PRP Records

Probable Primes Top 10000

(290751 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 (> 50000) Who ? When ?
825112^87212-3794118Lelio R Paula06/2016
825211^90376+7694117Lelio R Paula05/2016
8253(6^120946-11)/594114Paul Bourdelais11/2011
8254(2^312622+534)/294109Stefano Morozzi09/2020
8255(10^94096+191)/394096Robert Price11/2017
825623794^9005+9005^2379494093Hans Havermann09/2020
82572^312562-11268594091Enzo Doria06/2014
8258137^44026-294072Lelio R Paula10/2017
8259s(164441)94052Robert Price05/2020
82602^312404-86968810594043Lelio R Paula09/2016
82612^312387+279353394038Enzo Doria03/2016
826310^94016+9194017Robert Price04/2011
8262(15*2^312325-1)/720194017Lelio R Paula02/2014
826410^94016-18896394016Patrick De Geest08/2013
8265(17*2^312315-1)/4594016Lelio R Paula02/2014
8266(401*10^94010+13)/994012Robert Price09/2021
826723866^8691+8691^2386694010Hans Havermann08/2020
82686^120802+766194003Mike Oakes04/2011
8269(67607*2^312254+1)/17794001Lelio R Paula06/2014
8270(2^312245+702)/293995Stefano Morozzi09/2020
8271(56*10^93993+493)/993994Robert Price10/2021
8272(11*2^312207+1)/1993984Lelio R Paula09/2013
82732^312201+5193982Lelio R Paula11/2012
8274(4*6^120749+1)/593961Serge Batalov10/2014
8275(781*10^93942-7)/993944Robert Price12/2021
82763^196892+5893942Lelio R Paula05/2016
82772^312060+1891593940Lelio R Paula03/2016
827842^57867-4193933Norbert Schneider08/2018
82798*10^93921+8393922Robert Price11/2021
82802^311992-1620993919Enzo Doria04/2013
8281(85^48677+1)/8693917Paul Bourdelais08/2017
82822^311965-3993911Lelio R Paula11/2012
82832^311920-11168993898Enzo Doria05/2014
8284130^44414+12993889Norbert Schneider01/2019
8285(2^311892+2730)/293889Stefano Morozzi09/2020
82867*10^93887-4793888Robert Price02/2017
82879*10^93878-3793879Robert Price06/2021
8288(28*10^93874+323)/993875Robert Price10/2021
8289(2^311778+1530)/293855Stefano Morozzi09/2020
829012^86965-1393851Lelio R Paula06/2016
829124862^5953+5953^2486293848Hans Havermann09/2020
829222299^16148+16148^2229993837Hans Havermann08/2020
82932^311705+1609593833Lelio R Paula03/2016
8294(2^311701+3002)/293832Stefano Morozzi09/2020
82962^311665-8193821Lelio R Paula11/2012
8295(2^311665+2654)/293821Stefano Morozzi09/2020
8297(2^311648+3058)/293816Stefano Morozzi09/2020
8298(2^311639+2738)/293813Stefano Morozzi01/2021
8299730^32761+32761^73093806Norbert Schneider09/2017
830011^90073+9293802Lelio R Paula05/2016
83016*10^93792+4193793Robert Price01/2017
830210^93790+6461193791Patrick De Geest04/2020
8305(2^311580+7)/59132993790Lelio R Paula06/2013
830310^93790-12345678993790Robert Price02/2020
830410^93790-15751793790Patrick De Geest04/2020
8306(49*10^93782+293)/993783Robert Price03/2021
830712^86900-7793781Lelio R Paula06/2016
83082^311508-10976993774Enzo Doria04/2014
83092^311486-185962193767Enzo Doria03/2016
8310Phi(93811,10)/968129521/2109997013/3280113810431/63963778254583193765Kurt Beschorner04/2015
