PRP Records

Probable Primes Top 10000

(301668 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 ?
15012^901858+77689271487Enzo Doria06/2016
15022^901372+1875301271341Enzo Doria06/2016
15032^901146+219049271272Enzo Doria02/2024
1504(8*10^271039-77)/3271040Robert Price04/2023
15052^899999+1144031270927Norman Luhn09/2023
15062*10^270802-91270803Robert Price02/2023
150723*10^270799-7270801Robert Price10/2022
15082^899121-115033270663Enzo Doria07/2015
15092^898900+883021270596Enzo Doria12/2016
15102^898762-251511270555Enzo Doria12/2013
15112^898589+47270503Lelio R Paula03/2016
1512187322*10^270343-187321270349Danilo Nitsche09/2013
151348358*10^270343-48357270348Danilo Nitsche09/2013
1514(10^270343-1)/9270343Maksym Voznyy07/2007
15152^897867-3217270285Yves Minet12/2016
15162^897849-115273270280Enzo Doria07/2015
15172^897367+26289270135Enzo Doria03/2024
15182^896616-114179269909Enzo Doria12/2014
1519(12648^66049-1)/(12648^257-1)269881Ryan Propper11/2023
1520(10^(2*134811+1)+6*10^134811-1)/3269623Robert Price08/2024
1521(22*10^269517-19)/3269518Robert Price07/2023
152210^(2*134739+1)-7*10^134739-1269479Robert Price07/2023
15232^894928+583561269401Enzo Doria04/2017
15242^894673-39343269324Enzo Doria08/2015
15252^893836+23221269072Enzo Doria10/2023
15262^892718+29539268735Enzo Doria03/2024
15272^892660+213901268718Enzo Doria10/2023
1528F(1285607)268676Henri Lifchitz11/2008
15292^892234+22189268590Enzo Doria09/2023
15302^892151+24863268565Enzo Doria11/2023
15312^892112+187663268553Enzo Doria08/2016
1532(266*10^268407-17)/3268409Robert Price02/2023
1533(10^268207+1)/11268206Paul Bourdelais02/2010
15342^890957-69583268205Enzo Doria12/2015
153532841!^2+32840!^2+...+2!^2+1!^2268128Serge Batalov07/2017
15362^890122-351401267954Enzo Doria07/2015
1537(19^209359-1)/18267718Paul Bourdelais08/2010
15382^888852+229051267572Enzo Doria11/2024
1539(85^138647+1)/86267507Paul Bourdelais07/2019
1540(1005^89087-1)/1004267451Jinyuan Wang01/2024
1541(485^99523-1)/484267291Michael Stocker05/2020
15422^886324+77791266811Enzo Doria06/2016
15437*10^266731+87266732Robert Price11/2022
15442^886040+213901266725Enzo Doria10/2023
15452^885242+217909266485Enzo Doria01/2024
15462^884738+26809266333Enzo Doria12/2023
15472^884714+1880527266326Enzo Doria10/2016
15487*10^266024-47266025Robert Price08/2023
154911^255426+255426^11265999Serge Batalov05/2014
15502^883462-343421265949Enzo Doria07/2015
15512^883442+1875019265943Enzo Doria06/2016
15522^883333-291583265910Enzo Doria07/2015
15532^883132+30421265850Enzo Doria03/2024
155410^265566+3593037265567Paul Bourdelais08/2023
1555(2*10^265321-17)/3265321Serge Batalov11/2022
1556(16*10^265052-91)/3265053Robert Price11/2022
15572^880411+1882673265031Enzo Doria12/2016
15582^880101+228917264937Enzo Doria11/2024
1559(14*10^264791-11)/3264792Robert Price08/2022
15602^879530-2788031264765Enzo Doria12/2015
15612^879292+25171264694Enzo Doria11/2023
1562(2*10^264539+61)/9264539Serge Batalov11/2022
15632^878118+2793079264340Enzo Doria02/2016
1564(2^878073-7)/5264326Stefano Morozzi08/2022
1565(37^168527-1)/36264283Paul Bourdelais08/2019
15665^377865+3^377865-1264117Jon Grantham08/2023
1567(19*10^263971+131)/3263972Robert Price08/2023
15682^876202-17263764Stefano Morozzi07/2022
1569(14*10^263720-11)/3263721Robert Price08/2022
15702^875748-461129263627Enzo Doria07/2015
15712^875518-15263558Stefano Morozzi07/2022
1572(29*10^263523-17)/3263524Robert Price01/2023
15732^875181-2789923263456Enzo Doria12/2015
15742^875101-350083263432Enzo Doria08/2015
15752^874684+1883587263307Enzo Doria01/2017
15762^874616+1872211263286Enzo Doria05/2016
15772^874566+30049263271Enzo Doria03/2024
15783^551491+16263129Robert Price04/2020
15792^874073+2792957263123Enzo Doria02/2016
1580(7*10^263006-19)/3263007Robert Price10/2023
15812^873628+1878751262989Enzo Doria08/2016
15822^873497+20837262949Enzo Doria08/2023
15832^873288-269262886Yves Minet01/2015
