PRP Records

Probable Primes Top 10000

(293016 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 ?
150110^193566-10000000001193566Robert Price04/2021
15022^642888-24965193529Enzo Doria09/2013
15032^642448-114825193397Enzo Doria05/2015
15042^642437-1856623193393Enzo Doria10/2015
15052^642039-59797193273Enzo Doria11/2015
150610^193230+513861193231Patrick De Geest07/2018
150710^193230-8001193230Robert Price03/2018
1508(62*10^193225-233)/9193226Robert Price02/2022
15092^641692-286349193169Enzo Doria07/2015
15102^641690-24737193168Enzo Doria09/2013
15112^641514+1876549193115Enzo Doria07/2016
15122^640888-2785619192927Enzo Doria10/2015
15132^640874-2783741192923Enzo Doria09/2015
151410^192922+192207192923Patrick De Geest08/2021
151510^192922-7001192922Robert Price04/2021
15162^640854+25192917Stefano Morozzi05/2021
151734*10^192868-9192870Robert Price06/2020
1518(46*10^192841+683)/9192842Robert Price03/2019
15192^640181+467192714Lelio R Paula08/2013
15202^639536-1850249192520Enzo Doria08/2015
152140714<>40712<>...<>1086421357911<>...<>40711<>40713192464Hans Havermann12/2019
15225*10^192422-43192423Robert Price01/2019
15232^639110-2792441192392Enzo Doria02/2016
15242^638955-29827192345Enzo Doria08/2015
15252^638713-2784223192272Enzo Doria10/2015
1526(10^192216+7)/149192214Alfred Reich07/2021
15272^638490-113507192205Enzo Doria08/2014
15282^638189-39943192115Enzo Doria09/2015
15292^638110+1877119192091Enzo Doria07/2016
15302^638066-2785211192078Enzo Doria10/2015
1531(35*10^191973-341)/9191974Robert Price08/2021
1532(112*10^191900+17)/3191902Robert Price03/2020
15332^637475-115309191900Enzo Doria07/2015
1534(68*10^191754-113)/9191755Robert Price03/2021
15352^636930-11191736Stefano Morozzi07/2022
1536(47*10^191732+259)/9191733Robert Price03/2022
15372^636661+1876577191655Enzo Doria07/2016
1538(34^125101-1)/33191589Paul Bourdelais11/2017
15392^636177-1855123191509Enzo Doria09/2015
15402^636158-113627191503Enzo Doria08/2014
1541(37*25^136966+63)/4191472Curtis Bright05/2015
15422^636035+79823191466Enzo Doria06/2016
15432^636011-1860847191459Enzo Doria11/2015
15442^635926-1860611191433Enzo Doria11/2015
15453*10^191152-7191153Robert Price08/2015
15462^634883-1865677191119Enzo Doria02/2016
15472^634801+1871957191095Enzo Doria05/2016
1548(77*10^191080+157)/9191081Robert Price05/2022
1549(35*10^191073+1)/9191074Serge Batalov07/2010
15509*10^191018-41191019Robert Price08/2020
15512^634470-59861190995Enzo Doria11/2015
15522^634368-29519190964Enzo Doria08/2015
15532^634188-350609190910Enzo Doria06/2015
1554(65*10^190899+493)/9190900Robert Price08/2021
1555(62*10^190795-413)/9190796Robert Price09/2021
1556(26*10^190789-131)/3190790Robert Price10/2019
1557(13*10^190732-61)/3190733Robert Price11/2018
1558(7*10^190683+143)/3190684Robert Price03/2018
15592^633088-113879190579Enzo Doria10/2014
15602^633064+1874911190572Enzo Doria06/2016
1561(43*10^190547+83)/9190548Robert Price11/2018
156299*10^190543+7190545Robert Price05/2021
1563(299*10^190533+1)/3190535Robert Price04/2020
