PRP Records

Probable Primes Top 10000

(190562 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 ?
45012^282860-10972785150Enzo Doria04/2014
45022^282819+186941385138Enzo Doria05/2016
45033^178428+285132Ray Chandler07/2011
4504(22699*2^282742+1)/7385117Lelio R Paula06/2014
4505(16^70687+5^70687)/2185115Robert Price07/2013
4506(3^178352-2)/785095Lelio R Paula12/2012
450711^81699-279085081Enzo Doria12/2012
45082^282612-9585075Lelio R Paula08/2012
450975^45366-285065Lelio R Paula08/2013
45102^282511+6985045Lelio R Paula08/2012
451169^46249+285045Lelio R Paula06/2013
45123^178226+1085036Robert Price10/2013
4513(14*10^85010+73)/385011Robert Price04/2016
45149*2^282338-784994Lelio R Paula08/2014
4515(9913*2^282330-1)/157800384988Lelio R Paula04/2015
45162^282203+584952Lelio R Paula08/2012
45172^282184+1384946Lelio R Paula08/2012
451811^81568-240084945Enzo Doria12/2012
451911^81562-234084939Enzo Doria12/2012
4520(41*10^84927+31)/984928Robert Price05/2015
4521(2*10^84904-17)/384904Robert Price08/2014
4522(4^141017+23)/384901Robert Price02/2017
45236^109100-1865384897Enzo Doria03/2013
45242^281973+102584883Lelio R Paula09/2013
45252^281951-10965184876Enzo Doria04/2014
452611^81491-543084865Enzo Doria01/2013
4527((1+sqrt(3)+sqrt(2))^79357-1)*((1+sqrt(3)-sqrt(2))^79357-1)*((1-sqrt(3)+sqrt(2))^79357-1)*((1-sqrt(384849Mike Oakes04/2009
45282^281825-186148384838Enzo Doria03/2016
45292^281809-9730584833Lelio R Paula09/2013
45302^281780-11489384825Enzo Doria05/2015
45313^177719+6484794Lelio R Paula12/2015
45332^281675-19984793Lelio R Paula08/2012
45322^281673-11122384793Enzo Doria05/2014
4534(4*10^84779+149)/984779Robert Price03/2017
4535(72*10^84772-27)/984773Ray Chandler01/2011
453611^81398-63084768Enzo Doria11/2012
4537(25*2^281577-1)/2384764Lelio R Paula02/2014
45382^281500-45584740Yves Minet03/2012
453910^84725+114514191984726Marisa Kirisame03/2015
454010^84725+14204184726Patrick De Geest10/2015
454110^84725-13867784725Patrick De Geest02/2016
454276^45044+7584720Norbert Schneider02/2015
454354^48897-5384709Norbert Schneider08/2014
4544(9913*2^281377-1)/6584706Lelio R Paula04/2015
4545Phi(171124,10)/29946701/7761329021/5856034404184700Maksym Voznyy11/2015
45462^281337-11122384691Enzo Doria05/2014
45472^281308+5461584683Lelio R Paula09/2013
45487*5^121144-684677Lelio R Paula10/2014
4549(2^281252+47)/384665Lelio R Paula01/2013
455011^81297-315084663Enzo Doria12/2012
45512^281208-30384653Yves Minet02/2012
4552197^36892-284648Lelio R Paula10/2017
4553(21*2^281187+1)/248384644Lelio R Paula01/2013
455411^81247-8484611Lelio R Paula10/2015
455517^68747-6484590Lelio R Paula11/2015
45565^121018-1559684588Enzo Doria02/2013
45576^108702+784587Lelio R Paula11/2014
455810^84582+10067784583Patrick De Geest05/2016
455910^84582-800184582Robert Price03/2016
45603*5^121004-884579Lelio R Paula10/2014
45615^120996-8484573Lelio R Paula10/2015
4562(10223*2^280881+1)/6841984553Lelio R Paula06/2014
45632^280852+9768184545Yves Minet08/2004
45642^280848-120384544Lelio R Paula09/2013
45655^120946-2484538Lelio R Paula10/2015
45662^280810-211184533Yves Minet08/2013
456711^81161-516084521Enzo Doria01/2013
45682^280737-9384511Lelio R Paula08/2012
45692^280698+31584499Lelio R Paula09/2013
45703^177099-34084498Lelio R Paula12/2015
4571(5*10^84469-107)/384470Robert Price01/2017
4572(3^177002+7)/669602227216174484436Lelio R Paula12/2012
4573(2^280500-1017)/82384436Lelio R Paula01/2013
457414^73660-584424Lelio R Paula11/2015
4575(19*10^84409-61)/384410Robert Price04/2017
45762^280388+11784406Lelio R Paula08/2012
45772^280389-56653384406Paul Bourdelais03/2013
4578(141584^16384+1)/6553784390Syoichiro Yamada06/2008
45792^280240-17384361Lelio R Paula08/2012
4580(184*10^84348-1)/384350Robert Price02/2017
45814*10^84346+9384347Robert Price01/2017
45827*2^280156-584337Lelio R Paula08/2014
45838*7^99782-384327Lelio R Paula10/2014
