PRP Records

Probable Primes Top 10000

(202632 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 (> 30000) Who ? When ?
175191^65772-2128851Lelio R Paula05/2017
17522^428022+43128848Lelio R Paula05/2017
17532^427999-459397128841Enzo Doria05/2015
17542^427993+76847128839Enzo Doria05/2016
17552^427824-1851507128788Enzo Doria08/2015
17562^427807-21469128783Enzo Doria07/2013
175711^123594-240128710Enzo Doria09/2012
17582^427504-21503128692Enzo Doria07/2013
17592^427420+91128667Lelio R Paula05/2017
17602^427269-113635128621Enzo Doria08/2014
17612^427130+1877569128579Enzo Doria08/2016
17622^427016-115349128545Enzo Doria07/2015
17632^426889-112879128507Enzo Doria06/2014
17642^426804+1869931128481Enzo Doria05/2016
17652^426750+77635128465Enzo Doria05/2016
17662^426425-91128367Lelio R Paula05/2017
1767(15*2^426398-1)/11128359Lelio R Paula05/2014
17682^426352+74971128345Enzo Doria04/2016
17692^426300-1863689128330Enzo Doria03/2016
17702^426293+1881017128327Enzo Doria11/2016
17712^426043+35128252Robert Price11/2015
17722^425808-459959128181Enzo Doria06/2015
17732^425627-113605128127Enzo Doria08/2014
177418565^30002-30002^18565128070Norbert Schneider01/2015
1775(2^425287-9)/2737128021Lelio R Paula05/2015
1776(3*2^425233-1)/25128007Lelio R Paula05/2014
17772^425205+4911128000Marek Hubal02/2017
17782^425118-113663127974Enzo Doria08/2014
17792^425061+1869761127957Enzo Doria05/2016
17802^424918-21141127914Enzo Doria07/2013
17812^424864-29489127897Enzo Doria08/2015
1782(97*10^127858-1)/3127860Serge Batalov12/2014
17832^424632-2786639127827Enzo Doria03/2016
17842^424577-113755127811Enzo Doria09/2014
1785(7*2^424512-1)/3127792Lelio R Paula05/2014
178611^122629-720127705Enzo Doria11/2012
17872^423696-21429127546Enzo Doria07/2013
17882^423664-1864559127536Enzo Doria03/2016
17893^267267-4127519Henri Lifchitz10/2014
1790(19^99689+5^99689)/24127477Robert Price09/2013
1791(21*2^423372+1)/101127447Lelio R Paula05/2014
17922^423328-21537127435Enzo Doria07/2013
1793(2^423165-7)/25127384Lelio R Paula05/2015
1794(F(5)^182099-F(4)^182099)/F(3)127282Wayne Halsdorf08/2013
1795(234483*27^88884-145)/26127230Curtis Bright05/2015
17962^422515-114997127190Enzo Doria06/2015
17975*10^127179-3127180Robert Price07/2015
1798-516776642557847117490*Bern(37960)/34256837217082767928421792453127042Thomas Ritschel06/2017
1799(78^67141-1)/77127036Paul Bourdelais09/2017
18002^421860-113285126993Enzo Doria07/2014
1801(2^421827-7)/11126982Lelio R Paula05/2015
180211^121910-840126957Enzo Doria12/2012
1803(71^68539+1)/72126882Paul Bourdelais09/2017
1804331^50339-10004126846Enzo Doria07/2012
18052^421363-2790757126843Enzo Doria03/2016
1806(106*10^126839-1)/3126841Serge Batalov12/2014
1807(7*2^421243+1)/39126807Lelio R Paula05/2014
18082^421161-286183126783Enzo Doria06/2015
18092^420939-113935126716Enzo Doria10/2014
1810177^56363-2126703Lelio R Paula10/2017
18112^420741-113659126656Enzo Doria08/2014
18122^420694-21126642Lelio R Paula05/2017
1813(31*2^420556+1)/7126601Lelio R Paula05/2014
18142^420424-59189126561Enzo Doria10/2015
18152^420126+71893126471Enzo Doria04/2016
18162^419866+1877059126393Enzo Doria07/2016
1817F(604711)126377Henri Lifchitz02/2005
18182^419757+72707126360Enzo Doria04/2016
18192^419720-21569126349Enzo Doria07/2013
18202^419637+29126324Henri Lifchitz02/2006
18212^419612+1876741126316Enzo Doria07/2016
18222^419520+2793271126289Enzo Doria03/2016
1823(2^419447-5)/369126264Lelio R Paula05/2014