8311(10^93811-1)/(9*968129521*2109997013*3280113810431*639637782545831)93765Gord Palameta10/2018
83122^311471+31146993763Renaud Lifchitz01/2003
8313(88*10^93760-1)/393762Robert Price10/2017
83142^311426+7945993749Enzo Doria06/2016
831521537^21634+21634^2153793745Norbert Schneider04/2020
83162^311409+11154643593744Paul Bourdelais10/2021
8317(2^311360+3078)/293729Stefano Morozzi09/2020
8318(2^311341+2186)/293723Stefano Morozzi09/2020
8319(2^311313+774)/293715Stefano Morozzi09/2020
83212^311294+577593709Lelio R Paula03/2016
832025155^5312+5312^2515593709Hans Havermann09/2020
83222^311252-101793697Lelio R Paula03/2016
83232^311247-11204193695Enzo Doria06/2014
83247*10^93692-8393693Robert Price09/2017
83252^311205-10964593683Enzo Doria04/2014
83265^134027-8493681Lelio R Paula04/2016
8327(2^311148-1017)/55793663Lelio R Paula06/2013
8328(2^311027-2^155514+1)/59362811/2006
832926748^3161+3161^2674893614Hans Havermann08/2020
83303^196192-2893608Robert Price12/2013
8331216091#+26143393606Makoto Morimoto12/2015
83325^133917+6893604Lelio R Paula04/2016
83332^310924-170993598Yves Minet03/2013
833424555^6476+6476^2455593587Hans Havermann08/2020
8335(2^310867+734)/293580Stefano Morozzi09/2020
8336(266*10^93577-11)/393579Robert Price09/2016
8337(16*10^93577+161)/393578Robert Price05/2016
83383^196113-5693570Lelio R Paula04/2016
83392^310806-11034593562Enzo Doria05/2014
83403^196093+8693561Lelio R Paula04/2016
83412^310780-232793555Yves Minet10/2013
834230^63332+4193550Lelio R Paula08/2012
8343(21181*2^310707+1)/2193536Lelio R Paula06/2014
83448*5^133807+793528Lelio R Paula10/2014
83452^310686+819393526Lelio R Paula03/2016
834622681^13282+13282^2268193520Hans Havermann09/2020
83472^310646+6393514Lelio R Paula11/2012
8348(77*10^93508+31)/993509Robert Price10/2015
8349(1000907^15583+1)/100090893499Faysal YAtim04/2009
8350(2*10^93497+7)/993497Erik Branger03/2011
83513^195958-11285293496Enzo Doria07/2014
83522^310583+1638593495Lelio R Paula03/2016
8353(9913*2^310557-1)/3593490Lelio R Paula04/2015
83549*7^110614+293481Lelio R Paula11/2014
8355(19*10^93467+83)/393468Robert Price08/2020
83562^310469-829593461Lelio R Paula03/2016
83572^310459-115993458Yves Minet11/2012
83586^120075-9593437Lelio R Paula05/2016
8359(2^310362+1758)/293428Stefano Morozzi09/2020
8360148^43041-14793411Norbert Schneider05/2019
83612^310289+9832793407Yves Minet11/2010
836221769^19510+19510^2176993395Hans Havermann08/2020
83632^310217-11314393385Enzo Doria07/2014
83647^110494-6893379Lelio R Paula04/2016
83652^310184-11309393375Enzo Doria07/2014
83662^310180-11041793374Enzo Doria05/2014
8367gcd(V(1124905),5*F(224981)*(F(224981)-1)+1)93372Serge Batalov04/2015
8368(2^310173+3150)/293372Stefano Morozzi09/2020
83693^195669+6893358Lelio R Paula04/2016
837010^93356+9193357Robert Price04/2011
837110^93356-2831393356Patrick De Geest08/2013
8372(85*10^93346+23)/993347Robert Price11/2015
8373(3^195648-5)/315827693342Lelio R Paula04/2013
837410^93333-400000193333Robert Price07/2021