1584(2*10^262874+7)/9262874Rytis Slatkevicius01/2023
1585(28*10^262655-43)/3262656Robert Price04/2023
1586(2*10^262603-11)/9262603Serge Batalov11/2022
15872^871991-4207262496Yves Minet03/2021
1588(23*10^262324+7)/3262325Robert Price05/2023
15892^871146-3173262242Yves Minet07/2016
1590(10^(2*131020+1)+63*10^131020-1)/9262041Robert Price08/2024
15912^869601-163261776Yves Minet01/2015
1592(2*10^261704+61)/9261704Serge Batalov11/2022
15932^869326+282859261694Enzo Doria11/2016
15942^869035-114181261606Enzo Doria12/2014
15952^868817+26777261540Enzo Doria12/2023
15963^547850+9000004261391Enzo Doria10/2023
15974*10^261248+91261249Robert Price11/2022
159855083^55083+1282^1282261150Henri Lifchitz10/2024
15992^866908+34891260966Enzo Doria07/2024
16002^865715+80303260607Enzo Doria07/2016
16012^865474+23209260534Enzo Doria10/2023
16022^865238+214759260463Enzo Doria11/2023
16032^865048+1882411260406Enzo Doria12/2016
16042^864899-113871260361Enzo Doria10/2014
1605(16*10^260256-91)/3260257Robert Price11/2022
1606(7*10^260198-61)/9260198Erik Branger11/2011
16072^864298-2788421260180Enzo Doria12/2015
16082^864039-2791357260102Enzo Doria01/2016
16092^863621-113833259976Enzo Doria10/2014
161010^259945-11259945Mischa Rodermond04/2023
16112^863433+34877259920Enzo Doria07/2024
1612(28*10^259897+113)/3259898Robert Price06/2023
16132^862837+75767259740Enzo Doria05/2016
16142^862637-31259680Jorge Menendez05/2019
16152^862088+1874941259515Enzo Doria06/2016
16162^861987-134557259484Hans Havermann10/2018
1617(14*10^259431-143)/3259432Robert Price05/2023
16182^861516-1854029259343Enzo Doria09/2015
16192^860975-1853977259180Enzo Doria09/2015
16203^543128+16259138Robert Price04/2020
16212^860625-1858843259074Enzo Doria10/2015
16222^860110+77689258919Enzo Doria05/2016
16232^859600+1880371258766Enzo Doria10/2016
16242^859433+494711258716Makoto Morimoto10/2013
1626(2^859433-44)/(2^2*3)258715Makoto Morimoto08/2019
1625(2^859431-11)/3258715Stefano Morozzi08/2022
1627(13*10^258710-43)/3258711Robert Price08/2023
1628(2^859433+39899)/(73*3907*46301)258705Makoto Morimoto10/2016
16292^859240+1875271258658Enzo Doria06/2016
1630Tau(971^15738)258571Nik Lygeros / Olivier Rozier05/2015
16312^858812+30421258529Enzo Doria03/2024
1632(23*10^258494-47)/3258495Robert Price09/2023
1633(144^119671+1)/145258292Paul Bourdelais08/2019
16342^857608+105258166Stefano Morozzi05/2021
1635(11*2^857159-13)/15258031Renaud Lifchitz08/2011
16362^857016-633113257988Enzo Doria12/2013
16372^855732-113969257602Enzo Doria10/2014
1638(5*10^257431+91)/3257432Robert Price08/2023
16392^853682-3911256984Enzo Doria05/2014
164011^246668-90256879Enzo Doria12/2012
16412^853181+30287256834Enzo Doria03/2024
16425*2^852698+3256689Jon Grantham07/2023
1643(23*10^256654+7)/3256655Robert Price05/2023
16442^851904-113939256449Enzo Doria10/2014
16452^851725-851725^2256395Henri Lifchitz03/2019
164611^246167-90256357Enzo Doria12/2012
1647(85*10^256301-1)/3256303Robert Price12/2022
1648(10^256187+7)/63443/148782853256175Alfred Reich10/2021
16492^850700-569049256087Enzo Doria11/2013
16502^850675+153256079Stefano Morozzi05/2021
165121^193601-20^193601255983Jean-Louis Charton02/2015
1652(37^163193+1)/38255918Paul Bourdelais07/2019
1653(14*10^255805-83)/3255806Robert Price11/2022
16542^849316+25861255670Enzo Doria12/2023
16552^849177-114025255628Enzo Doria12/2014
16562*10^255442-21255443Robert Price08/2023
16572^848502-3173255425Yves Minet07/2016
16582^848178-140291255328Enzo Doria01/2014
16597*10^255167+87255168Robert Price11/2022
16602^847622-2441255160Yves Minet02/2016
16612^847291+182843255061Enzo Doria11/2016
16622^847174+1879429255025Enzo Doria09/2016
16632^846881+215837254937Enzo Doria12/2023
166424*29^174239+13361254809Curtis Bright04/2015
166522*10^254639+7254641Robert Price10/2022
16662^845633-933075254561Paul Bourdelais11/2021
16672^845610-1868591254554Enzo Doria04/2016