45842^280116+13384324Lelio R Paula08/2012
45852^280118+5461584324Lelio R Paula09/2013
4586(509203*2^280090-1)/384321Lelio R Paula04/2015
45876^108354+4784316Lelio R Paula12/2015
458810^84305+14196384306Patrick De Geest07/2013
458910^84305-5784305Robert Price05/2011
45909^88339+3*8^88339-2*4^88339-3*2^8833984297Mike Oakes01/2011
45913^176648-11280484283Enzo Doria06/2014
45926^108310+11584282Lelio R Paula12/2015
4593(11*2^279968-1)/584280Lelio R Paula02/2014
45946^108288-1664384265Enzo Doria02/2013
45952^279917-5869584264Lelio R Paula08/2013
459665^46477+3684259Lelio R Paula01/2016
45972^279866-190784249Yves Minet05/2013
4598(3^176580-5)/2807684246Lelio R Paula12/2012
4599(p(17530)#+4)/284246Robert Price09/2017
4600(2*10^84239+1)/384239Serge Batalov07/2009
460118^67103-4184233Lelio R Paula11/2015
460220^64743-4384233Lelio R Paula01/2016
4603143^39070+39070^14384209Serge Batalov05/2014
460411^80857-540084204Enzo Doria01/2013
4605(13*10^84179+161)/384180Robert Price04/2017
46062^279634-11040584179Enzo Doria05/2014
4607(74*10^84170+313)/984171Robert Price11/2017
46082^279582-101784163Lelio R Paula08/2013
4609(22*10^84159-19)/384160Robert Price02/2017
4610p(17513)#/2+51284156Robert Price05/2017
4611(19*10^84144-43)/384145Robert Price10/2017
4612(9*2^279507-1)/13784139Lelio R Paula02/2014
461311^80792-81084137Enzo Doria11/2012
4614(97*10^84134-1)/384136Serge Batalov12/2014
4615p(17507)#/2+3284125Robert Price12/2016
461621485^8224+8224^2148584116Hans Havermann04/2017
46173^176294-34084114Lelio R Paula12/2015
4618(3^176287+4)/219184107Lelio R Paula12/2012
46192^279388-71984105Yves Minet05/2012
4620(22699*2^279378+1)/22184104Lelio R Paula06/2014
46212^279332-11044784088Enzo Doria05/2014
46222^279320+784084Lelio R Paula06/2012
4623127^39966-284081Lelio R Paula10/2017
4624(11*2^279240-1)/9584059Lelio R Paula02/2014
46252^279218-11134784053Enzo Doria05/2014
462635^54435+284052Lelio R Paula05/2013
4627(31*2^279191-1)/1251152384040Lelio R Paula02/2014
462820996^10059+10059^2099684038Hans Havermann05/2017
462997*10^84033-384035Robert Price01/2017
463021234^9067+9067^2123484033Hans Havermann05/2017
46312^279095-10971784016Enzo Doria04/2014
463214^73282-9983991Lelio R Paula11/2015
463321457^8200+8200^2145783979Hans Havermann06/2017
463489*10^83976-783978Robert Price03/2017
46352^278955+17383974Lelio R Paula06/2012
4636(7*2^278851+1)/3983942Lelio R Paula12/2012
4637(9913*2^278844-1)/4080383940Lelio R Paula04/2015
46385^120076-1484683930Enzo Doria02/2013
4639(85*10^83921-1)/383923Robert Price07/2017
4640(2^278770-3)/2383917Lelio R Paula12/2012
4641(10^83916+449)/983916Serge Batalov12/2014
46422^278715+9983902Lelio R Paula06/2012
464340235!2-2^4023583899Robert Price09/2015
46442^278698-17183897Lelio R Paula06/2012
4645(19*10^83894-43)/383895Robert Price10/2017
46466^107802+2583887Lelio R Paula12/2015
46478*10^83880+3983881Robert Price01/2017
4648(58*10^83878+23)/983879Robert Price09/2015
46497^99244-9083871Lelio R Paula10/2015
46502^278554+425783854Lelio R Paula08/2013
46512^278504-10961983839Enzo Doria04/2014
46522^278499+187043383837Enzo Doria05/2016
4653105^41475+10483829Norbert Schneider11/2016
465415^71276-6883828Lelio R Paula11/2015
46552^278464-21641383827Enzo Doria04/2013
4656(76*10^83816-211)/983817Robert Price10/2017
4657(8*10^83811-101)/383812Robert Price10/2017
46582^278400+4075583807Lelio R Paula08/2013
4659(9*2^278381-1)/783802Lelio R Paula02/2014
46603*9^87813+6^87813+2*4^8781383796Mike Oakes12/2010
466119551^19268+19268^1955183773Hans Havermann05/2017
466220625^11522+11522^2062583770Hans Havermann05/2017
4663(44*10^83768-791)/983769Robert Price10/2017
4664(87^43189+1)/8883764Paul Bourdelais08/2017
46652^278235-4983758Lelio R Paula06/2012
466623543^3610+3610^2354383755Hans Havermann05/2017
466818^66711-9183741Lelio R Paula11/2015