83753^195556+868093304Lelio R Paula04/2016
83762^309942-10999193302Enzo Doria04/2014
83772^309926-186730193298Enzo Doria03/2016
83782^309924+8595193297Yves Minet03/2011
83792^309896-422993288Yves Minet08/2018
8380(86*10^93263-77)/993264Robert Price05/2016
83816^119836-12593251Lelio R Paula05/2016
8382(77*10^93249-257)/993250Robert Price10/2017
838321822^18749+18749^2182293245Hans Havermann09/2020
83843^195430-293244Theodore Burton02/2007
8385(13*10^93236+47)/393237Robert Price01/2017
8386(67*10^93226-7)/393228Robert Price10/2017
8387(86*10^93217-221)/993218Robert Price06/2017
83882^309637-1632993211Enzo Doria04/2013
8389(41*10^93207+49)/993208Robert Price04/2016
839014^81312-5793194Lelio R Paula06/2016
839141^57783-4093192Theodore Burton02/2007
83923*10^93179-9793180Robert Price08/2017
83935*7^110252-493175Lelio R Paula11/2014
839422022^16959+16959^2202293140Hans Havermann08/2020
839583061!4-51293137Robert Price11/2019
839625169^5016+5016^2516993135Hans Havermann08/2020
8397(483641^16384+1)/293135Richard Fischer02/2021
83982^309380-2793133Lelio R Paula11/2012
839925653^4268+4268^2565393127Hans Havermann08/2020
8400(2^309355+1826)/293125Stefano Morozzi02/2021
8401(2^309334+2710)/293119Stefano Morozzi09/2020
840223*10^93116-793118Robert Price03/2016
8403(2^309270+3214)/293100Stefano Morozzi09/2020
8404(29*10^93082+1)/393083Robert Price11/2015
8405(2^309198+3738)/293078Stefano Morozzi09/2020
8406(58*10^93062-13)/993063Robert Price09/2015
8407(2^309138+1794)/293060Stefano Morozzi01/2021
84082^309131+186938393058Enzo Doria05/2016
8409(2^309114+3610)/293053Stefano Morozzi09/2020
84102^309066-9393039Lelio R Paula11/2012
84112^309063-11326993038Enzo Doria07/2014
84123^194965+1693022Robert Price10/2013
8413(89*10^93019-737)/993020Robert Price01/2022
84142^308979+186914393012Enzo Doria05/2016
84155^133064+5493008Lelio R Paula04/2016
8416(2^308947+2750)/293003Stefano Morozzi01/2021
8417(2^308905-509203)/11992988Lelio R Paula06/2013
8418(94*10^92981-49)/9992981Ray Chandler07/2011
8419(2*10^92976-17)/392976Robert Price08/2014
842024783^5642+5642^2478392972Hans Havermann08/2020
8421(472489^16384+1)/292969Richard Fischer01/2021
84222^308809+3796792961Phil Moore03/2008
8423(3^194825+5)/1165692952Lelio R Paula04/2013
8424(2^308679+5)/157392919Lelio R Paula06/2013
84252^308650+51392913Lelio R Paula02/2016
84265*7^109936+692908Lelio R Paula10/2014
84272*10^92897+8992898Robert Price07/2016
8428(2^308585+3182)/292894Stefano Morozzi09/2020
8429(467307^16384+1)/292891Richard Fischer01/2021
843012^86073-2992889Lelio R Paula06/2016
84312^308566-11792888Lelio R Paula11/2012
843211594^22851-22851^1159492872Norbert Schneider03/2022
8433(17*10^92869-11)/392870Robert Price07/2015
84342^308459+7543192856Enzo Doria04/2016
84352^308426-186637792846Enzo Doria03/2016
843624810^5521+5521^2481092840Hans Havermann09/2020
8437(96^46831-1)/9592830Paul Bourdelais09/2017
84382^308349-11211192823Enzo Doria06/2014