16682^845484+81931254517Enzo Doria08/2016
16692^845402-114761254492Enzo Doria05/2015
167098*10^254173-9254175Robert Price05/2023
16712^844334-2792441254170Enzo Doria02/2016
16722*10^254162+69254163Robert Price08/2023
1673(4*10^254107+11)/3254108Tyler Busby02/2023
167411^243796-90253888Enzo Doria12/2012
1675(10^253891+7)/44777/79843/16940711253875Alfred Reich10/2021
167630^171733-29^171733253671Jean-Louis Charton10/2018
16772^842325+25907253566Enzo Doria11/2023
16782^842209+1876037253531Enzo Doria07/2016
16792^842123-59197253505Enzo Doria10/2015
1680(8*10^253313-53)/9253313Serge Batalov11/2022
1681(28*10^253210+191)/3253211Robert Price07/2023
16822^840797-3253106Paul Bourdelais06/2019
16832^840716-2969253081Yves Minet05/2016
16842^840358-462491252973Enzo Doria08/2015
16852^840310+1878379252959Enzo Doria08/2016
16862^840203-21252927Stefano Morozzi07/2022
168711^242579-60252620Enzo Doria10/2012
168845^152659+2252378Robert Price09/2015
1689(95^127583+1)/96252322Paul Bourdelais07/2019
16907*10^252209-17252210Robert Price12/2022
16912^837725+1869377252181Enzo Doria05/2016
16922^837536-311039252124Enzo Doria06/2015
169321^190632-2252058Robert Price07/2015
16942^837242+1873297252035Enzo Doria06/2016
16952^836995+226575251961Enzo Doria10/2024
16962^836656-2787929251859Enzo Doria11/2015
16972^836548+219061251827Enzo Doria02/2024
16982^836380+1875541251776Enzo Doria07/2016
1699(359^98327-1)/358251233Alexander Zhirkov11/2017
1700tau(41^28288)250924Nik Lygeros / Olivier Rozier10/2013
1701(28*10^250655+113)/3250656Robert Price06/2023
17022^832511-461197250611Enzo Doria07/2015
17032^832505+1881137250609Enzo Doria11/2016
17042^832363+583295250567Enzo Doria12/2016
17052^832244-403635250531Enzo Doria01/2014
1706(14*10^250336-41)/9250337Serge Batalov01/2023
17072^831528+24811250315Enzo Doria11/2023
17082^831157+1880657250204Enzo Doria11/2016
17092^831088-7200899250183Enzo Doria01/2015
17102^830956-1349250143Yves Minet07/2015
17112^830699+220583250066Enzo Doria03/2024
17122^830037+282317249867Enzo Doria09/2016
17132^829589-113653249732Enzo Doria09/2014
1714(4*10^249550-7)/3249551Serge Batalov01/2023
1715(103*10^249399+17)/3249401Robert Price04/2023
17162^828281-3193249338Yves Minet08/2016
1717(2^828140-19)/3249295Stefano Morozzi08/2022
17182^828064-2785619249273Enzo Doria10/2015
17192^827602+60409249134Enzo Doria03/2016
17202^827306+212419249044Enzo Doria09/2023
172110^249010+348861249011Patrick De Geest04/2016
172210^249010-21249010Serge Batalov12/2014
17232^826733+1882907248872Enzo Doria12/2016
17242^825800+22441248591Enzo Doria10/2023
17252^825682+1876549248556Enzo Doria07/2016
17262^824991-114121248348Enzo Doria12/2014
17272^824642-362727248242Enzo Doria12/2013
17282^824565-114265248219Enzo Doria01/2015
17292^824325-25248147Boyan Hu12/2024
1730(73*10^248145-1)/9248146Robert Price01/2015
17312^823321+219407247845Enzo Doria02/2024
1732(2^823337+1)/(3*362268281)247841Gord Palameta08/2018
1733(13*10^247793-43)/3247794Robert Price08/2023
1734(2^822971-1)/6583769/28211445881/21255852651726486149207247700Robert Kinser09/2016
17352^822296+76501247536Enzo Doria05/2016
17362^821590-114167247324Enzo Doria12/2014
17372^821512-2790659247300Enzo Doria12/2015
1738(21996^57121-1)/(21996^239-1)247002Ryan Propper11/2023
17392^820356+7246952Jon Grantham08/2023
17402^820077+382847246868Enzo Doria11/2016
17412^820008+81246848Henri Lifchitz01/2025
17422^820001+81269246845Enzo Doria07/2016
17432^819463-59197246683Enzo Doria10/2015
17442^819296+80581246633Enzo Doria07/2016
17452^818764+21573246473Enzo Doria11/2023
17462^817852+215491246198Enzo Doria11/2023
17472^817160-350369245990Enzo Doria06/2015
17482^816039-19245653Stefano Morozzi07/2022
17492^816029+219407245650Enzo Doria02/2024
1750(71*10^245558-17)/9245559Serge Batalov01/2023


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 20 2025 15:18 (Time in France)

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