PRP Records

Probable Primes Top 10000

(291192 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 ?
850122576^15875+15875^2257694836Hans Havermann09/2020
8502(16*10^94822+53)/394823Robert Price12/2016
85038*6^121849-794818Lelio R Paula10/2014
8504(85*10^94802+473)/994803Robert Price03/2017
850521767^21852-21852^2176794790Norbert Schneider06/2020
85062^314870-10876194786Enzo Doria03/2014
85075*2^314841-394778Lelio R Paula08/2014
8508(2^314842+550)/294777Stefano Morozzi09/2020
850911738^23289-23289^1173894777Norbert Schneider05/2022
8510(2^314787+2630)/294761Stefano Morozzi09/2020
85116^121772+11394758Lelio R Paula05/2016
8512(2^314740+3642)/294746Stefano Morozzi09/2020
85136^121756-1625394745Enzo Doria02/2013
85142^314718-11279394740Enzo Doria06/2014
85152^314697-184729394734Enzo Doria07/2015
851622836^14065+14065^2283694727Hans Havermann09/2020
85182^314548-24994689Yves Minet02/2012
85175^135469+4294689Lelio R Paula04/2016
8519gcd(V(1137755),5*F(227551)*(F(227551)-1)+1)94676Serge Batalov04/2015
852025773^4712+4712^2577394670Hans Havermann08/2020
8521(2^314485+3614)/294670Stefano Morozzi09/2020
8522(2*10^94604+547)/994604Robert Price10/2017
8523(2^314164+2562)/294573Stefano Morozzi09/2020
85243*2^314152+594570Lelio R Paula08/2014
85252*6^121530-594570Lelio R Paula10/2014
85267*10^94563+8794564Robert Price11/2016
85272^314114-10967794558Enzo Doria04/2014
8528(218389#+240867)/(3*11*811)94557Makoto Morimoto10/2017
85292^314059+7658394542Enzo Doria05/2016
85302^314041-403594536Lelio R Paula03/2016
8531(2^314028+3102)/294532Stefano Morozzi09/2020
8532(2^314012+618)/294527Stefano Morozzi09/2020
8533(7*2^314003-11)/1594524Renaud Lifchitz03/2011
853411^90760-471094517Enzo Doria01/2013
853521675^21796+21796^2167594507Norbert Schneider04/2020
85362^313942+10028024506594506Paul Bourdelais10/2021
8537(7*2^313926-1)/14882194497Lelio R Paula02/2014
853894*10^94493-394495Robert Price11/2016
8539(1000547^15749+1)/100054894492Faysal YAtim12/2008
8540(2^313859+2706)/294481Stefano Morozzi09/2020
8541(F(3*75345)^2+L(3*75345)^2)/494477Henri Lifchitz10/2017
85427^111792-3294476Lelio R Paula04/2016
8543(2^313800+822)/294463Stefano Morozzi01/2021
85449*10^94462-4794463Robert Price11/2021
854511*10^94460+394462Robert Price07/2021
8546(202*10^94441-1)/394443Robert Price05/2020
854711^90680-585094434Enzo Doria01/2013
8548(752^32833-1)/75194432Michael Stocker05/2020
85492^313675-11012594426Enzo Doria04/2014
8550(2999*29^64556-2427)/494410Curtis Bright05/2015
85512^313609-11222594406Enzo Doria06/2014
85522^313584+7290194399Enzo Doria04/2016
8553(2^313567+1310)/294393Stefano Morozzi02/2021
8554(2^313562+730)/294392Stefano Morozzi09/2020
85552^313510-11286594376Enzo Doria06/2014
85567*10^94373+8794374Robert Price11/2016
8557(9^98897+8^98897)/1794371Robert Price12/2012
85582^313453-11470394359Enzo Doria04/2015
85598*10^94357-5194358Robert Price10/2017
856025903^4392+4392^2590394356Hans Havermann09/2020
856131706^945+945^3170694340Hans Havermann09/2020
