PRP Records

Probable Primes Top 10000

(201620 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 (> 30000) Who ? When ?
17512^426293+1881017128327Enzo Doria11/2016
17522^426043+35128252Robert Price11/2015
17532^425808-459959128181Enzo Doria06/2015
17542^425627-113605128127Enzo Doria08/2014
175518565^30002-30002^18565128070Norbert Schneider01/2015
1756(2^425287-9)/2737128021Lelio R Paula05/2015
1757(3*2^425233-1)/25128007Lelio R Paula05/2014
17582^425205+4911128000Marek Hubal02/2017
17592^425118-113663127974Enzo Doria08/2014
17602^425061+1869761127957Enzo Doria05/2016
17612^424918-21141127914Enzo Doria07/2013
17622^424864-29489127897Enzo Doria08/2015
1763(97*10^127858-1)/3127860Serge Batalov12/2014
17642^424632-2786639127827Enzo Doria03/2016
17652^424577-113755127811Enzo Doria09/2014
1766(7*2^424512-1)/3127792Lelio R Paula05/2014
176711^122629-720127705Enzo Doria11/2012
17682^423696-21429127546Enzo Doria07/2013
17692^423664-1864559127536Enzo Doria03/2016
17703^267267-4127519Henri Lifchitz10/2014
1771(19^99689+5^99689)/24127477Robert Price09/2013
1772(21*2^423372+1)/101127447Lelio R Paula05/2014
17732^423328-21537127435Enzo Doria07/2013
1774(2^423165-7)/25127384Lelio R Paula05/2015
1775(F(5)^182099-F(4)^182099)/F(3)127282Wayne Halsdorf08/2013
1776(234483*27^88884-145)/26127230Curtis Bright05/2015
17772^422515-114997127190Enzo Doria06/2015
17785*10^127179-3127180Robert Price07/2015
1779-516776642557847117490*Bern(37960)/34256837217082767928421792453127042Thomas Ritschel06/2017
1780(78^67141-1)/77127036Paul Bourdelais09/2017
17812^421860-113285126993Enzo Doria07/2014
1782(2^421827-7)/11126982Lelio R Paula05/2015
178311^121910-840126957Enzo Doria12/2012
1784(71^68539+1)/72126882Paul Bourdelais09/2017
1785331^50339-10004126846Enzo Doria07/2012
17862^421363-2790757126843Enzo Doria03/2016
1787(106*10^126839-1)/3126841Serge Batalov12/2014
1788(7*2^421243+1)/39126807Lelio R Paula05/2014
17892^421161-286183126783Enzo Doria06/2015
17902^420939-113935126716Enzo Doria10/2014
1791177^56363-2126703Lelio R Paula10/2017
17922^420741-113659126656Enzo Doria08/2014
17932^420694-21126642Lelio R Paula05/2017
1794(31*2^420556+1)/7126601Lelio R Paula05/2014
17952^420424-59189126561Enzo Doria10/2015
17962^420126+71893126471Enzo Doria04/2016
17972^419866+1877059126393Enzo Doria07/2016
1798F(604711)126377Henri Lifchitz02/2005
17992^419757+72707126360Enzo Doria04/2016
18002^419720-21569126349Enzo Doria07/2013
18012^419637+29126324Henri Lifchitz02/2006
18022^419612+1876741126316Enzo Doria07/2016
18032^419520+2793271126289Enzo Doria03/2016
1804(2^419447-5)/369126264Lelio R Paula05/2014
18052^419328-1859939126231Enzo Doria03/2016
18062^419282-1851507126217Enzo Doria08/2015
18072^419251+1866143126208Enzo Doria03/2016
180811^121185+2126202Robert Price05/2014
1809(23*2^419036-1)/1393126141Lelio R Paula05/2014
18102^418851+23126087Robert Price09/2015
1811(2^418849-9)/2681126083Lelio R Paula05/2014