1564(1744*10^190519-1747)/3190522Robert Price12/2020
15652^632815-15190497Stefano Morozzi07/2022
15662^632795-351205190491Enzo Doria06/2015
156741171^41272+41272^41171190454Norbert Schneider05/2023
1568(16*10^190420-19)/3190421Robert Price02/2019
1569(43*10^190351+101)/9190352Robert Price11/2018
15702^632156+78391190298Enzo Doria06/2016
157197*10^190295-3190297Robert Price05/2020
15722^632082-1851971190276Enzo Doria08/2015
15732^632020+1880311190257Enzo Doria09/2016
1574(5*10^190242-77)/9190242Robert Price04/2021
15757*10^190210+13190211Robert Price03/2021
15762^631637-462373190142Enzo Doria08/2015
15772*10^190126-21190127Robert Price09/2020
1578(28*10^190105+191)/3190106Robert Price02/2020
15792*10^190093+33190094Robert Price11/2021
1580(68*10^190053-113)/9190054Robert Price03/2021
15812^631122-39251189987Enzo Doria08/2015
1582(26*10^189928-89)/9189929Robert Price06/2018
15832^630839-97189902Yves Minet07/2017
158499*10^189876-7189878Robert Price07/2020
15852^630359+1788953189757Enzo Doria05/2016
15862^630228+1871971189718Enzo Doria05/2016
15872^630108+781189682Lelio R Paula08/2013
15882^629870-1867811189610Enzo Doria04/2016
1589(359^74189-1)/358189558Alexander Zhirkov11/2017
15902^629326+2792929189447Enzo Doria02/2016
15914*10^189401+13189402Robert Price02/2021
1592(10^189385-61)/3189385Serge Batalov12/2014
15932^629036+1874011189359Enzo Doria06/2016
15942^628930+80779189327Enzo Doria07/2016
1595(134*10^189309-11)/3189311Robert Price01/2022
15969*10^189306-11189307Mischa Rodermond04/2023
15972^628582+1179439189223Enzo Doria06/2016
1598(44*10^188999-503)/9189000Robert Price12/2018
1599(16*10^188823+167)/3188824Robert Price06/2019
1600(10^188796+7)/4967/71933188788Alfred Reich08/2021
16012^627037-2785843188757Enzo Doria10/2015
1602(10^188566+7)/311640753181661188552Alfred Reich04/2022
1603(16*10^188457+161)/3188458Robert Price02/2019
1604L(901657)188436Renaud Lifchitz11/2008
1605(19*10^188375+137)/3188376Robert Price03/2022
16062^625651+74213188340Enzo Doria04/2016
16072^625584-460919188320Enzo Doria06/2015
1608(8*10^188308-71)/9188308Serge Batalov11/2022
1609(14*10^188218+139)/9188219Robert Price11/2021
1610(10^188164+359)/9188164Serge Batalov12/2014
16112^624481-113611187988Enzo Doria08/2014
1614(2^624389+125582)/2187960Stefano Morozzi09/2019
1612(2^624389+166982)/2187960Stefano Morozzi09/2019
1613(2^624389+179886)/2187960Stefano Morozzi09/2019
1615(2^624387+64466)/2187959Stefano Morozzi09/2019
1616(2^624378+112990)/2187957Stefano Morozzi09/2019
1617(2^624380+161986)/2187957Stefano Morozzi09/2019
1619(2^624376+55762)/2187956Stefano Morozzi09/2019
1618(2^624377+169506)/2187956Stefano Morozzi09/2019
1620(2^624355+80178)/2187950Stefano Morozzi09/2019
1621(2^624351+61350)/2187949Stefano Morozzi09/2019
1622(2^624341+63462)/2187946Stefano Morozzi09/2019
1623(2^624344+135990)/2187946Stefano Morozzi09/2019
1624(2^624344+183898)/2187946Stefano Morozzi09/2019
1626(2^624340+126982)/2187945Stefano Morozzi09/2019
1625(2^624338+196110)/2187945Stefano Morozzi09/2019
