PRP Records

Probable Primes Top 10000

(255244 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 ?
4501(10^94096+191)/394096Robert Price11/2017
45022^312562-11268594091Enzo Doria06/2014
4503137^44026-294072Lelio R Paula10/2017
45042^312404-86968810594043Lelio R Paula09/2016
45052^312387+279353394038Enzo Doria03/2016
450710^94016+9194017Robert Price04/2011
4506(15*2^312325-1)/720194017Lelio R Paula02/2014
450810^94016-18896394016Patrick De Geest08/2013
4509(17*2^312315-1)/4594016Lelio R Paula02/2014
45106^120802+766194003Mike Oakes04/2011
4511(67607*2^312254+1)/17794001Lelio R Paula06/2014
4512(11*2^312207+1)/1993984Lelio R Paula09/2013
45132^312201+5193982Lelio R Paula11/2012
4514(4*6^120749+1)/593961Serge Batalov10/2014
45153^196892+5893942Lelio R Paula05/2016
45162^312060+1891593940Lelio R Paula03/2016
451742^57867-4193933Norbert Schneider08/2018
45182^311992-1620993919Enzo Doria04/2013
4519(85^48677+1)/8693917Paul Bourdelais08/2017
45202^311965-3993911Lelio R Paula11/2012
45212^311920-11168993898Enzo Doria05/2014
4522130^44414+12993889Norbert Schneider01/2019
45237*10^93887-4793888Robert Price02/2017
452412^86965-1393851Lelio R Paula06/2016
45252^311705+1609593833Lelio R Paula03/2016
45262^311665-8193821Lelio R Paula11/2012
4527730^32761+32761^73093806Norbert Schneider09/2017
452811^90073+9293802Lelio R Paula05/2016
45296*10^93792+4193793Robert Price01/2017
4530(2^311580+7)/59132993790Lelio R Paula06/2013
453112^86900-7793781Lelio R Paula06/2016
45322^311508-10976993774Enzo Doria04/2014
45332^311486-185962193767Enzo Doria03/2016
4534Phi(93811,10)/968129521/2109997013/3280113810431/63963778254583193765Kurt Beschorner04/2015
4535(10^93811-1)/(9*968129521*2109997013*3280113810431*639637782545831)93765Gord Palameta10/2018
45362^311471+31146993763Renaud Lifchitz01/2003
4537(88*10^93760-1)/393762Robert Price10/2017
45382^311426+7945993749Enzo Doria06/2016
45392^311294+577593709Lelio R Paula03/2016
45402^311252-101793697Lelio R Paula03/2016
45412^311247-11204193695Enzo Doria06/2014
45427*10^93692-8393693Robert Price09/2017
45432^311205-10964593683Enzo Doria04/2014
45445^134027-8493681Lelio R Paula04/2016
4545(2^311148-1017)/55793663Lelio R Paula06/2013
4546(2^311027-2^155514+1)/59362811/2006
45473^196192-2893608Robert Price12/2013
4548216091#+26143393606Makoto Morimoto12/2015
45495^133917+6893604Lelio R Paula04/2016
45502^310924-170993598Yves Minet03/2013
4551(266*10^93577-11)/393579Robert Price09/2016
4552(16*10^93577+161)/393578Robert Price05/2016
45533^196113-5693570Lelio R Paula04/2016
45542^310806-11034593562Enzo Doria05/2014
45553^196093+8693561Lelio R Paula04/2016
45562^310780-232793555Yves Minet10/2013
455730^63332+4193550Lelio R Paula08/2012
4558(21181*2^310707+1)/2193536Lelio R Paula06/2014
45598*5^133807+793528Lelio R Paula10/2014
45602^310686+819393526Lelio R Paula03/2016
45612^310646+6393514Lelio R Paula11/2012
4562(77*10^93508+31)/993509Robert Price10/2015
4563(1000907^15583+1)/100090893499Faysal YAtim04/2009
4564(2*10^93497+7)/993497Erik Branger03/2011
45653^195958-11285293496Enzo Doria07/2014
45662^310583+1638593495Lelio R Paula03/2016
4567(9913*2^310557-1)/3593490Lelio R Paula04/2015
45689*7^110614+293481Lelio R Paula11/2014
45692^310469-829593461Lelio R Paula03/2016
45702^310459-115993458Yves Minet11/2012
45716^120075-9593437Lelio R Paula05/2016
4572148^43041-14793411Norbert Schneider05/2019
45732^310289+9832793407Yves Minet11/2010
45742^310217-11314393385Enzo Doria07/2014
45757^110494-6893379Lelio R Paula04/2016
45762^310184-11309393375Enzo Doria07/2014
45772^310180-11041793374Enzo Doria05/2014
4578gcd(V(1124905),5*F(224981)*(F(224981)-1)+1)93372Serge Batalov04/2015
45793^195669+6893358Lelio R Paula04/2016
458010^93356+9193357Robert Price04/2011
458110^93356-2831393356Patrick De Geest08/2013