18122^418829+167126081Lelio R Paula01/2012
1813(31*2^418782-1)/75891126063Lelio R Paula05/2014
1814(19*2^418754-1)/15126058Lelio R Paula05/2014
18152^418319-109501125927Enzo Doria04/2014
18162^418316-112373125926Enzo Doria06/2014
18172^417968+1869811125821Enzo Doria06/2016
18182^417902+63125802Lelio R Paula09/2015
1819(10^125792-91)/9125792Serge Batalov12/2014
18202^417704+77011125742Enzo Doria05/2016
1821(10^125706+149)/3125706Serge Batalov12/2014
18222^417419-115309125656Enzo Doria07/2015
18232^417300+77281125620Enzo Doria05/2016
18242^417095-1657125559Yves Minet07/2014
18252^416773-25125462Lelio R Paula09/2015
1826(289511#+292834)/(2^3*146417)125444Makoto Morimoto10/2017
1827(11*2^416691+1)/43125436Lelio R Paula05/2014
1828(21*2^416566-1)/17125399Lelio R Paula05/2014
18292^416530+1870429125389Enzo Doria05/2016
18302^416490+1875109125376Enzo Doria09/2016
18312^416416-114929125354Enzo Doria05/2015
1832(172*10^125292-1)/9125294Serge Batalov12/2014
18332^416134+1865899125269Enzo Doria03/2016
1834(9*2^415992+1)/13560845125220Lelio R Paula05/2014
1835(23^91943-1)/22125201Robert Price01/2012
183643125^27010-106125185Enzo Doria08/2012
18372^415765-112603125158Enzo Doria06/2014
18382^415290-113591125015Enzo Doria08/2014
18392^415276-460919125011Enzo Doria06/2015
18402^415259+77243125006Enzo Doria05/2016
18412^415144-3683124971Yves Minet10/2011
18422^414874+79124890Lelio R Paula01/2015
1843(2^414765+7)/1389124854Lelio R Paula05/2014
18442^414618+79459124813Enzo Doria06/2016
18452^414432-1846709124757Enzo Doria07/2015
1846(13*2^414274-1)/153124708Lelio R Paula05/2014
18472^414032-5124637Henri Lifchitz07/2006
18482^414032+1872331124637Enzo Doria05/2016
184914120^30009-30009^14120124533Norbert Schneider02/2015
185064^68909-63^68909124463Robert Price07/2013
18512^413387+76253124442Enzo Doria04/2016
1852287117#+391613124424Nicolas PALAU01/2017
1853(27*2^413207-1)/108335124385Lelio R Paula05/2014
18542^412868-120599124286Paul Bourdelais02/2012
185545^75145-2124231Lelio R Paula08/2015
18562^412645-112213124219Enzo Doria06/2014
18572^412248+74611124100Enzo Doria04/2016
18582^412192-3329124083Yves Minet12/2014
1859(25*2^412191-1)/23124082Lelio R Paula05/2014
1860F(593689)124074Henri Lifchitz01/2005
1861(11*2^412161+1)/19124073Lelio R Paula05/2014
18622^411884-113279123990Enzo Doria07/2014
1863(2^411832+1)/257123972Lelio R Paula05/2014
18642^411790-1853531123962Enzo Doria08/2015
1865(5^177337+1)/6123953Paul Bourdelais11/2008
18662^411711-113257123938Enzo Doria07/2014
1867(23*2^411675-1)/3123928Lelio R Paula05/2014
18682^411325-351103123822Enzo Doria06/2015
18692^411052+1872481123739Enzo Doria05/2016
18702^410997+39123723Lelio R Paula05/2014
18712^410596-39123602Lelio R Paula05/2014
18722^410540-115079123585Enzo Doria06/2015
1873(3*2^410392-1)/9229123537Lelio R Paula05/2014
18742^410206-113081123485Enzo Doria07/2014
1875(25*2^410192+1)/10397123478Lelio R Paula04/2014
