PRP Records

Probable Primes Top 10000

(247113 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 ?
40014^157583+2214794875Mike Oakes01/2011
40022^315098+12394854Lelio R Paula11/2012
40033^198791-3494848Robert Price11/2013
40043*2^315067+794846Lelio R Paula08/2014
4005(9*2^315057+1)/7394841Lelio R Paula09/2013
4006(16*10^94822+53)/394823Robert Price12/2016
40078*6^121849-794818Lelio R Paula10/2014
4008(85*10^94802+473)/994803Robert Price03/2017
40092^314870-10876194786Enzo Doria03/2014
40105*2^314841-394778Lelio R Paula08/2014
40116^121772+11394758Lelio R Paula05/2016
40126^121756-1625394745Enzo Doria02/2013
40132^314718-11279394740Enzo Doria06/2014
40142^314697-184729394734Enzo Doria07/2015
40162^314548-24994689Yves Minet02/2012
40155^135469+4294689Lelio R Paula04/2016
4017gcd(V(1137755),5*F(227551)*(F(227551)-1)+1)94676Serge Batalov04/2015
4018(2*10^94604+547)/994604Robert Price10/2017
40193*2^314152+594570Lelio R Paula08/2014
40202*6^121530-594570Lelio R Paula10/2014
40217*10^94563+8794564Robert Price11/2016
40222^314114-10967794558Enzo Doria04/2014
4023(218389#+240867)/(3*11*811)94557Makoto Morimoto10/2017
40242^314059+7658394542Enzo Doria05/2016
40252^314041-403594536Lelio R Paula03/2016
4026(7*2^314003-11)/1594524Renaud Lifchitz03/2011
402711^90760-471094517Enzo Doria01/2013
4028(7*2^313926-1)/14882194497Lelio R Paula02/2014
402994*10^94493-394495Robert Price11/2016
4030(1000547^15749+1)/100054894492Faysal YAtim12/2008
4031(F(3*75345)^2+L(3*75345)^2)/494477Henri Lifchitz10/2017
40327^111792-3294476Lelio R Paula04/2016
403311^90680-585094434Enzo Doria01/2013
40342^313675-11012594426Enzo Doria04/2014
4035(2999*29^64556-2427)/494410Curtis Bright05/2015
40362^313609-11222594406Enzo Doria06/2014
40372^313584+7290194399Enzo Doria04/2016
40382^313510-11286594376Enzo Doria06/2014
40397*10^94373+8794374Robert Price11/2016
4040(9^98897+8^98897)/1794371Robert Price12/2012
40412^313453-11470394359Enzo Doria04/2015
40428*10^94357-5194358Robert Price10/2017
4043(379*10^94337-1)/994339Robert Price08/2017
40442^313344-313344+194326Robert Price10/2014
404520^72481-4994300Lelio R Paula05/2016
404644725!2+12894289Robert Price03/2015
40474*10^94286+994287Robert Price05/2015
404817^76621+2494279Lelio R Paula07/2016
40492^313156-11285994270Enzo Doria06/2014
40506^121130-5994258Lelio R Paula05/2016
40513^197542+2894252Robert Price11/2013
4052(3^197521+2)/5165594237Lelio R Paula04/2013
40532^313045-595594236Lelio R Paula03/2016
4054(67*10^94212+23)/994213Ray Chandler02/2011
40552^312909-186520394195Enzo Doria03/2016
40562^312848-14994177Lelio R Paula11/2012
40574^156403-7759794164Mike Oakes04/2011
405818^75004-8594151Lelio R Paula06/2016
405919^73622-4894145Lelio R Paula06/2016
4060(11^90397-3^90397)/894138Robert Price04/2011
4061(3^197287+5)/1694129Lelio R Paula04/2013
406212^87212-3794118Lelio R Paula06/2016
406311^90376+7694117Lelio R Paula05/2016
4064(6^120946-11)/594114Paul Bourdelais11/2011
4065(10^94096+191)/394096Robert Price11/2017
40662^312562-11268594091Enzo Doria06/2014
4067137^44026-294072Lelio R Paula10/2017
40682^312404-86968810594043Lelio R Paula09/2016
40692^312387+279353394038Enzo Doria03/2016
407110^94016+9194017Robert Price04/2011
4070(15*2^312325-1)/720194017Lelio R Paula02/2014
407310^94016-18896394016Patrick De Geest08/2013
4072(17*2^312315-1)/4594016Lelio R Paula02/2014
40746^120802+766194003Mike Oakes04/2011
4075(67607*2^312254+1)/17794001Lelio R Paula06/2014
4076(11*2^312207+1)/1993984Lelio R Paula09/2013
40772^312201+5193982Lelio R Paula11/2012
4078(4*6^120749+1)/593961Serge Batalov10/2014
40793^196892+5893942Lelio R Paula05/2016
40802^312060+1891593940Lelio R Paula03/2016
408142^57867-4193933Norbert Schneider08/2018
40822^311992-1620993919Enzo Doria04/2013
4083(85^48677+1)/8693917Paul Bourdelais08/2017