46674*10^83740-8983741Robert Price08/2017
4669(3*2^278172-1)/1183738Lelio R Paula02/2014
4670(15*29^57251+2561)/2883724Curtis Bright05/2015
46714*7^99059-983716Lelio R Paula10/2014
4672(2^278128-3)/12684472414983714Lelio R Paula12/2012
46732^278077+186721183710Enzo Doria03/2016
46742^278059-2783705Lelio R Paula06/2012
4675214^35917+35917^21483702Norbert Schneider12/2014
4676(23*10^83693+7)/383694Robert Price10/2015
467785^43375-283689Lelio R Paula09/2013
46785*3^175360+483669Lelio R Paula07/2014
4679(23^61441-1)/2283665Robert Price01/2012
468020091^14596+14596^2009183664Hans Havermann03/2017
46812^277907-11062983659Enzo Doria05/2014
468219522^19283+19283^1952283656Hans Havermann04/2017
46838*5^119664-383643Lelio R Paula10/2014
46848*3^175299-783640Lelio R Paula07/2014
4685(26*10^83638-413)/983639Robert Price10/2017
46863^175250+2283616Robert Price12/2013
468711^80285+3083609Lelio R Paula10/2015
468826870^1293+1293^2687083609Hans Havermann03/2017
46892^277691+187442383594Enzo Doria06/2016
469013^75022-6083571Lelio R Paula11/2015
469114^72905-5183559Lelio R Paula11/2015
4692(17*2^277565-1)/54383554Lelio R Paula02/2014
46935^119532-1283550Lelio R Paula10/2015
46946^107358-1625383541Enzo Doria02/2013
46952^277478-46021183530Enzo Doria06/2015
4696(22*10^83525-7)/383526Erik Branger09/2014
4697(30^56543+1)/3183520Robert Price07/2013
46982^277417-46078383511Paul Bourdelais04/2013
4699(22699*2^277387+1)/21983504Lelio R Paula06/2014
4700(31*2^277383-1)/24783500Lelio R Paula02/2014
470121368^8085+8085^2136883500Hans Havermann04/2017
4702(9*2^277342+1)/1383489Lelio R Paula12/2012
47035^119439-6683485Lelio R Paula10/2015
4704(14*10^83471-101)/383472Robert Price04/2017
47055*6^107263+783468Lelio R Paula10/2014
4706(64*10^83461-1)/983462Serge Batalov11/2010
470717^67796-9283420Lelio R Paula11/2015
47082^277106-11005783418Enzo Doria04/2014
47096^107200-1983418Lelio R Paula12/2015
471011^80096-183083412Enzo Doria12/2012
47113^174801+5683402Lelio R Paula12/2015
47122^277033-11197383396Enzo Doria05/2014
471320519^11572+11572^2051983378Hans Havermann03/2017
471420850^9971+9971^2085083374Hans Havermann03/2017
47156^107122-1886383358Enzo Doria03/2013
47164*10^83354-8983355Robert Price08/2017
47173^174697-3483352Robert Price11/2013
4718(9787*2^276855-1)/234583343Lelio R Paula04/2015
47192^276825+7522783333Enzo Doria04/2016
47205^119214+8483328Lelio R Paula10/2015
47212^276803-15983327Lelio R Paula06/2012
4722(3*2^276753-1)/2583311Lelio R Paula02/2014
4723114^40495+40495^11483295Norbert Schneider12/2014
472439967!2+102483282Robert Price02/2015
47252^276641+5783278Lelio R Paula06/2012
472635^53934-341483278Enzo Doria03/2013
4727(2^276655+78557)/36542583276Lelio R Paula12/2012
47282^276615-403583270Lelio R Paula08/2013
47292^276588+115583262Lelio R Paula08/2013
47312^276587-93783261Yves Minet10/2009
47302^276584-11318383261Enzo Doria07/2014
4732(2^276592-1017)/1384373983256Lelio R Paula12/2012
47332^276547-10959183249Enzo Doria04/2014
473413^74733-3283249Lelio R Paula11/2015
47352^276523-258783242Yves Minet07/2014
473618^66311-4383239Lelio R Paula11/2015
473711^79919-153083228Enzo Doria12/2012
47382^276468-10974583226Enzo Doria04/2014
47392^276462+538583224Lelio R Paula08/2013
4740(9787*2^276422-1)/383215Lelio R Paula04/2015
47422^276391-1583202Lelio R Paula06/2012
4741(4*10^83201+173)/383202Robert Price01/2017
47432^276316-10965583180Enzo Doria04/2014
47442^276305-11206383177Enzo Doria06/2014
4745(10^(2*41585+1)+54*10^41585-1)/983171Robert Price04/2017
474674913!4-283161Robert Price07/2017
47472^276227-183720783153Enzo Doria05/2015
4748(2^276227+3)/783152Lelio R Paula12/2012
47492^276184-6338983140Paul Bourdelais02/2012
47502^276066-11160383105Enzo Doria05/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: November, 17 2017 23:50 (Time in France)

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