PRP Records

Probable Primes Top 10000

(271000 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 ?
52518*6^121849-794818Lelio R Paula10/2014
5252(85*10^94802+473)/994803Robert Price03/2017
525321767^21852-21852^2176794790Norbert Schneider06/2020
52542^314870-10876194786Enzo Doria03/2014
52555*2^314841-394778Lelio R Paula08/2014
5256(2^314842+550)/294777Stefano Morozzi09/2020
5257(2^314787+2630)/294761Stefano Morozzi09/2020
52586^121772+11394758Lelio R Paula05/2016
5259(2^314740+3642)/294746Stefano Morozzi09/2020
52606^121756-1625394745Enzo Doria02/2013
52612^314718-11279394740Enzo Doria06/2014
52622^314697-184729394734Enzo Doria07/2015
526322836^14065+14065^2283694727Hans Havermann09/2020
52652^314548-24994689Yves Minet02/2012
52645^135469+4294689Lelio R Paula04/2016
5266gcd(V(1137755),5*F(227551)*(F(227551)-1)+1)94676Serge Batalov04/2015
526725773^4712+4712^2577394670Hans Havermann08/2020
5268(2^314485+3614)/294670Stefano Morozzi09/2020
5269(2*10^94604+547)/994604Robert Price10/2017
5270(2^314164+2562)/294573Stefano Morozzi09/2020
52713*2^314152+594570Lelio R Paula08/2014
52722*6^121530-594570Lelio R Paula10/2014
52737*10^94563+8794564Robert Price11/2016
52742^314114-10967794558Enzo Doria04/2014
5275(218389#+240867)/(3*11*811)94557Makoto Morimoto10/2017
52762^314059+7658394542Enzo Doria05/2016
52772^314041-403594536Lelio R Paula03/2016
5278(2^314028+3102)/294532Stefano Morozzi09/2020
5279(2^314012+618)/294527Stefano Morozzi09/2020
5280(7*2^314003-11)/1594524Renaud Lifchitz03/2011
528111^90760-471094517Enzo Doria01/2013
528221675^21796+21796^2167594507Norbert Schneider04/2020
5283(7*2^313926-1)/14882194497Lelio R Paula02/2014
528494*10^94493-394495Robert Price11/2016
5285(1000547^15749+1)/100054894492Faysal YAtim12/2008
5286(2^313859+2706)/294481Stefano Morozzi09/2020
5287(F(3*75345)^2+L(3*75345)^2)/494477Henri Lifchitz10/2017
52887^111792-3294476Lelio R Paula04/2016
5289(202*10^94441-1)/394443Robert Price05/2020
529011^90680-585094434Enzo Doria01/2013
5291(752^32833-1)/75194432Michael Stocker05/2020
52922^313675-11012594426Enzo Doria04/2014
5293(2999*29^64556-2427)/494410Curtis Bright05/2015
52942^313609-11222594406Enzo Doria06/2014
52952^313584+7290194399Enzo Doria04/2016
5296(2^313562+730)/294392Stefano Morozzi09/2020
52972^313510-11286594376Enzo Doria06/2014
52987*10^94373+8794374Robert Price11/2016
5299(9^98897+8^98897)/1794371Robert Price12/2012
53002^313453-11470394359Enzo Doria04/2015
53018*10^94357-5194358Robert Price10/2017
530225903^4392+4392^2590394356Hans Havermann09/2020
530331706^945+945^3170694340Hans Havermann09/2020
5304(379*10^94337-1)/994339Robert Price08/2017
53052^313344-313344+194326Robert Price10/2014
5306(2^313313+3662)/294317Stefano Morozzi09/2020
530720^72481-4994300Lelio R Paula05/2016
530844725!2+12894289Robert Price03/2015
53094*10^94286+994287Robert Price05/2015
531017^76621+2494279Lelio R Paula07/2016
531126274^3875+3875^2627494279Hans Havermann09/2020