40842^311965-3993911Lelio R Paula11/2012
40852^311920-11168993898Enzo Doria05/2014
40867*10^93887-4793888Robert Price02/2017
408712^86965-1393851Lelio R Paula06/2016
40882^311705+1609593833Lelio R Paula03/2016
40892^311665-8193821Lelio R Paula11/2012
4090730^32761+32761^73093806Norbert Schneider09/2017
409111^90073+9293802Lelio R Paula05/2016
40926*10^93792+4193793Robert Price01/2017
4093(2^311580+7)/59132993790Lelio R Paula06/2013
409412^86900-7793781Lelio R Paula06/2016
40952^311508-10976993774Enzo Doria04/2014
40962^311486-185962193767Enzo Doria03/2016
4097Phi(93811,10)/968129521/2109997013/3280113810431/63963778254583193765Kurt Beschorner04/2015
4098(10^93811-1)/(9*968129521*2109997013*3280113810431*639637782545831)93765Gord Palameta10/2018
40992^311471+31146993763Renaud Lifchitz01/2003
4100(88*10^93760-1)/393762Robert Price10/2017
41012^311426+7945993749Enzo Doria06/2016
41022^311294+577593709Lelio R Paula03/2016
41032^311252-101793697Lelio R Paula03/2016
41042^311247-11204193695Enzo Doria06/2014
41057*10^93692-8393693Robert Price09/2017
41062^311205-10964593683Enzo Doria04/2014
41075^134027-8493681Lelio R Paula04/2016
4108(2^311148-1017)/55793663Lelio R Paula06/2013
4109(2^311027-2^155514+1)/59362811/2006
41103^196192-2893608Robert Price12/2013
4111216091#+26143393606Makoto Morimoto12/2015
41125^133917+6893604Lelio R Paula04/2016
41132^310924-170993598Yves Minet03/2013
4114(266*10^93577-11)/393579Robert Price09/2016
4115(16*10^93577+161)/393578Robert Price05/2016
41163^196113-5693570Lelio R Paula04/2016
41172^310806-11034593562Enzo Doria05/2014
41183^196093+8693561Lelio R Paula04/2016
41192^310780-232793555Yves Minet10/2013
412030^63332+4193550Lelio R Paula08/2012
4121(21181*2^310707+1)/2193536Lelio R Paula06/2014
41228*5^133807+793528Lelio R Paula10/2014
41232^310686+819393526Lelio R Paula03/2016
41242^310646+6393514Lelio R Paula11/2012
4125(77*10^93508+31)/993509Robert Price10/2015
4126(1000907^15583+1)/100090893499Faysal YAtim04/2009
4127(2*10^93497+7)/993497Erik Branger03/2011
41283^195958-11285293496Enzo Doria07/2014
41292^310583+1638593495Lelio R Paula03/2016
4130(9913*2^310557-1)/3593490Lelio R Paula04/2015
41319*7^110614+293481Lelio R Paula11/2014
41322^310469-829593461Lelio R Paula03/2016
41332^310459-115993458Yves Minet11/2012
41346^120075-9593437Lelio R Paula05/2016
41352^310289+9832793407Yves Minet11/2010
41362^310217-11314393385Enzo Doria07/2014
41377^110494-6893379Lelio R Paula04/2016
41382^310184-11309393375Enzo Doria07/2014
41392^310180-11041793374Enzo Doria05/2014
4140gcd(V(1124905),5*F(224981)*(F(224981)-1)+1)93372Serge Batalov04/2015
41413^195669+6893358Lelio R Paula04/2016
414210^93356+9193357Robert Price04/2011
414310^93356-2831393356Patrick De Geest08/2013
4144(85*10^93346+23)/993347Robert Price11/2015
4145(3^195648-5)/315827693342Lelio R Paula04/2013
41463^195556+868093304Lelio R Paula04/2016
41472^309942-10999193302Enzo Doria04/2014
41482^309926-186730193298Enzo Doria03/2016
41492^309924+8595193297Yves Minet03/2011
41502^309896-422993288Yves Minet08/2018
4151(86*10^93263-77)/993264Robert Price05/2016
41526^119836-12593251Lelio R Paula05/2016
4153(77*10^93249-257)/993250Robert Price10/2017
41543^195430-293244Theodore Burton02/2007
4155(13*10^93236+47)/393237Robert Price01/2017
4156(67*10^93226-7)/393228Robert Price10/2017
4157(86*10^93217-221)/993218Robert Price06/2017
41582^309637-1632993211Enzo Doria04/2013
4159(41*10^93207+49)/993208Robert Price04/2016
416014^81312-5793194Lelio R Paula06/2016
416141^57783-4093192Theodore Burton02/2007
41623*10^93179-9793180Robert Price08/2017
41635*7^110252-493175Lelio R Paula11/2014
41642^309380-2793133Lelio R Paula11/2012
416523*10^93116-793118Robert Price03/2016
4166(29*10^93082+1)/393083Robert Price11/2015
4167(58*10^93062-13)/993063Robert Price09/2015
