert Price07/2013
5283(10^75707+77)/375707Robert Price01/2017
52842^251466+19375699Lelio R Paula03/2012
5285(5*2^251464+1)/942375695Lelio R Paula07/2012
52862^251422-10999175686Enzo Doria04/2014
52874*5^108245-375661Lelio R Paula10/2014
528812^70067-11^7006775615Jean-Louis Charton11/2006
528912^70066+9575614Lelio R Paula02/2015
5290-E20534/206375607Thomas Ritschel02/2017
529119^59120-5075600Lelio R Paula01/2015
529218^60222-469775596Enzo Doria03/2013
529318^60211-435575582Enzo Doria03/2013
52947*2^251014-975564Lelio R Paula06/2014
52956^97101-2575560Lelio R Paula01/2015
52968^83663-7^8366375556Jean-Louis Charton01/2004
52973^158331-14075544Lelio R Paula01/2015
5298(37^48157-1)/3675519Robert Price03/2012
529910^75516+3146775517Patrick De Geest03/2016
530110^75516-10^2256-175516Serge Batalov01/2011
530010^75516-6659175516Patrick De Geest03/2016
53022^250851-18775514Lelio R Paula03/2012
5303(43*10^75498-7)/975499Robert Price12/2014
5304(3^158244-5)/24791675497Lelio R Paula06/2012
53054*5^107971-375470Lelio R Paula10/2014
5306(25*10^75465+71)/375466Robert Price01/2017
5307(5*2^250681-1)/99975461Lelio R Paula01/2014
5308(182*10^75456+1)/375458Robert Price02/2017
5309(2^250669-9)/9889772975451Lelio R Paula07/2012
531010^75441+1375442Robert Price01/2011
531110^75441-992375441Patrick De Geest05/2013
5312(27*2^250546-1)/645775420Lelio R Paula01/2014
53135*7^89231-675410Lelio R Paula10/2014
53152^250503-1699575409Lelio R Paula05/2013
531411^72411-2875409Lelio R Paula02/2015
53163*5^107860-875392Lelio R Paula10/2014
53182^250426+2983575386Lelio R Paula05/2013
53178*3^157999-775386Lelio R Paula05/2014
5319(88*10^75381-43)/975382Robert Price11/2015
53202^250382-11175575373Enzo Doria05/2014
53212^250374-279805175371Eric Chen03/2016
5322(22*10^75368-1)/375369Robert Price12/2014
5323(19*10^75338+119)/375339Robert Price02/2017
53242^250223-185916775325Enzo Doria03/2016
5325(3^157854-7)/6602528275308Lelio R Paula06/2012
53263^157831-9875305Lelio R Paula01/2015
5327(46^45281+11^45281)/5775290Serge Batalov12/2016
532892^38335-9175282Norbert Schneider01/2016
53292^250020+1891575264Lelio R Paula05/2013
53302^250002+819375259Lelio R Paula05/2013
5331(11*2^249977-7)/1575251Renaud Lifchitz02/2011
5332(2^249968+78557)/6375247Lelio R Paula07/2012
5333(5*10^75244+91)/375245Robert Price11/2016
5334(10489!)^2+Prime(10489)75242Robert Price08/2014
533514^65644+6775237Lelio R Paula01/2015
5336(2^249928-5)/1185905975229Lelio R Paula06/2012
5337129^35638+275218Lelio R Paula05/2013
53382^249853-11047575214Enzo Doria05/2014
53392^249762+7540975186Enzo Doria04/2016
5340565^27318+27318^56575181Norbert Schneider12/2016
5341(2^249741-7)/68575177Lelio R Paula06/2012
53422^249726-11218175176Enzo Doria06/2014
53432^249721+1171575174Lelio R Paula05/2013
5344(38661^16384+1)/275158Lelio R Paula11/2011
53452^249658-4735575155Lelio R Paula05/2013
5346155^34311+275153Lelio R Paula05/2013
5347(10^87682+1)/(10^12526+1)/99009900990175145Maksym Voznyy06/2015
5348(23*2^249602+1)/9375138Lelio R Paula08/2012
53492^249522+841575114Lelio R Paula05/2013
53502^249489-11091175104Enzo Doria05/2014
5351(28*10^75078+131)/375079Robert Price02/2017
5352(206*10^75073-17)/975075Robert Price03/2017
53532^249368-11057375068Enzo Doria05/2014
5354NaturalLogarithmOf10(75067)75067Eric W. Weisstein10/2015
5355(2^249375+78557)/4505612575062Lelio R Paula07/2012