18762^409909-189123395Enzo Doria05/2014
18772^409896-109043123391Enzo Doria04/2014
18782^409890+75409123390Enzo Doria04/2016
1879133^58076-2123345Lelio R Paula10/2017
1880F(590041)123311Henri Lifchitz01/2005
18812^409566-113501123292Enzo Doria08/2014
18822^409533+77747123282Enzo Doria05/2016
18832^409436-112799123253Enzo Doria06/2014
18842^409225+1873787123189Enzo Doria06/2016
18852^409174+73009123174Enzo Doria04/2016
18862^409058-112685123139Enzo Doria06/2014
18872^408778+77689123055Enzo Doria05/2016
18882^408690-75123028Lelio R Paula11/2013
18892^408574-2787341122994Enzo Doria03/2016
1890Phi(157825,10)122961Maksym Voznyy06/2015
1891(13*2^408283+1)/1665122904Lelio R Paula05/2014
1892(11*2^408100-1)/35122850Lelio R Paula04/2014
1893(2^407821-lucasV(1,2,407821)+1)/2122767Mike Oakes11/2016
1894(21*2^407604-1)/215122701Lelio R Paula04/2014
1895(21*2^407433-1)/13122650Lelio R Paula04/2014
1896(73*10^122592-1)/9122593Robert Price01/2015
18972^407179-112075122574Enzo Doria06/2014
1898(21*2^407131+1)/207517523122552Lelio R Paula04/2014
1899(66^67349+1)/67122543Paul Bourdelais09/2017
19002^407008-1867919122522Enzo Doria04/2016
190111^117642-300122512Enzo Doria10/2012
1902(F(3*97700+1)^2+L(3*97700+1)^2)/2122509Henri Lifchitz10/2017
19032^406949+72197122504Enzo Doria04/2016
19042^406826-65122467Lelio R Paula11/2013
19052^406821-2797363122466Enzo Doria04/2016
19062^406758-17122447Lelio R Paula11/2013
1907(30^82883-1)/29122427Robert Price12/2011
1908(2^406583-1)/813167122388Jens K. Andersen02/2009
190997^61575-2122336Lelio R Paula12/2014
19102^406298+2799109122308Enzo Doria04/2016
1911(27*2^406241-1)/10277122289Lelio R Paula04/2014
19122^406229-1849993122288Enzo Doria08/2015
19133*10^122274+7122275Robert Price07/2015
19142^406117+1876577122254Enzo Doria07/2016
19153^256199-2^256199122238Mike Oakes06/2005
19162^405774+179149122151Enzo Doria06/2016
19172^405514-3311122072Yves Minet12/2014
19182^405514-115511122072Enzo Doria07/2015
19192^405422-113261122045Enzo Doria07/2014
19202^405173+71237121970Enzo Doria04/2016
1921(2^405016+1)/257121920Lelio R Paula04/2014
19222^404858+71329121875Enzo Doria04/2016
19232^404813-114703121861Enzo Doria04/2015
19242^404764+77791121847Enzo Doria05/2016
1925317^48694+48694^317121787Norbert Schneider08/2015
19262^404536-115259121778Enzo Doria06/2015
19272^404501-631121767Yves Minet07/2012
192863^67620+2121672Lelio R Paula08/2015
1929(17*10^121621+1)/9121622Serge Batalov05/2010
1930(15*2^403912+1)/271121589Lelio R Paula05/2014
1931(10^121543-79)/3121543Robert Price01/2018
19322^403676+76831121519Enzo Doria05/2016
19332^403363-113635121425Enzo Doria08/2014
19342^403336-1861469121417Enzo Doria03/2016
1935p(24442)#/2-64121381Robert Price04/2017
193611^116555-720121380Enzo Doria11/2012
19372^403100-461267121346Enzo Doria07/2015
19382^403093-112213121344Enzo Doria06/2014
1939(316^48539+1)/317121330Eric Chen10/2017