41682^309131+186938393058Enzo Doria05/2016
41692^309066-9393039Lelio R Paula11/2012
41702^309063-11326993038Enzo Doria07/2014
41713^194965+1693022Robert Price10/2013
41722^308979+186914393012Enzo Doria05/2016
41735^133064+5493008Lelio R Paula04/2016
4174(2^308905-509203)/11992988Lelio R Paula06/2013
4175(94*10^92981-49)/9992981Ray Chandler07/2011
4176(2*10^92976-17)/392976Robert Price08/2014
41772^308809+3796792961Phil Moore03/2008
4178(3^194825+5)/1165692952Lelio R Paula04/2013
4179(2^308679+5)/157392919Lelio R Paula06/2013
41802^308650+51392913Lelio R Paula02/2016
41815*7^109936+692908Lelio R Paula10/2014
41822*10^92897+8992898Robert Price07/2016
418312^86073-2992889Lelio R Paula06/2016
41842^308566-11792888Lelio R Paula11/2012
4185(17*10^92869-11)/392870Robert Price07/2015
41862^308459+7543192856Enzo Doria04/2016
41872^308426-186637792846Enzo Doria03/2016
4188(96^46831-1)/9592830Paul Bourdelais09/2017
41892^308349-11211192823Enzo Doria06/2014
41909*10^92821+1992822Robert Price05/2016
41912^308337-7592819Lelio R Paula11/2012
41924*3^194508+792805Lelio R Paula08/2014
419322*25^66379-11392796Curtis Bright05/2015
419411^89101-108092790Enzo Doria12/2012
41952^308236-186785992789Enzo Doria04/2016
419612^85963+2592770Lelio R Paula06/2016
41977^109750-6692750Lelio R Paula04/2016
41989*10^92742+1192743Robert Kinser01/2017
4199(21*2^308046-1)/885792729Lelio R Paula02/2014
42002^307997-11065592717Enzo Doria05/2014
4201L(443609)92709Renaud Lifchitz11/2003
420210^92691+992692Robert Price03/2011
420310^92691-25229192691Patrick De Geest08/2013
42042^307879-252192681Yves Minet07/2014
4205(2^307780-7)/1995966992644Lelio R Paula06/2013
420614^80831+4792643Lelio R Paula06/2016
420715^78744+9292611Lelio R Paula07/2016
420865^51083-6492610Norbert Schneider11/2014
42096^118996-1694392597Enzo Doria02/2013
4210(16*10^92591+41)/392592Robert Price10/2017
4211(3^194014-7)/292568Lelio R Paula04/2013
4212(63^51439+1)/6492555Paul Bourdelais08/2017
4213(26*10^92546-77)/392547Robert Price02/2017
42143^193954+34092540Lelio R Paula04/2016
42152^307407-307407^292539Henri Lifchitz05/2005
4216(17*10^92513-11)/392514Robert Price07/2015
42172^307318-421192512Yves Minet06/2011
42182^307280+19392501Lelio R Paula11/2012
421920^71075-3392471Lelio R Paula05/2016
42202^307126-7879592455Lelio R Paula02/2016
42212^307125-4978992454Henri Lifchitz08/2005
42222^307099+2392447Lelio R Paula11/2012
42237*10^92414-6992415Robert Price01/2017
4224(9787*2^306975-1)/212915592407Lelio R Paula04/2015
42252^306915+187337392391Enzo Doria06/2016
42262^306908+1291592389Lelio R Paula02/2016
422719^72244-8092383Lelio R Paula06/2016
42282^306849+7592371Lelio R Paula11/2012
4229(397*10^92369+53)/992371Robert Price11/2017
42302^306813-86968810592360Lelio R Paula08/2016
42312^306672-10905992318Enzo Doria04/2014
42326^118604-1706392292Enzo Doria02/2013
4233(31*2^306487-1)/229192260Lelio R Paula02/2014
42342^306467-183561192256Enzo Doria04/2015
42352^306433+7642792246Enzo Doria05/2016
42362^306430-11331392245Enzo Doria07/2014
4237(23*10^92244-59)/992245Robert Price03/2017
4238(47*2^306398+1)/138480392231Lelio R Paula04/2015
4239(25*10^92186+59)/392187Robert Price05/2016
42402^306213-28618392180Enzo Doria06/2015
424110^92178+6192179Robert Price04/2011
424210^92178-17550992178Patrick De Geest07/2013
42432^306200+118592176Lelio R Paula02/2016
42442^306153+1192162Lelio R Paula11/2012
4245(2^306141-7)/592157Lelio R Paula06/2013
4246(26*10^92152-23)/392153Robert Price08/2016
4247(2*10^92152+67)/392152Robert Price04/2017
42484*10^92099+3*7^9209992100Mike Oakes12/2010
4249115^44684+11492081Norbert Schneider07/2018
4250(2^305867-2^152934+1)/59207511/2006


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 11 2018 05:54 (Time in France)

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