PRP Records

Probable Primes Top 10000

(180278 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
350111^90376+7694117Lelio R Paula05/2016
3502(6^120946-11)/594114Paul Bourdelais11/2011
35032^312562-11268594091Enzo Doria06/2014
35042^312404-86968810594043Lelio R Paula09/2016
35052^312387+279353394038Enzo Doria03/2016
350610^94016+9194017Robert Price04/2011
3507(15*2^312325-1)/720194017Lelio R Paula02/2014
350910^94016-18896394016Patrick De Geest08/2013
3508(17*2^312315-1)/4594016Lelio R Paula02/2014
35106^120802+766194003Mike Oakes04/2011
3511(67607*2^312254+1)/17794001Lelio R Paula06/2014
3512(11*2^312207+1)/1993984Lelio R Paula09/2013
35132^312201+5193982Lelio R Paula11/2012
3514(4*6^120749+1)/593961Serge Batalov10/2014
35153^196892+5893942Lelio R Paula05/2016
35162^312060+1891593940Lelio R Paula03/2016
35172^311992-1620993919Enzo Doria04/2013
35182^311965-3993911Lelio R Paula11/2012
35192^311920-11168993898Enzo Doria05/2014
35207*10^93887-4793888Robert Price02/2017
352112^86965-1393851Lelio R Paula06/2016
35222^311705+1609593833Lelio R Paula03/2016
35232^311665-8193821Lelio R Paula11/2012
352411^90073+9293802Lelio R Paula05/2016
35256*10^93792+4193793Robert Price01/2017
3526(2^311580+7)/59132993790Lelio R Paula06/2013
352712^86900-7793781Lelio R Paula06/2016
35282^311508-10976993774Enzo Doria04/2014
35292^311486-185962193767Enzo Doria03/2016
3530Phi(93811,10)/968129521/2109997013/3280113810431/63963778254583193765Kurt Beschorner04/2015
35312^311471+31146993763Renaud Lifchitz01/2003
35322^311426+7945993749Enzo Doria06/2016
35332^311294+577593709Lelio R Paula03/2016
35342^311252-101793697Lelio R Paula03/2016
35352^311247-11204193695Enzo Doria06/2014
35362^311205-10964593683Enzo Doria04/2014
35375^134027-8493681Lelio R Paula04/2016
3538(2^311148-1017)/55793663Lelio R Paula06/2013
3539(2^311027-2^155514+1)/59362811/2006
35403^196192-2893608Robert Price12/2013
3541216091#+26143393606Makoto Morimoto12/2015
35425^133917+6893604Lelio R Paula04/2016
35432^310924-170993598Yves Minet03/2013
3544(266*10^93577-11)/393579Robert Price09/2016
3545(16*10^93577+161)/393578Robert Price05/2016
35463^196113-5693570Lelio R Paula04/2016
35472^310806-11034593562Enzo Doria05/2014
35483^196093+8693561Lelio R Paula04/2016
35492^310780-232793555Yves Minet10/2013
355030^63332+4193550Lelio R Paula08/2012
3551(21181*2^310707+1)/2193536Lelio R Paula06/2014
35528*5^133807+793528Lelio R Paula10/2014
35532^310686+819393526Lelio R Paula03/2016
35542^310646+6393514Lelio R Paula11/2012
3555(77*10^93508+31)/993509Robert Price10/2015
3556(1000907^15583+1)/100090893499Faysal YAtim04/2009
3557(2*10^93497+7)/993497Erik Branger03/2011
35583^195958-11285293496Enzo Doria07/2014
35592^310583+1638593495Lelio R Paula03/2016
3560(9913*2^310557-1)/3593490Lelio R Paula04/2015
35619*7^110614+293481Lelio R Paula11/2014
35622^310469-829593461Lelio R Paula03/2016
35632^310459-115993458Yves Minet11/2012
35646^120075-9593437Lelio R Paula05/2016
35652^310289+9832793407Yves Minet11/2010
35662^310217-11314393385Enzo Doria07/2014
35677^110494-6893379Lelio R Paula04/2016
35682^310184-11309393375Enzo Doria07/2014
35692^310180-11041793374Enzo Doria05/2014
3570gcd(V(1124905),5*F(224981)*(F(224981)-1)+1)93372Serge Batalov04/2015
35713^195669+6893358Lelio R Paula04/2016
357210^93356+9193357Robert Price04/2011
357310^93356-2831393356Patrick De Geest08/2013
3574(85*10^93346+23)/993347Robert Price11/2015
3575(3^195648-5)/315827693342Lelio R Paula04/2013
35763^195556+868093304Lelio R Paula04/2016
35772^309942-10999193302Enzo Doria04/2014
35782^309926-186730193298Enzo Doria03/2016
35792^309924+8595193297Yves Minet03/2011
3580(86*10^93263-77)/993264Robert Price05/2016
35816^119836-12593251Lelio R Paula05/2016
35823^195430-293244Theodore Burton02/2007