4582(85*10^93346+23)/993347Robert Price11/2015
4583(3^195648-5)/315827693342Lelio R Paula04/2013
45843^195556+868093304Lelio R Paula04/2016
45852^309942-10999193302Enzo Doria04/2014
45862^309926-186730193298Enzo Doria03/2016
45872^309924+8595193297Yves Minet03/2011
45882^309896-422993288Yves Minet08/2018
4589(86*10^93263-77)/993264Robert Price05/2016
45906^119836-12593251Lelio R Paula05/2016
4591(77*10^93249-257)/993250Robert Price10/2017
45923^195430-293244Theodore Burton02/2007
4593(13*10^93236+47)/393237Robert Price01/2017
4594(67*10^93226-7)/393228Robert Price10/2017
4595(86*10^93217-221)/993218Robert Price06/2017
45962^309637-1632993211Enzo Doria04/2013
4597(41*10^93207+49)/993208Robert Price04/2016
459814^81312-5793194Lelio R Paula06/2016
459941^57783-4093192Theodore Burton02/2007
46003*10^93179-9793180Robert Price08/2017
46015*7^110252-493175Lelio R Paula11/2014
460283061!4-51293137Robert Price11/2019
46032^309380-2793133Lelio R Paula11/2012
460423*10^93116-793118Robert Price03/2016
4605(29*10^93082+1)/393083Robert Price11/2015
4606(58*10^93062-13)/993063Robert Price09/2015
46072^309131+186938393058Enzo Doria05/2016
46082^309066-9393039Lelio R Paula11/2012
46092^309063-11326993038Enzo Doria07/2014
46103^194965+1693022Robert Price10/2013
46112^308979+186914393012Enzo Doria05/2016
46125^133064+5493008Lelio R Paula04/2016
4613(2^308905-509203)/11992988Lelio R Paula06/2013
4614(94*10^92981-49)/9992981Ray Chandler07/2011
4615(2*10^92976-17)/392976Robert Price08/2014
46162^308809+3796792961Phil Moore03/2008
4617(3^194825+5)/1165692952Lelio R Paula04/2013
4618(2^308679+5)/157392919Lelio R Paula06/2013
46192^308650+51392913Lelio R Paula02/2016
46205*7^109936+692908Lelio R Paula10/2014
46212*10^92897+8992898Robert Price07/2016
462212^86073-2992889Lelio R Paula06/2016
46232^308566-11792888Lelio R Paula11/2012
4624(17*10^92869-11)/392870Robert Price07/2015
46252^308459+7543192856Enzo Doria04/2016
46262^308426-186637792846Enzo Doria03/2016
4627(96^46831-1)/9592830Paul Bourdelais09/2017
46282^308349-11211192823Enzo Doria06/2014
46299*10^92821+1992822Robert Price05/2016
46302^308337-7592819Lelio R Paula11/2012
46314*3^194508+792805Lelio R Paula08/2014
463222*25^66379-11392796Curtis Bright05/2015
463311^89101-108092790Enzo Doria12/2012
46342^308236-186785992789Enzo Doria04/2016
463512^85963+2592770Lelio R Paula06/2016
46367^109750-6692750Lelio R Paula04/2016
46379*10^92742+1192743Robert Kinser01/2017
4638(21*2^308046-1)/885792729Lelio R Paula02/2014
46392^307997-11065592717Enzo Doria05/2014
4640L(443609)92709Renaud Lifchitz11/2003
464110^92691+992692Robert Price03/2011
464210^92691-25229192691Patrick De Geest08/2013
46432^307879-252192681Yves Minet07/2014
4644(2^307780-7)/1995966992644Lelio R Paula06/2013
464514^80831+4792643Lelio R Paula06/2016
464615^78744+9292611Lelio R Paula07/2016
464765^51083-6492610Norbert Schneider11/2014
4648131^43737-13092604Norbert Schneider02/2019
46496^118996-1694392597Enzo Doria02/2013
4650(16*10^92591+41)/392592Robert Price10/2017
4651(3^194014-7)/292568Lelio R Paula04/2013
4652(63^51439+1)/6492555Paul Bourdelais08/2017
4653(26*10^92546-77)/392547Robert Price02/2017
46543^193954+34092540Lelio R Paula04/2016
46552^307407-307407^292539Henri Lifchitz05/2005
4656(17*10^92513-11)/392514Robert Price07/2015
46572^307318-421192512Yves Minet06/2011
46582^307280+19392501Lelio R Paula11/2012
465920^71075-3392471Lelio R Paula05/2016
46602^307126-7879592455Lelio R Paula02/2016
46612^307125-4978992454Henri Lifchitz08/2005
46622^307099+2392447Lelio R Paula11/2012
4663129^43798+12892440Norbert Schneider01/2019
4664Phi(277314,10)/332776992430Makoto Kamada05/2019
46657*10^92414-6992415Robert Price01/2017
4666(9787*2^306975-1)/212915592407Lelio R Paula04/2015
46672^306915+187337392391Enzo Doria06/2016
46682^306908+1291592389Lelio R Paula02/2016