84399*10^92821+1992822Robert Price05/2016
84402^308337-7592819Lelio R Paula11/2012
84414*3^194508+792805Lelio R Paula08/2014
844222*25^66379-11392796Curtis Bright05/2015
844324538^6047+6047^2453892792Hans Havermann09/2020
844411^89101-108092790Enzo Doria12/2012
84452^308236-186785992789Enzo Doria04/2016
844612^85963+2592770Lelio R Paula06/2016
844723692^8221+8221^2369292753Hans Havermann08/2020
84487^109750-6692750Lelio R Paula04/2016
84499*10^92742+1192743Robert Kinser01/2017
8450(2^308054+778)/292734Stefano Morozzi09/2020
8451(21*2^308046-1)/885792729Lelio R Paula02/2014
84522^307997-11065592717Enzo Doria05/2014
8453L(443609)92709Renaud Lifchitz11/2003
845410^92691+992692Robert Price03/2011
845510^92691-25229192691Patrick De Geest08/2013
8456(2^307883+3506)/292682Stefano Morozzi09/2020
84572^307879-252192681Yves Minet07/2014
845821269^21412+21412^2126992666Norbert Schneider04/2020
8459(2^307780-7)/1995966992644Lelio R Paula06/2013
846014^80831+4792643Lelio R Paula06/2016
846115^78744+9292611Lelio R Paula07/2016
846265^51083-6492610Norbert Schneider11/2014
8463(2^307639+506)/292609Stefano Morozzi09/2020
8464131^43737-13092604Norbert Schneider02/2019
84656^118996-1694392597Enzo Doria02/2013
8466(16*10^92591+41)/392592Robert Price10/2017
8467(2^307566+3094)/292587Stefano Morozzi09/2020
8468(2^307528+1578)/292575Stefano Morozzi09/2020
84699*10^92573+8392574Robert Price11/2020
8470(3^194014-7)/292568Lelio R Paula04/2013
8471(2^307498+570)/292566Stefano Morozzi09/2020
8472(63^51439+1)/6492555Paul Bourdelais08/2017
8473(26*10^92546-77)/392547Robert Price02/2017
84743^193954+34092540Lelio R Paula04/2016
84752^307407-307407^292539Henri Lifchitz05/2005
847624299^6430+6430^2429992536Hans Havermann08/2020
8478(17*10^92513-11)/392514Robert Price07/2015
84772^307322-39907192514Harrison Mesh06/2022
84792^307318-421192512Yves Minet06/2011
84802^307280+19392501Lelio R Paula11/2012
848120^71075-3392471Lelio R Paula05/2016
84822^307126-7879592455Lelio R Paula02/2016
84832^307125-4978992454Henri Lifchitz08/2005
84842^307099+2392447Lelio R Paula11/2012
8485129^43798+12892440Norbert Schneider01/2019
848621826^17181+17181^2182692435Hans Havermann09/2020
8487Phi(277314,10)/332776992430Makoto Kamada05/2019
8488(2^307022+1038)/292423Stefano Morozzi09/2020
84897*10^92414-6992415Robert Price01/2017
8490(9787*2^306975-1)/212915592407Lelio R Paula04/2015
849122280^14037+14037^2228092402Hans Havermann09/2020
84922^306915+187337392391Enzo Doria06/2016
84932^306908+1291592389Lelio R Paula02/2016
849421620^18759+18759^2162092387Hans Havermann09/2020
8495(2^306897+1142)/292385Stefano Morozzi09/2020
849619^72244-8092383Lelio R Paula06/2016
84982^306849+7592371Lelio R Paula11/2012
8497(397*10^92369+53)/992371Robert Price11/2017
84992^306813-86968810592360Lelio R Paula08/2016
8500(2^306797+2694)/292355Stefano Morozzi09/2020


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 23 2022 21:24 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!