1627(2^624337+105162)/2187944Stefano Morozzi09/2019
1628(2^624333+44594)/2187943Stefano Morozzi09/2019
1629(2^624321+88742)/2187940Stefano Morozzi09/2019
1630(2^624324+135178)/2187940Stefano Morozzi09/2019
1631(2^624317+14186)/2187938Stefano Morozzi09/2019
1632(2^624313+24450)/2187937Stefano Morozzi09/2019
1633(2^624309+184590)/2187936Stefano Morozzi09/2019
1635(2^624307+152658)/2187935Stefano Morozzi09/2019
1634(2^624307+185978)/2187935Stefano Morozzi09/2019
1636(2^624303+40814)/2187934Stefano Morozzi09/2019
1637(2^624304+99238)/2187934Stefano Morozzi09/2019
16382^624077-112723187866Enzo Doria07/2014
16392^624008+1874941187846Enzo Doria06/2016
16402^623870+78679187804Enzo Doria05/2016
16412^623714-114035187757Enzo Doria11/2014
16422^623651-1834251187738Enzo Doria07/2015
1643(7*10^187645+53)/3187646Robert Price05/2018
164421650^43269+43269^21650187591Norbert Schneider02/2023
16452^623146+1879609187586Enzo Doria09/2016
1646(401*10^187512+13)/9187514Robert Price09/2021
1647(5*10^187471+91)/3187472Robert Price04/2018
16482^622500+81931187392Enzo Doria08/2016
1649(13*10^187382-157)/9187383Robert Price05/2021
16502^622300-1861739187331Enzo Doria12/2015
1651(22*10^187317-91)/3187318Robert Price02/2022
1652(38*10^187281+349)/9187282Robert Price10/2018
16532^622052+76771187257Enzo Doria05/2016
16542^622005-24091187243Enzo Doria08/2013
16557*10^187205-57187206Robert Price06/2020
16562^621879-351787187205Enzo Doria07/2015
1657(5*10^187168-53)/3187169Robert Price09/2020
1658(23*10^187164-143)/3187165Robert Price12/2019
16592^621700+79411187151Enzo Doria06/2016
1660(7*10^187101+131)/3187102Robert Price06/2020
1661(2*10^187062-71)/3187062Robert Price12/2017
16622^620929-113203186919Enzo Doria07/2014
166310^186842+168223186843Patrick De Geest07/2018
166410^186842-8001186842Robert Price03/2018
16652^620347-1777186744Lelio R Paula07/2013
1666(11*10^186659+133)/9186660Robert Price04/2022
166711^179143-4170186559Enzo Doria12/2012
1668(5^266863+1)/6186529Paul Bourdelais07/2010
16692*10^186517+33186518Robert Price11/2021
16702^619297-2792353186427Enzo Doria02/2016
1671(49*10^186409+383)/9186410Robert Price04/2019
16722^618940-460139186320Enzo Doria06/2015
16732^618046+74179186051Enzo Doria04/2016
16743*10^186019+11186020Robert Price07/2018
1675(16*10^185978-19)/3185979Robert Price02/2019
1676(22*10^185950-7)/3185951Robert Price12/2022
16772*10^185930-3185931Robert Price07/2015
1678(82^97151+1)/83185928Paul Bourdelais10/2017
16794*10^185905+91185906Robert Price08/2018
1680(34*10^185902-601)/9185903Robert Price07/2022
1681(19*10^185873+131)/3185874Robert Price06/2020
1682(37*10^185811+377)/9185812Robert Price11/2018
16832^617250+9385185811Lelio R Paula07/2013
16842^617130+9185775Stefano Morozzi05/2021
168539^116749+2185756Robert Price04/2015
16862^616924-39719185713Enzo Doria09/2015
16872^616712+1867621185649Enzo Doria04/2016
1688(3^388897+2^388897)/5185551Jean-Louis Charton09/2011
16898*10^185529-67185530Robert Price08/2019
1690(5*10^185520-11)/3185521Tyler Busby02/2023