8562(379*10^94337-1)/994339Robert Price08/2017
85632^313344-313344+194326Robert Price10/2014
8564(2^313313+3662)/294317Stefano Morozzi09/2020
856520^72481-4994300Lelio R Paula05/2016
8566(34*10^94293-259)/994294Robert Price12/2021
856744725!2+12894289Robert Price03/2015
85684*10^94286+994287Robert Price05/2015
856917^76621+2494279Lelio R Paula07/2016
857026274^3875+3875^2627494279Hans Havermann09/2020
85714*10^94270-3394271Robert Price04/2021
85722^313156-11285994270Enzo Doria06/2014
8573(49*10^94262-211)/994263Robert Price06/2022
85746^121130-5994258Lelio R Paula05/2016
85753^197542+2894252Robert Price11/2013
8576(2^313076+3550)/294245Stefano Morozzi09/2020
8577(3^197521+2)/5165594237Lelio R Paula04/2013
85782^313045-595594236Lelio R Paula03/2016
857922099^18358+18358^2209994227Hans Havermann08/2020
8580(67*10^94212+23)/994213Ray Chandler02/2011
85812^312909-186520394195Enzo Doria03/2016
858225013^5830+5830^2501394191Hans Havermann09/2020
85832^312848-14994177Lelio R Paula11/2012
8584(2^312819+3278)/294168Stefano Morozzi02/2021
85854^156403-7759794164Mike Oakes04/2011
858618^75004-8594151Lelio R Paula06/2016
858719^73622-4894145Lelio R Paula06/2016
8588(11^90397-3^90397)/894138Robert Price04/2011
8589(3^197287+5)/1694129Lelio R Paula04/2013
8590(23*10^94123-29)/394124Robert Price03/2022
859124220^7691+7691^2422094119Hans Havermann09/2020
859212^87212-3794118Lelio R Paula06/2016
859311^90376+7694117Lelio R Paula05/2016
8594(6^120946-11)/594114Paul Bourdelais11/2011
8595(2^312622+534)/294109Stefano Morozzi09/2020
8596(10^94096+191)/394096Robert Price11/2017
859723794^9005+9005^2379494093Hans Havermann09/2020
85982^312562-11268594091Enzo Doria06/2014
8599137^44026-294072Lelio R Paula10/2017
8600s(164441)94052Robert Price05/2020
86012^312404-86968810594043Lelio R Paula09/2016
86022^312387+279353394038Enzo Doria03/2016
860410^94016+9194017Robert Price04/2011
8603(15*2^312325-1)/720194017Lelio R Paula02/2014
860510^94016-18896394016Patrick De Geest08/2013
8606(17*2^312315-1)/4594016Lelio R Paula02/2014
8607(401*10^94010+13)/994012Robert Price09/2021
860823866^8691+8691^2386694010Hans Havermann08/2020
86096^120802+766194003Mike Oakes04/2011
8610(67607*2^312254+1)/17794001Lelio R Paula06/2014
8611(2^312245+702)/293995Stefano Morozzi09/2020
8612(56*10^93993+493)/993994Robert Price10/2021
8613(11*2^312207+1)/1993984Lelio R Paula09/2013
86142^312201+5193982Lelio R Paula11/2012
8615(4*6^120749+1)/593961Serge Batalov10/2014
8616(781*10^93942-7)/993944Robert Price12/2021
86173^196892+5893942Lelio R Paula05/2016
86182^312060+1891593940Lelio R Paula03/2016
861942^57867-4193933Norbert Schneider08/2018
86208*10^93921+8393922Robert Price11/2021
86212^311992-1620993919Enzo Doria04/2013
8622(85^48677+1)/8693917Paul Bourdelais08/2017
86232^311965-3993911Lelio R Paula11/2012
86242^311920-11168993898Enzo Doria05/2014
8625130^44414+12993889Norbert Schneider01/2019
8626(2^311892+2730)/293889Stefano Morozzi09/2020