18242^419328-1859939126231Enzo Doria03/2016
18252^419282-1851507126217Enzo Doria08/2015
18262^419251+1866143126208Enzo Doria03/2016
182711^121185+2126202Robert Price05/2014
1828(23*2^419036-1)/1393126141Lelio R Paula05/2014
18292^418851+23126087Robert Price09/2015
1830(2^418849-9)/2681126083Lelio R Paula05/2014
18312^418829+167126081Lelio R Paula01/2012
1832(31*2^418782-1)/75891126063Lelio R Paula05/2014
1833(19*2^418754-1)/15126058Lelio R Paula05/2014
18342^418319-109501125927Enzo Doria04/2014
18352^418316-112373125926Enzo Doria06/2014
18362^417968+1869811125821Enzo Doria06/2016
18372^417902+63125802Lelio R Paula09/2015
1838(10^125792-91)/9125792Serge Batalov12/2014
18392^417704+77011125742Enzo Doria05/2016
1840(10^125706+149)/3125706Serge Batalov12/2014
18412^417419-115309125656Enzo Doria07/2015
18422^417300+77281125620Enzo Doria05/2016
18432^417095-1657125559Yves Minet07/2014
18442^416773-25125462Lelio R Paula09/2015
1845(289511#+292834)/(2^3*146417)125444Makoto Morimoto10/2017
1846(11*2^416691+1)/43125436Lelio R Paula05/2014
1847(21*2^416566-1)/17125399Lelio R Paula05/2014
18482^416530+1870429125389Enzo Doria05/2016
18492^416490+1875109125376Enzo Doria09/2016
18502^416416-114929125354Enzo Doria05/2015
1851(172*10^125292-1)/9125294Serge Batalov12/2014
18522^416134+1865899125269Enzo Doria03/2016
1853(9*2^415992+1)/13560845125220Lelio R Paula05/2014
1854(23^91943-1)/22125201Robert Price01/2012
185543125^27010-106125185Enzo Doria08/2012
18562^415765-112603125158Enzo Doria06/2014
18572^415290-113591125015Enzo Doria08/2014
18582^415276-460919125011Enzo Doria06/2015
18592^415259+77243125006Enzo Doria05/2016
18602^415144-3683124971Yves Minet10/2011
18612^414874+79124890Lelio R Paula01/2015
1862(2^414765+7)/1389124854Lelio R Paula05/2014
18632^414618+79459124813Enzo Doria06/2016
18642^414432-1846709124757Enzo Doria07/2015
1865(13*2^414274-1)/153124708Lelio R Paula05/2014
18672^414032-5124637Henri Lifchitz07/2006
18662^414032+1872331124637Enzo Doria05/2016
186814120^30009-30009^14120124533Norbert Schneider02/2015
186964^68909-63^68909124463Robert Price07/2013
18702^413387+76253124442Enzo Doria04/2016
1871287117#+391613124424Nicolas PALAU01/2017
1872(4*10^124420+83)/3124421Robert Price02/2018
1873(27*2^413207-1)/108335124385Lelio R Paula05/2014
18742^412868-120599124286Paul Bourdelais02/2012
187545^75145-2124231Lelio R Paula08/2015
18762^412645-112213124219Enzo Doria06/2014
18772^412248+74611124100Enzo Doria04/2016
18782^412192-3329124083Yves Minet12/2014
1879(25*2^412191-1)/23124082Lelio R Paula05/2014
1880F(593689)124074Henri Lifchitz01/2005
1881(11*2^412161+1)/19124073Lelio R Paula05/2014
18822^411884-113279123990Enzo Doria07/2014
1883(2^411832+1)/257123972Lelio R Paula05/2014
18842^411790-1853531123962Enzo Doria08/2015
1885(5^177337+1)/6123953Paul Bourdelais11/2008
18862^411711-113257123938Enzo Doria07/2014
1887(23*2^411675-1)/3123928Lelio R Paula05/2014
18882^411325-351103123822Enzo Doria06/2015
18892^411052+1872481123739Enzo Doria05/2016
18902^410997+39123723Lelio R Paula05/2014
18912^410596-39123602Lelio R Paula05/2014
18922^410540-115079123585Enzo Doria06/2015
1893(3*2^410392-1)/9229123537Lelio R Paula05/2014
18942^410206-113081123485Enzo Doria07/2014
1895(25*2^410192+1)/10397123478Lelio R Paula04/2014
18962^409909-189123395Enzo Doria05/2014
18972^409896-109043123391Enzo Doria04/2014
18982^409890+75409123390Enzo Doria04/2016
1899133^58076-2123345Lelio R Paula10/2017
1900F(590041)123311Henri Lifchitz01/2005