53122^313156-11285994270Enzo Doria06/2014
53136^121130-5994258Lelio R Paula05/2016
53143^197542+2894252Robert Price11/2013
5315(2^313076+3550)/294245Stefano Morozzi09/2020
5316(3^197521+2)/5165594237Lelio R Paula04/2013
53172^313045-595594236Lelio R Paula03/2016
531822099^18358+18358^2209994227Hans Havermann08/2020
5319(67*10^94212+23)/994213Ray Chandler02/2011
53202^312909-186520394195Enzo Doria03/2016
532125013^5830+5830^2501394191Hans Havermann09/2020
53222^312848-14994177Lelio R Paula11/2012
53234^156403-7759794164Mike Oakes04/2011
532418^75004-8594151Lelio R Paula06/2016
532519^73622-4894145Lelio R Paula06/2016
5326(11^90397-3^90397)/894138Robert Price04/2011
5327(3^197287+5)/1694129Lelio R Paula04/2013
532824220^7691+7691^2422094119Hans Havermann09/2020
532912^87212-3794118Lelio R Paula06/2016
533011^90376+7694117Lelio R Paula05/2016
5331(6^120946-11)/594114Paul Bourdelais11/2011
5332(2^312622+534)/294109Stefano Morozzi09/2020
5333(10^94096+191)/394096Robert Price11/2017
533423794^9005+9005^2379494093Hans Havermann09/2020
53352^312562-11268594091Enzo Doria06/2014
5336137^44026-294072Lelio R Paula10/2017
5337s(164441)94052Robert Price05/2020
53382^312404-86968810594043Lelio R Paula09/2016
53392^312387+279353394038Enzo Doria03/2016
534110^94016+9194017Robert Price04/2011
5340(15*2^312325-1)/720194017Lelio R Paula02/2014
534210^94016-18896394016Patrick De Geest08/2013
5343(17*2^312315-1)/4594016Lelio R Paula02/2014
534423866^8691+8691^2386694010Hans Havermann08/2020
53456^120802+766194003Mike Oakes04/2011
5346(67607*2^312254+1)/17794001Lelio R Paula06/2014
5347(2^312245+702)/293995Stefano Morozzi09/2020
5348(11*2^312207+1)/1993984Lelio R Paula09/2013
53492^312201+5193982Lelio R Paula11/2012
5350(4*6^120749+1)/593961Serge Batalov10/2014
53513^196892+5893942Lelio R Paula05/2016
53522^312060+1891593940Lelio R Paula03/2016
535342^57867-4193933Norbert Schneider08/2018
53542^311992-1620993919Enzo Doria04/2013
5355(85^48677+1)/8693917Paul Bourdelais08/2017
53562^311965-3993911Lelio R Paula11/2012
53572^311920-11168993898Enzo Doria05/2014
5358130^44414+12993889Norbert Schneider01/2019
5359(2^311892+2730)/293889Stefano Morozzi09/2020
53607*10^93887-4793888Robert Price02/2017
5361(2^311778+1530)/293855Stefano Morozzi09/2020
536212^86965-1393851Lelio R Paula06/2016
536324862^5953+5953^2486293848Hans Havermann09/2020
536422299^16148+16148^2229993837Hans Havermann08/2020
53652^311705+1609593833Lelio R Paula03/2016
5366(2^311701+3002)/293832Stefano Morozzi09/2020
53682^311665-8193821Lelio R Paula11/2012
5367(2^311665+2654)/293821Stefano Morozzi09/2020
5369(2^311648+3058)/293816Stefano Morozzi09/2020
5370730^32761+32761^73093806Norbert Schneider09/2017
537111^90073+9293802Lelio R Paula05/2016
53726*10^93792+4193793Robert Price01/2017
537310^93790+6461193791Patrick De Geest04/2020
5376(2^311580+7)/59132993790Lelio R Paula06/2013
537410^93790-12345678993790Robert Price02/2020