3583(13*10^93236+47)/393237Robert Price01/2017
3584(86*10^93217-221)/993218Robert Price06/2017
35852^309637-1632993211Enzo Doria04/2013
3586(41*10^93207+49)/993208Robert Price04/2016
358714^81312-5793194Lelio R Paula06/2016
358841^57783-4093192Theodore Burton02/2007
35893*10^93179-9793180Robert Price08/2017
35905*7^110252-493175Lelio R Paula11/2014
35912^309380-2793133Lelio R Paula11/2012
359223*10^93116-793118Robert Price03/2016
3593(29*10^93082+1)/393083Robert Price11/2015
3594(58*10^93062-13)/993063Robert Price09/2015
35952^309131+186938393058Enzo Doria05/2016
35962^309066-9393039Lelio R Paula11/2012
35972^309063-11326993038Enzo Doria07/2014
35983^194965+1693022Robert Price10/2013
35992^308979+186914393012Enzo Doria05/2016
36005^133064+5493008Lelio R Paula04/2016
3601(2^308905-509203)/11992988Lelio R Paula06/2013
3602(94*10^92981-49)/9992981Ray Chandler07/2011
3603(2*10^92976-17)/392976Robert Price08/2014
36042^308809+3796792961Phil Moore03/2008
3605(3^194825+5)/1165692952Lelio R Paula04/2013
3606(2^308679+5)/157392919Lelio R Paula06/2013
36072^308650+51392913Lelio R Paula02/2016
36085*7^109936+692908Lelio R Paula10/2014
36092*10^92897+8992898Robert Price07/2016
361012^86073-2992889Lelio R Paula06/2016
36112^308566-11792888Lelio R Paula11/2012
3612(17*10^92869-11)/392870Robert Price07/2015
36132^308459+7543192856Enzo Doria04/2016
36142^308426-186637792846Enzo Doria03/2016
36152^308349-11211192823Enzo Doria06/2014
36169*10^92821+1992822Robert Price05/2016
36172^308337-7592819Lelio R Paula11/2012
36184*3^194508+792805Lelio R Paula08/2014
361922*25^66379-11392796Curtis Bright05/2015
362011^89101-108092790Enzo Doria12/2012
36212^308236-186785992789Enzo Doria04/2016
362212^85963+2592770Lelio R Paula06/2016
36237^109750-6692750Lelio R Paula04/2016
36249*10^92742+1192743Robert Kinser01/2017
3625(21*2^308046-1)/885792729Lelio R Paula02/2014
36262^307997-11065592717Enzo Doria05/2014
3627L(443609)92709Renaud Lifchitz11/2003
362810^92691+992692Robert Price03/2011
362910^92691-25229192691Patrick De Geest08/2013
36302^307879-252192681Yves Minet07/2014
3631(2^307780-7)/1995966992644Lelio R Paula06/2013
363214^80831+4792643Lelio R Paula06/2016
363315^78744+9292611Lelio R Paula07/2016
363465^51083-6492610Norbert Schneider11/2014
36356^118996-1694392597Enzo Doria02/2013
3636(3^194014-7)/292568Lelio R Paula04/2013
3637(26*10^92546-77)/392547Robert Price02/2017
36383^193954+34092540Lelio R Paula04/2016
36392^307407-307407^292539Henri Lifchitz05/2005
3640(17*10^92513-11)/392514Robert Price07/2015
36412^307318-421192512Yves Minet06/2011
36422^307280+19392501Lelio R Paula11/2012
364320^71075-3392471Lelio R Paula05/2016
36442^307126-7879592455Lelio R Paula02/2016
36452^307125-4978992454Henri Lifchitz08/2005
36462^307099+2392447Lelio R Paula11/2012
36477*10^92414-6992415Robert Price01/2017
3648(9787*2^306975-1)/212915592407Lelio R Paula04/2015
36492^306915+187337392391Enzo Doria06/2016
36502^306908+1291592389Lelio R Paula02/2016
365119^72244-8092383Lelio R Paula06/2016
36522^306849+7592371Lelio R Paula11/2012
36532^306813-86968810592360Lelio R Paula08/2016
36542^306672-10905992318Enzo Doria04/2014
36556^118604-1706392292Enzo Doria02/2013
3656(31*2^306487-1)/229192260Lelio R Paula02/2014
36572^306467-183561192256Enzo Doria04/2015
36582^306433+7642792246Enzo Doria05/2016
36592^306430-11331392245Enzo Doria07/2014
3660(23*10^92244-59)/992245Robert Price03/2017
3661(47*2^306398+1)/138480392231Lelio R Paula04/2015
3662(25*10^92186+59)/392187Robert Price05/2016
36632^306213-28618392180Enzo Doria06/2015
366410^92178+6192179Robert Price04/2011
366510^92178-17550992178Patrick De Geest07/2013
36662^306200+118592176Lelio R Paula02/2016
36672^306153+1192162Lelio R Paula11/2012
3668(2^306141-7)/592157Lelio R Paula06/2013