16914*10^185355+9185356Robert Price05/2015
1692(16*10^185347+89)/3185348Robert Price03/2021
16932^615622+76639185321Enzo Doria05/2016
16942^615591+1879223185312Enzo Doria08/2016
16952^615503+1876643185285Enzo Doria07/2016
16965^265007-4^265007185232Jean-Louis Charton02/2013
1697(4*10^185221-91)/3185222Robert Price03/2018
1698(7*10^185221+131)/3185222Robert Price06/2020
1699(62*10^185216-413)/9185217Robert Price09/2021
1700(232*10^185180+17)/3185182Robert Price04/2021
170156*10^185139-3185141Robert Price03/2020
1702(28*10^185105+47)/3185106Robert Price02/2021
17032^614783-2790097185069Enzo Doria12/2015
17042^614745-29323185057Enzo Doria07/2015
1705(((((((((((2^3+3)^3+30)^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+66768)^3+300840185052Serge Batalov07/2013
1706(49*10^184993-67)/9184994Robert Price03/2019
1707(5*10^184954-191)/3184955Robert Price05/2021
1708(14*10^184950+211)/9184951Robert Price04/2018
17092^614315+81353184928Enzo Doria08/2016
17102^614294-1849961184921Enzo Doria08/2015
17112^614266+1877809184913Enzo Doria08/2016
1712(185*10^184878-11)/3184880Robert Price10/2020
171391*10^184867-9184869Robert Price06/2021
1714(85*10^184768+77)/9184769Robert Price07/2022
17152^613715-1860727184747Enzo Doria11/2015
1716(4*10^184730+89)/3184731Robert Price08/2021
17172*10^184723+41184724Robert Price05/2018
1718(49*10^184703+293)/9184704Robert Price03/2021
17192^613487-349987184678Enzo Doria07/2015
1720(95^93377+1)/96184672Paul Bourdelais11/2017
172114^161089-161089^14184629Serge Batalov05/2016
17222^613033-114621184542Enzo Doria05/2015
1723(9^193247+1)/10184404Paul Bourdelais02/2010
17242^612341-1604809184334Enzo Doria05/2015
1725(11*10^184308-161)/3184309Robert Price11/2021
1726(2^611999-1)/18464214225958267477777390354183184199Dario Alpern06/2017
1727(14*10^184150+37)/3184151Robert Price12/2018
17282^611731-4837184150Yves Minet08/2018
17293*10^184124-7184125Robert Price08/2015
17309*10^184122-11184123Mischa Rodermond04/2023
17312^611628-24537184119Enzo Doria08/2013
17323*10^184110+13184111Robert Price07/2018
1733(194*10^184093+1)/3184095Robert Price01/2022
17342^611460+71881184068Enzo Doria04/2016
17354*10^184004-63184005Robert Price10/2018
17362^610982-1867301183924Enzo Doria03/2016
17373*10^183872-49183873Robert Price07/2018
17382^610597+1178897183809Enzo Doria05/2016
1739(8*10^183773-269)/9183773Robert Price09/2021
1740(65*10^183768-29)/9183769Robert Price01/2021
1741(17*10^183764+31)/3183765Robert Price01/2019
1742(28*10^183760-1)/9183761Serge Batalov10/2014
17432^610401+1277183750Lelio R Paula07/2013
17442^610356-1849019183736Enzo Doria08/2015
1745(63^102103+1)/64183717Paul Bourdelais10/2017
174623*10^183710-7183712Robert Price02/2020
1747(2^610289+1)/(3*528882550291)183704Gord Palameta08/2018
1748(4*10^183659+149)/9183659Robert Price04/2018
1749(4*10^183657+41)/9183657Serge Batalov11/2022
17507*10^183596+39183597Robert Price01/2023


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 04 2023 08:38 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!