537510^93790-15751793790Patrick De Geest04/2020
537712^86900-7793781Lelio R Paula06/2016
53782^311508-10976993774Enzo Doria04/2014
53792^311486-185962193767Enzo Doria03/2016
5380Phi(93811,10)/968129521/2109997013/3280113810431/63963778254583193765Kurt Beschorner04/2015
5381(10^93811-1)/(9*968129521*2109997013*3280113810431*639637782545831)93765Gord Palameta10/2018
53822^311471+31146993763Renaud Lifchitz01/2003
5383(88*10^93760-1)/393762Robert Price10/2017
53842^311426+7945993749Enzo Doria06/2016
538521537^21634+21634^2153793745Norbert Schneider04/2020
5386(2^311360+3078)/293729Stefano Morozzi09/2020
5387(2^311341+2186)/293723Stefano Morozzi09/2020
5388(2^311313+774)/293715Stefano Morozzi09/2020
53902^311294+577593709Lelio R Paula03/2016
538925155^5312+5312^2515593709Hans Havermann09/2020
53912^311252-101793697Lelio R Paula03/2016
53922^311247-11204193695Enzo Doria06/2014
53937*10^93692-8393693Robert Price09/2017
53942^311205-10964593683Enzo Doria04/2014
53955^134027-8493681Lelio R Paula04/2016
5396(2^311148-1017)/55793663Lelio R Paula06/2013
5397(2^311027-2^155514+1)/59362811/2006
539826748^3161+3161^2674893614Hans Havermann08/2020
53993^196192-2893608Robert Price12/2013
5400216091#+26143393606Makoto Morimoto12/2015
54015^133917+6893604Lelio R Paula04/2016
54022^310924-170993598Yves Minet03/2013
540324555^6476+6476^2455593587Hans Havermann08/2020
5404(2^310867+734)/293580Stefano Morozzi09/2020
5405(266*10^93577-11)/393579Robert Price09/2016
5406(16*10^93577+161)/393578Robert Price05/2016
54073^196113-5693570Lelio R Paula04/2016
54082^310806-11034593562Enzo Doria05/2014
54093^196093+8693561Lelio R Paula04/2016
54102^310780-232793555Yves Minet10/2013
541130^63332+4193550Lelio R Paula08/2012
5412(21181*2^310707+1)/2193536Lelio R Paula06/2014
54138*5^133807+793528Lelio R Paula10/2014
54142^310686+819393526Lelio R Paula03/2016
541522681^13282+13282^2268193520Hans Havermann09/2020
54162^310646+6393514Lelio R Paula11/2012
5417(77*10^93508+31)/993509Robert Price10/2015
5418(1000907^15583+1)/100090893499Faysal YAtim04/2009
5419(2*10^93497+7)/993497Erik Branger03/2011
54203^195958-11285293496Enzo Doria07/2014
54212^310583+1638593495Lelio R Paula03/2016
5422(9913*2^310557-1)/3593490Lelio R Paula04/2015
54239*7^110614+293481Lelio R Paula11/2014
5424(19*10^93467+83)/393468Robert Price08/2020
54252^310469-829593461Lelio R Paula03/2016
54262^310459-115993458Yves Minet11/2012
54276^120075-9593437Lelio R Paula05/2016
5428(2^310362+1758)/293428Stefano Morozzi09/2020
5429148^43041-14793411Norbert Schneider05/2019
54302^310289+9832793407Yves Minet11/2010
543121769^19510+19510^2176993395Hans Havermann08/2020
54322^310217-11314393385Enzo Doria07/2014
54337^110494-6893379Lelio R Paula04/2016
54342^310184-11309393375Enzo Doria07/2014
54352^310180-11041793374Enzo Doria05/2014
5436gcd(V(1124905),5*F(224981)*(F(224981)-1)+1)93372Serge Batalov04/2015
5437(2^310173+3150)/293372Stefano Morozzi09/2020
54383^195669+6893358Lelio R Paula04/2016