19402^403004+1866361121317Enzo Doria03/2016
19412^402953+89121301Lelio R Paula10/2013
19422^402944-2788319121299Enzo Doria03/2016
1943(27*2^402865+1)/5121276Lelio R Paula04/2014
19442^402828-113183121264Enzo Doria07/2014
1945(17*10^121242+1)/9121243Serge Batalov05/2010
1946(15*2^402757+1)/101121242Lelio R Paula05/2014
19472^402715+1874223121230Enzo Doria06/2016
1948(91^61879+1)/92121222Paul Bourdelais09/2017
19497*10^121144+9121145Robert Price09/2015
19502^401725-113251120932Enzo Doria07/2014
1951(15*2^401677-1)/19120917Lelio R Paula05/2014
19522^401652+73711120910Enzo Doria04/2016
1953(2^401632+3)/79120902Lelio R Paula04/2014
19542^401406-2791331120836Enzo Doria03/2016
1955(28^83497+1)/29120832Robert Price07/2013
19562^401369+1867367120825Enzo Doria03/2016
1957(10^120782+29)/3120782Serge Batalov12/2014
19582^401215-1657120778Yves Minet07/2014
19592^401159+53120761Lelio R Paula10/2013
19602^401031-113047120723Enzo Doria07/2014
1961(29*2^400909-1)/303120685Lelio R Paula04/2014
19622^400571-15120584Lelio R Paula10/2013
1963(10^120574+359)/9120574Serge Batalov12/2014
19642^400424-216413120540Enzo Doria04/2013
1965(17*2^400200-1)/587120471Lelio R Paula05/2014
19662^400166+1874899120462Enzo Doria06/2016
1967(3*2^400045-1)/865120424Lelio R Paula04/2014
19682^399966+73759120402Enzo Doria04/2016
1969(112*10^120395-1)/3120397Serge Batalov12/2014
19702^399918-95120388Lelio R Paula04/2013
19712^399792-1849259120350Enzo Doria08/2015
19729*10^120342-7120343Robert Price09/2015
19732^399526-1861721120270Enzo Doria11/2015
1974(10^(2*60126+1)+36*10^60126-1)/9120253Robert Price10/2015
19752^399322-2798111120208Enzo Doria04/2016
197672^64693-71^64693120157Robert Price03/2014
19772^399111-28489120145Enzo Doria08/2015
19792^398877+105120074Donovan Johnson01/2006
1978(101*10^120072-87)/7120074Hans Havermann02/2015
1980(88^61751+1)/89120072Paul Bourdelais09/2017
19812^398710+57120024Lelio R Paula04/2013
19822^398691-115057120018Enzo Doria06/2015
1983L(574219)120005Renaud Lifchitz03/2004
19842^398571+60413119982Yves Minet03/2011
1985p(24179)#/2-64119949Robert Price04/2017
19862^398448+1872001119945Enzo Doria05/2016
19878*10^119930-3119931Ray Chandler04/2011
1988(10^119880+179)/9119880Serge Batalov12/2014
1989(9*2^398145+1)/73119853Lelio R Paula04/2014
1990(10^119836+77)/3119836Robert Price01/2018
19912^398029+1872527119819Enzo Doria05/2016
19922^397897-113541119779Enzo Doria08/2014
1993(21*2^397661-1)/27593119705Lelio R Paula04/2014
1994(58^67853-1)/57119653Paul Bourdelais09/2017
19952^397426+73849119638Enzo Doria04/2016
19962^396933-112723119489Enzo Doria06/2014
199711^114738-150119488Enzo Doria10/2012
19982^396790-21119446Lelio R Paula04/2013
1999(2^396633-7)/5119398Lelio R Paula04/2014
2000105^59050+104119352Norbert Schneider11/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 21 2018 09:45 (Time in France)

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