466919^72244-8092383Lelio R Paula06/2016
46712^306849+7592371Lelio R Paula11/2012
4670(397*10^92369+53)/992371Robert Price11/2017
46722^306813-86968810592360Lelio R Paula08/2016
46732^306672-10905992318Enzo Doria04/2014
46746^118604-1706392292Enzo Doria02/2013
4675(31*2^306487-1)/229192260Lelio R Paula02/2014
46762^306467-183561192256Enzo Doria04/2015
46772^306433+7642792246Enzo Doria05/2016
46792^306430-11331392245Enzo Doria07/2014
4678(23*10^92244-59)/992245Robert Price03/2017
4680(47*2^306398+1)/138480392231Lelio R Paula04/2015
4681(25*10^92186+59)/392187Robert Price05/2016
46822^306213-28618392180Enzo Doria06/2015
468310^92178+6192179Robert Price04/2011
468410^92178-17550992178Patrick De Geest07/2013
46852^306200+118592176Lelio R Paula02/2016
46862^306153+1192162Lelio R Paula11/2012
4687(2^306141-7)/592157Lelio R Paula06/2013
4688(26*10^92152-23)/392153Robert Price08/2016
4689(2*10^92152+67)/392152Robert Price04/2017
46904*10^92099+3*7^9209992100Mike Oakes12/2010
4691115^44684+11492081Norbert Schneider07/2018
4692(2^305867-2^152934+1)/59207511/2006
46932^305851-10949592071Enzo Doria04/2014
469512^85300+3592055Lelio R Paula06/2016
4694((10^46026-1)*1000/9+739)*10^46026+(10^46026-1)/992055Hans Havermann05/2019
46963^192911+9292042Lelio R Paula04/2016
46972^305723-27627192032Enzo Doria07/2015
46982^305676+9392018Donovan Johnson06/2008
46993^192819+491999Lelio R Paula04/2013
4700(38*10^91997-83)/9991997Ray Chandler07/2011
47012^305539+7291191977Enzo Doria04/2016
4702Phi(212014,10)91960Makoto Kamada04/2019
4703(2^305427-5)/129799821391934Lelio R Paula06/2013
470482077!4-12891928Robert Price11/2019
470585^47642+8491922Norbert Schneider10/2015
470610^91920+18765191921Patrick De Geest07/2013
470710^91920-3991920Robert Price05/2011
4708(22*10^91903+41)/991904Robert Price02/2015
47102^305275-2791897Lelio R Paula11/2012
47093^192607-772691897Enzo Doria05/2014
4711(7*10^91856-61)/991856Erik Branger12/2009
4712(89*10^91839-53)/991840Robert Price11/2015
47138*5^131351+791812Lelio R Paula10/2014
47143^192426-6891811Lelio R Paula04/2016
47152^304973+11791807Lelio R Paula11/2012
47162^304939-186372791796Enzo Doria03/2016
47172^304902+841591785Lelio R Paula02/2016
471818^73119+6191785Lelio R Paula06/2016
4719(78557*2^304740+1)/15991739Lelio R Paula06/2014
47202^304747+7135591738Lelio R Paula02/2016
47218*3^192251+591728Lelio R Paula08/2014
47222^304674-8791717Lelio R Paula11/2012
4723(28*10^91715+701)/991716Robert Price11/2017
4724(2^304698+9)/136280995391715Lelio R Paula06/2013
4725(5*10^91707-119)/391708Robert Price04/2016
47262^304633-11277191704Enzo Doria06/2014
47279*10^91693+2391694Robert Price11/2017
47282^304578-1671391688Enzo Doria05/2013
47296^117824-1871391685Enzo Doria03/2013
4730(17^74509-1)/1691679Paul Bourdelais03/2010
4731(2^304551-7)/891223191673Lelio R Paula06/2013
4732(2^304532-3)/301391670Lelio R Paula06/2013
47332^304507-1664591666Enzo Doria04/2013
4734(29*2^304489+1)/3191661Lelio R Paula09/2013
47352^304471-183612791655Enzo Doria04/2015
47362^304433+3276991644Lelio R Paula02/2016
47372^304410-1662591637Enzo Doria04/2013
4738183^40500-291630Lelio R Paula10/2017
4739(203*10^91613+1)/391615Robert Price09/2017
47404*5^131052+791603Lelio R Paula10/2014
47412^304278-400191597Yves Minet04/2017
47422^304272-186637791595Enzo Doria03/2016
47432^304268+1968391594Lelio R Paula02/2016
47442^304162-16191562Lelio R Paula11/2012
47455*7^108331+691552Lelio R Paula10/2014
47462^304082-278782191538Enzo Doria03/2016
47472^304015+6413391518David Broadhurst06/2002
4748(7*2^303963+1)/391503Lelio R Paula09/2013
4749(2^303945-9)/361791494Lelio R Paula06/2013
47502^303930+188052791493Enzo Doria10/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: November, 10 2019 12:07 (Time in France)

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