53562^249272+19375039Lelio R Paula03/2012
535714^65468+4375035Lelio R Paula01/2015
535837^47844+3675030Norbert Schneider05/2014
5359(52*10^75027-7)/975028Robert Price12/2014
536020^57653+8975009Lelio R Paula01/2015
53612^249061-186835374975Enzo Doria04/2016
53627^88713+2*3^8871374972Mike Oakes07/2010
53632*6^96313+574947Lelio R Paula10/2014
5364(8*10^74944+49)/374945Robert Price03/2016
5365300^30247+30247^30074926Norbert Schneider11/2014
53662^248866-17174917Lelio R Paula03/2012
53676*5^107168-774908Lelio R Paula10/2014
536811^71926+7874904Lelio R Paula02/2015
53692^248824+186939174904Enzo Doria05/2016
53702^248816+111174902Lelio R Paula01/2011
5371V(388219)74890Serge Batalov03/2015
53722*F(358297)-174880Henri Lifchitz12/2009
5373(22*10^74874-31)/974875Robert Price04/2015
537411^71892-7680000074868Enzo Doria01/2013
53759*5^107107-474866Lelio R Paula10/2014
53762^248678-71011174860Paul Bourdelais03/2013
537713^67194+1274851Lelio R Paula01/2015
5378(7*2^248634+1)/7174846Lelio R Paula08/2012
537911^71867-309074842Enzo Doria12/2012
53802^248609+26214574839Lelio R Paula05/2013
53813^156852+5074838Lelio R Paula01/2015
538218^59607-1174824Lelio R Paula01/2015
53832^248556-11050774823Enzo Doria05/2014
53847^88531-3674818Lelio R Paula01/2015
53854*3^156740-574785Lelio R Paula05/2014
5386(32*10^74773-41)/974774Robert Price05/2015
5387(29*2^248384-1)/1374772Lelio R Paula01/2014
538819401!+19401#+174765D. Gazzoni Filho & Lucas Teixeira06/2005
53892^248357-1279741374763Enzo Doria03/2016
539042^46057+4174762Lelio R Paula07/2012
539111^71784-300074756Enzo Doria12/2012
539219^58458+1874754Lelio R Paula01/2015
539312^69265-3574750Lelio R Paula02/2015
539411^71771-4800074742Enzo Doria12/2012
5395(2^248282-5)/5012974736Lelio R Paula06/2012
53962^248252-11010574732Enzo Doria04/2014
5397(7*10^74729+71)/374730Robert Price03/2016
53983^156614-5074724Lelio R Paula01/2015
5399(7*2^248213+1)/13574719Lelio R Paula07/2012
5400(2^248173+78557)/76774705Lelio R Paula07/2012
5401125^35622+12474697Norbert Schneider02/2015
5402(19*2^248099-1)/2974686Lelio R Paula01/2014
5403(86*10^74676-41)/974677Robert Price11/2015
540410^74670+3174671Robert Price01/2011
540510^74670-12246374670Patrick De Geest05/2013
54062^248036-6974667Lelio R Paula03/2012
540711^71698-600074666Enzo Doria12/2012
540858*(10^(3*24887)-1)/111-174661Robert Price10/2014
540914^65139-4574658Lelio R Paula01/2015
54106^95921-13374642Lelio R Paula01/2015
541111^71675+7874642Lelio R Paula02/2015
541218^59449-9174625Lelio R Paula01/2015
54136^95864-1604374597Enzo Doria02/2013
54145*7^88261+674590Lelio R Paula10/2014
54159*5^106710+474589Lelio R Paula10/2014
5416(777*2^247788+1)/(11*754121)74588Jens K. Andersen09/2007
5417(265*10^74579+17)/374581Robert Price05/2016
5418(2^247759-1017)/331831171774574Lelio R Paula07/2012
54195^106682-2474568Lelio R Paula08/2014
5420474^27863+27863^47474556Norbert Schneider01/2017
5421(35365^16384+1)/274524Lelio R Paula11/2011
54223^156161+266074508Lelio R Paula01/2015
54232^247474-5869574498Lelio R Paula05/2013
542411^71519-9074480Enzo Doria07/2012
5425(19*2^247419-1)/2320298374475Lelio R Paula01/2014
5427(2^247394-7)/374473Lelio R Paula06/2012
542618^59328+1774473Lelio R Paula01/2015
54282^247379-18174469Lelio R Paula03/2012
5429(15*2^247370-1)/47974465Lelio R Paula01/2014