86277*10^93887-4793888Robert Price02/2017
86289*10^93878-3793879Robert Price06/2021
8629(28*10^93874+323)/993875Robert Price10/2021
8630(2^311778+1530)/293855Stefano Morozzi09/2020
863112^86965-1393851Lelio R Paula06/2016
863224862^5953+5953^2486293848Hans Havermann09/2020
863322299^16148+16148^2229993837Hans Havermann08/2020
86342^311705+1609593833Lelio R Paula03/2016
8635(2^311701+3002)/293832Stefano Morozzi09/2020
8636norm(Mod(x,x^3-x-1)^768329-1)93831Paul Vanderveen09/2022
86382^311665-8193821Lelio R Paula11/2012
8637(2^311665+2654)/293821Stefano Morozzi09/2020
8639(2^311648+3058)/293816Stefano Morozzi09/2020
8640(2^311639+2738)/293813Stefano Morozzi01/2021
8641730^32761+32761^73093806Norbert Schneider09/2017
864211^90073+9293802Lelio R Paula05/2016
86436*10^93792+4193793Robert Price01/2017
864410^93790+6461193791Patrick De Geest04/2020
8647(2^311580+7)/59132993790Lelio R Paula06/2013
864510^93790-12345678993790Robert Price02/2020
864610^93790-15751793790Patrick De Geest04/2020
8648(49*10^93782+293)/993783Robert Price03/2021
864912^86900-7793781Lelio R Paula06/2016
86502^311508-10976993774Enzo Doria04/2014
86512^311486-185962193767Enzo Doria03/2016
8652Phi(93811,10)/968129521/2109997013/3280113810431/63963778254583193765Kurt Beschorner04/2015
8653(10^93811-1)/(9*968129521*2109997013*3280113810431*639637782545831)93765Gord Palameta10/2018
86542^311471+31146993763Renaud Lifchitz01/2003
8655(88*10^93760-1)/393762Robert Price10/2017
86562^311426+7945993749Enzo Doria06/2016
865721537^21634+21634^2153793745Norbert Schneider04/2020
86582^311409+11154643593744Paul Bourdelais10/2021
8659(2^311360+3078)/293729Stefano Morozzi09/2020
8660(2^311341+2186)/293723Stefano Morozzi09/2020
8661(2^311313+774)/293715Stefano Morozzi09/2020
86632^311294+577593709Lelio R Paula03/2016
866225155^5312+5312^2515593709Hans Havermann09/2020
86642^311252-101793697Lelio R Paula03/2016
86652^311247-11204193695Enzo Doria06/2014
86667*10^93692-8393693Robert Price09/2017
86672^311205-10964593683Enzo Doria04/2014
86685^134027-8493681Lelio R Paula04/2016
8669(2^311148-1017)/55793663Lelio R Paula06/2013
8670(2^311027-2^155514+1)/59362811/2006
867126748^3161+3161^2674893614Hans Havermann08/2020
86723^196192-2893608Robert Price12/2013
8673216091#+26143393606Makoto Morimoto12/2015
86745^133917+6893604Lelio R Paula04/2016
86752^310924-170993598Yves Minet03/2013
867624555^6476+6476^2455593587Hans Havermann08/2020
8677(2^310867+734)/293580Stefano Morozzi09/2020
8678(266*10^93577-11)/393579Robert Price09/2016
8679(16*10^93577+161)/393578Robert Price05/2016
86803^196113-5693570Lelio R Paula04/2016
86812^310806-11034593562Enzo Doria05/2014
86823^196093+8693561Lelio R Paula04/2016
86832^310780-232793555Yves Minet10/2013
868430^63332+4193550Lelio R Paula08/2012
8685(21181*2^310707+1)/2193536Lelio R Paula06/2014
86868*5^133807+793528Lelio R Paula10/2014
86872^310686+819393526Lelio R Paula03/2016
868822681^13282+13282^2268193520Hans Havermann09/2020