3669(26*10^92152-23)/392153Robert Price08/2016
3670(2*10^92152+67)/392152Robert Price04/2017
36714*10^92099+3*7^9209992100Mike Oakes12/2010
3672(2^305867-2^152934+1)/59207511/2006
36732^305851-10949592071Enzo Doria04/2014
367412^85300+3592055Lelio R Paula06/2016
36753^192911+9292042Lelio R Paula04/2016
36762^305723-27627192032Enzo Doria07/2015
36772^305676+9392018Donovan Johnson06/2008
36783^192819+491999Lelio R Paula04/2013
3679(38*10^91997-83)/9991997Ray Chandler07/2011
36802^305539+7291191977Enzo Doria04/2016
3681(2^305427-5)/129799821391934Lelio R Paula06/2013
368285^47642+8491922Norbert Schneider10/2015
368310^91920+18765191921Patrick De Geest07/2013
368410^91920-3991920Robert Price05/2011
3685(22*10^91903+41)/991904Robert Price02/2015
36872^305275-2791897Lelio R Paula11/2012
36863^192607-772691897Enzo Doria05/2014
3688(7*10^91856-61)/991856Erik Branger12/2009
3689(89*10^91839-53)/991840Robert Price11/2015
36908*5^131351+791812Lelio R Paula10/2014
36913^192426-6891811Lelio R Paula04/2016
36922^304973+11791807Lelio R Paula11/2012
36932^304939-186372791796Enzo Doria03/2016
36942^304902+841591785Lelio R Paula02/2016
369518^73119+6191785Lelio R Paula06/2016
3696(78557*2^304740+1)/15991739Lelio R Paula06/2014
36972^304747+7135591738Lelio R Paula02/2016
36988*3^192251+591728Lelio R Paula08/2014
36992^304674-8791717Lelio R Paula11/2012
3700(2^304698+9)/136280995391715Lelio R Paula06/2013
3701(5*10^91707-119)/391708Robert Price04/2016
37022^304633-11277191704Enzo Doria06/2014
37032^304578-1671391688Enzo Doria05/2013
37046^117824-1871391685Enzo Doria03/2013
3705(17^74509-1)/1691679Paul Bourdelais03/2010
3706(2^304551-7)/891223191673Lelio R Paula06/2013
3707(2^304532-3)/301391670Lelio R Paula06/2013
37082^304507-1664591666Enzo Doria04/2013
3709(29*2^304489+1)/3191661Lelio R Paula09/2013
37102^304471-183612791655Enzo Doria04/2015
37112^304433+3276991644Lelio R Paula02/2016
37122^304410-1662591637Enzo Doria04/2013
37134*5^131052+791603Lelio R Paula10/2014
37142^304278-400191597Yves Minet04/2017
37152^304272-186637791595Enzo Doria03/2016
37162^304268+1968391594Lelio R Paula02/2016
37172^304162-16191562Lelio R Paula11/2012
37185*7^108331+691552Lelio R Paula10/2014
37192^304082-278782191538Enzo Doria03/2016
37202^304015+6413391518David Broadhurst06/2002
3721(7*2^303963+1)/391503Lelio R Paula09/2013
3722(2^303945-9)/361791494Lelio R Paula06/2013
37232^303930+188052791493Enzo Doria10/2016
37243^191684-6891457Lelio R Paula04/2016
3725(21*2^303813-1)/16991456Lelio R Paula02/2014
372611^87797-12091432Enzo Doria07/2012
37272^303698-184723191423Enzo Doria07/2015
3728(38^28933-1)^2-291416Norbert Schneider06/2016
37292^303554+7729991379Enzo Doria05/2016
37302^303542+1270591376Lelio R Paula02/2016
373131^61269-291375Lelio R Paula09/2013
37322^303516-6487591368Lelio R Paula02/2016
3733(24737*2^303428+1)/391345Lelio R Paula06/2014
3734(21181*2^303357+1)/3236191320Lelio R Paula06/2014
37352^303344-278696991316Enzo Doria03/2016
37366^117346+6591313Lelio R Paula05/2016
37372^303321+85591309Lelio R Paula02/2016
373812^84606+4791306Lelio R Paula06/2016
37392^303288+187431191299Enzo Doria06/2016
374011^87663-171091292Enzo Doria12/2012
37412^303224+253391280Henri Lifchitz05/2005
37426^117302+14391279Lelio R Paula05/2016
37433^191306-11288091277Enzo Doria07/2014
37442^303207+1291591275Lelio R Paula02/2016
37452^303191-11125991270Enzo Doria05/2014
374710^91230+9^(91230+1)91231Robert Price08/2016
374610^91230+792191231Patrick De Geest11/2016
374810^91230-91114191230Patrick De Geest11/2016
37496^117232-1742391225Enzo Doria02/2013
37507*10^91215+391216Erik Branger11/2009


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 20 2017 08:36 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!