54302^247344+204774458Lelio R Paula05/2013
54312^247311-101774449Lelio R Paula05/2013
54322^247280+774439Lelio R Paula03/2012
5433(68*10^74434+13)/974435Ray Chandler11/2010
54343^156004-6274433Lelio R Paula01/2015
543536095!2-6474416Robert Price06/2015
54362^247165-374405M. Frind & P. Underwood07/2002
54372^247150+3276974400Lelio R Paula05/2013
543812^68911+7374368Lelio R Paula01/2015
54392^246999+7490374355Enzo Doria04/2016
54402^246989-11064374352Enzo Doria05/2014
5441(10^74350+11)/374350Robert Price11/2014
544210^74335+1365974336Patrick De Geest05/2013
544310^74335-5374335Robert Price05/2011
54442^246906-121574327Lelio R Paula05/2013
54452^246848+11174309Lelio R Paula03/2012
54466^95490-1844374306Enzo Doria03/2013
544718^59188-236974298Enzo Doria03/2013
5448(1363*2^246767+1)/(3*5*7*13^2*743)74281Jens K. Andersen09/2007
54492^246744+4075574278Lelio R Paula05/2013
5450(29*10^74276+91)/374277Robert Price03/2016
54516^95441+16374268Lelio R Paula01/2015
5452V(390863)74258Serge Batalov03/2015
545310^74254+9174255Robert Price03/2011
5454(19*10^74253-1)/974254Ray Chandler02/2012
545510^74254-13056974254Patrick De Geest05/2013
5456771^25718+25718^77174250Norbert Schneider10/2016
54572^246618+42774240Henri Lifchitz02/2005
545888*10^74234+374236Robert Price11/2016
54598*10^74234-4974235Robert Price04/2016
54602^246578+1228574228Lelio R Paula05/2013
5461(3^155569-5)/274225Lelio R Paula06/2012
546213^66628+4674220Lelio R Paula01/2015
54632^246476-1729574197Lelio R Paula05/2013
5464(15185*2^246432-1)/1374187Lelio R Paula04/2015
54655*2^246413-374179Lelio R Paula05/2014
54662^246386-2863574170Lelio R Paula05/2013
54672^246334-11124574154Enzo Doria05/2014
54683*9^77708+7^77708-2*4^77708-374153Mike Oakes12/2010
546915^63045+8274147Lelio R Paula01/2015
547019255!+19255#+174140D. Gazzoni Filho & Lucas Teixeira06/2005
54712^246268-11050774135Enzo Doria05/2014
54723^155328+266074111Lelio R Paula01/2015
54732^246148-278624974098Enzo Doria03/2016
5474(16*10^74092-19)/374093Robert Price03/2016
54752^246115-11076774088Enzo Doria05/2014
54767^87666-6874087Lelio R Paula08/2014
547710^74079+114514191974080Marisa Kirisame03/2015
547810^74079+621974080Patrick De Geest03/2016
547910^74079-28270774079Patrick De Geest03/2016
5480129^35098+274078Lelio R Paula05/2013
54812^246025-11212374061Enzo Doria06/2014
5482(67*10^74045+17)/374047Robert Price02/2017
54832^245823+6683174001Marek Hubal02/2017
54845^105869+4274000Lelio R Paula08/2014
5485(21*2^245806+1)/63455573991Lelio R Paula08/2012
5486(22699*2^245762+1)/11973985Lelio R Paula06/2014
5487(3^155048-7)/26273975Lelio R Paula06/2012
54889998*2^245696+373966Donovan Johnson10/2004
548913^66400-8073966Lelio R Paula01/2015
5490(2^245704+9)/2573963Lelio R Paula07/2012
549111^71023-717073963Enzo Doria01/2013
5492(31*2^245660-1)/11419573948Lelio R Paula01/2014
54932^245629-279781373942Eric Chen03/2016
54942^245557-15373921Lelio R Paula03/2012
54952^245525+186988173911Enzo Doria06/2016
54962^245522+15973910Lelio R Paula03/2012
549719^57783-5673891Lelio R Paula01/2015
54987*10^73888+7973889Robert Price02/2017
54996^94948+17428173884Mike Oakes02/2011
550011^70939-486073876Enzo Doria01/2013


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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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