86892^310646+6393514Lelio R Paula11/2012
8690(77*10^93508+31)/993509Robert Price10/2015
8691(1000907^15583+1)/100090893499Faysal YAtim04/2009
8692(2*10^93497+7)/993497Erik Branger03/2011
86933^195958-11285293496Enzo Doria07/2014
86942^310583+1638593495Lelio R Paula03/2016
8695(9913*2^310557-1)/3593490Lelio R Paula04/2015
86969*7^110614+293481Lelio R Paula11/2014
8697(19*10^93467+83)/393468Robert Price08/2020
86982^310469-829593461Lelio R Paula03/2016
86992^310459-115993458Yves Minet11/2012
87006^120075-9593437Lelio R Paula05/2016
8701(2^310362+1758)/293428Stefano Morozzi09/2020
8702148^43041-14793411Norbert Schneider05/2019
87032^310289+9832793407Yves Minet11/2010
870421769^19510+19510^2176993395Hans Havermann08/2020
87052^310217-11314393385Enzo Doria07/2014
87067^110494-6893379Lelio R Paula04/2016
87072^310184-11309393375Enzo Doria07/2014
87082^310180-11041793374Enzo Doria05/2014
8709gcd(V(1124905),5*F(224981)*(F(224981)-1)+1)93372Serge Batalov04/2015
8710(2^310173+3150)/293372Stefano Morozzi09/2020
87113^195669+6893358Lelio R Paula04/2016
871210^93356+9193357Robert Price04/2011
871310^93356-2831393356Patrick De Geest08/2013
8714(85*10^93346+23)/993347Robert Price11/2015
8715(3^195648-5)/315827693342Lelio R Paula04/2013
871610^93333+19106193334Patrick De Geest09/2022
871810^93333-400000193333Robert Price07/2021
871710^93333-4480793333Patrick De Geest09/2022
87193^195556+868093304Lelio R Paula04/2016
87202^309942-10999193302Enzo Doria04/2014
87212^309926-186730193298Enzo Doria03/2016
87222^309924+8595193297Yves Minet03/2011
87232^309896-422993288Yves Minet08/2018
8724(86*10^93263-77)/993264Robert Price05/2016
87256^119836-12593251Lelio R Paula05/2016
8726(77*10^93249-257)/993250Robert Price10/2017
872721822^18749+18749^2182293245Hans Havermann09/2020
87283^195430-293244Theodore Burton02/2007
8729(13*10^93236+47)/393237Robert Price01/2017
8730(67*10^93226-7)/393228Robert Price10/2017
8731(86*10^93217-221)/993218Robert Price06/2017
87322^309637-1632993211Enzo Doria04/2013
8733(41*10^93207+49)/993208Robert Price04/2016
873414^81312-5793194Lelio R Paula06/2016
873541^57783-4093192Theodore Burton02/2007
87363*10^93179-9793180Robert Price08/2017
87375*7^110252-493175Lelio R Paula11/2014
873822022^16959+16959^2202293140Hans Havermann08/2020
873983061!4-51293137Robert Price11/2019
874025169^5016+5016^2516993135Hans Havermann08/2020
8741(483641^16384+1)/293135Richard Fischer02/2021
87422^309380-2793133Lelio R Paula11/2012
874325653^4268+4268^2565393127Hans Havermann08/2020
8744(2^309355+1826)/293125Stefano Morozzi02/2021
8745(2^309334+2710)/293119Stefano Morozzi09/2020
874623*10^93116-793118Robert Price03/2016
8747(2^309270+3214)/293100Stefano Morozzi09/2020
8748(29*10^93082+1)/393083Robert Price11/2015
8749(2^309198+3738)/293078Stefano Morozzi09/2020
8750(58*10^93062-13)/993063Robert Price09/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 22 2022 18:03 (Time in France)

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