543910^93356+9193357Robert Price04/2011
544010^93356-2831393356Patrick De Geest08/2013
5441(85*10^93346+23)/993347Robert Price11/2015
5442(3^195648-5)/315827693342Lelio R Paula04/2013
54433^195556+868093304Lelio R Paula04/2016
54442^309942-10999193302Enzo Doria04/2014
54452^309926-186730193298Enzo Doria03/2016
54462^309924+8595193297Yves Minet03/2011
54472^309896-422993288Yves Minet08/2018
5448(86*10^93263-77)/993264Robert Price05/2016
54496^119836-12593251Lelio R Paula05/2016
5450(77*10^93249-257)/993250Robert Price10/2017
545121822^18749+18749^2182293245Hans Havermann09/2020
54523^195430-293244Theodore Burton02/2007
5453(13*10^93236+47)/393237Robert Price01/2017
5454(67*10^93226-7)/393228Robert Price10/2017
5455(86*10^93217-221)/993218Robert Price06/2017
54562^309637-1632993211Enzo Doria04/2013
5457(41*10^93207+49)/993208Robert Price04/2016
545814^81312-5793194Lelio R Paula06/2016
545941^57783-4093192Theodore Burton02/2007
54603*10^93179-9793180Robert Price08/2017
54615*7^110252-493175Lelio R Paula11/2014
546222022^16959+16959^2202293140Hans Havermann08/2020
546383061!4-51293137Robert Price11/2019
546425169^5016+5016^2516993135Hans Havermann08/2020
54652^309380-2793133Lelio R Paula11/2012
546625653^4268+4268^2565393127Hans Havermann08/2020
5467(2^309334+2710)/293119Stefano Morozzi09/2020
546823*10^93116-793118Robert Price03/2016
5469(2^309270+3214)/293100Stefano Morozzi09/2020
5470(29*10^93082+1)/393083Robert Price11/2015
5471(2^309198+3738)/293078Stefano Morozzi09/2020
5472(58*10^93062-13)/993063Robert Price09/2015
54732^309131+186938393058Enzo Doria05/2016
5474(2^309114+3610)/293053Stefano Morozzi09/2020
54752^309066-9393039Lelio R Paula11/2012
54762^309063-11326993038Enzo Doria07/2014
54773^194965+1693022Robert Price10/2013
54782^308979+186914393012Enzo Doria05/2016
54795^133064+5493008Lelio R Paula04/2016
5480(2^308905-509203)/11992988Lelio R Paula06/2013
5481(94*10^92981-49)/9992981Ray Chandler07/2011
5482(2*10^92976-17)/392976Robert Price08/2014
548324783^5642+5642^2478392972Hans Havermann08/2020
54842^308809+3796792961Phil Moore03/2008
5485(3^194825+5)/1165692952Lelio R Paula04/2013
5486(2^308679+5)/157392919Lelio R Paula06/2013
54872^308650+51392913Lelio R Paula02/2016
54885*7^109936+692908Lelio R Paula10/2014
54892*10^92897+8992898Robert Price07/2016
5490(2^308585+3182)/292894Stefano Morozzi09/2020
549112^86073-2992889Lelio R Paula06/2016
54922^308566-11792888Lelio R Paula11/2012
5493(17*10^92869-11)/392870Robert Price07/2015
54942^308459+7543192856Enzo Doria04/2016
54952^308426-186637792846Enzo Doria03/2016
549624810^5521+5521^2481092840Hans Havermann09/2020
5497(96^46831-1)/9592830Paul Bourdelais09/2017
54982^308349-11211192823Enzo Doria06/2014
54999*10^92821+1992822Robert Price05/2016
55002^308337-7592819Lelio R Paula11/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 29 2020 00:24 (Time in France)

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