19012^409566-113501123292Enzo Doria08/2014
19022^409533+77747123282Enzo Doria05/2016
19032^409436-112799123253Enzo Doria06/2014
19042^409225+1873787123189Enzo Doria06/2016
19052^409174+73009123174Enzo Doria04/2016
19062^409058-112685123139Enzo Doria06/2014
19072^408778+77689123055Enzo Doria05/2016
19082^408690-75123028Lelio R Paula11/2013
19092^408574-2787341122994Enzo Doria03/2016
1910Phi(157825,10)122961Maksym Voznyy06/2015
1911(13*2^408283+1)/1665122904Lelio R Paula05/2014
1912(11*2^408100-1)/35122850Lelio R Paula04/2014
1913(2^407821-lucasV(1,2,407821)+1)/2122767Mike Oakes11/2016
1914(21*2^407604-1)/215122701Lelio R Paula04/2014
1915(21*2^407433-1)/13122650Lelio R Paula04/2014
1916(73*10^122592-1)/9122593Robert Price01/2015
19172^407179-112075122574Enzo Doria06/2014
1918(21*2^407131+1)/207517523122552Lelio R Paula04/2014
1919(66^67349+1)/67122543Paul Bourdelais09/2017
19202^407008-1867919122522Enzo Doria04/2016
192111^117642-300122512Enzo Doria10/2012
1922(F(3*97700+1)^2+L(3*97700+1)^2)/2122509Henri Lifchitz10/2017
19232^406949+72197122504Enzo Doria04/2016
19242^406826-65122467Lelio R Paula11/2013
19252^406821-2797363122466Enzo Doria04/2016
19262^406758-17122447Lelio R Paula11/2013
1927(30^82883-1)/29122427Robert Price12/2011
1928(2^406583-1)/813167122388Jens K. Andersen02/2009
192997^61575-2122336Lelio R Paula12/2014
19302^406298+2799109122308Enzo Doria04/2016
1931(27*2^406241-1)/10277122289Lelio R Paula04/2014
19322^406229-1849993122288Enzo Doria08/2015
19333*10^122274+7122275Robert Price07/2015
19342^406117+1876577122254Enzo Doria07/2016
19353^256199-2^256199122238Mike Oakes06/2005
19362^405774+179149122151Enzo Doria06/2016
19372^405514-3311122072Yves Minet12/2014
19382^405514-115511122072Enzo Doria07/2015
19392^405422-113261122045Enzo Doria07/2014
19402^405173+71237121970Enzo Doria04/2016
1941(2^405016+1)/257121920Lelio R Paula04/2014
19422^404858+71329121875Enzo Doria04/2016
19432^404813-114703121861Enzo Doria04/2015
19442^404764+77791121847Enzo Doria05/2016
1945317^48694+48694^317121787Norbert Schneider08/2015
19462^404536-115259121778Enzo Doria06/2015
19472^404501-631121767Yves Minet07/2012
194863^67620+2121672Lelio R Paula08/2015
1949(17*10^121621+1)/9121622Serge Batalov05/2010
1950(15*2^403912+1)/271121589Lelio R Paula05/2014
1951(10^121543-79)/3121543Robert Price01/2018
19522^403676+76831121519Enzo Doria05/2016
19532^403363-113635121425Enzo Doria08/2014
19542^403336-1861469121417Enzo Doria03/2016
1955p(24442)#/2-64121381Robert Price04/2017
195611^116555-720121380Enzo Doria11/2012
19572^403100-461267121346Enzo Doria07/2015
19582^403093-112213121344Enzo Doria06/2014
1959(316^48539+1)/317121330Eric Chen10/2017
19602^403004+1866361121317Enzo Doria03/2016
19612^402953+89121301Lelio R Paula10/2013
19622^402944-2788319121299Enzo Doria03/2016
1963(27*2^402865+1)/5121276Lelio R Paula04/2014
19642^402828-113183121264Enzo Doria07/2014
1965(17*10^121242+1)/9121243Serge Batalov05/2010
1966(15*2^402757+1)/101121242Lelio R Paula05/2014
19672^402715+1874223121230Enzo Doria06/2016
1968(91^61879+1)/92121222Paul Bourdelais09/2017
19697*10^121144+9121145Robert Price09/2015
19702^401725-113251120932Enzo Doria07/2014
1971(15*2^401677-1)/19120917Lelio R Paula05/2014
19722^401652+73711120910Enzo Doria04/2016
1973(2^401632+3)/79120902Lelio R Paula04/2014
19742^401406-2791331120836Enzo Doria03/2016
1975(28^83497+1)/29120832Robert Price07/2013
19762^401369+1867367120825Enzo Doria03/2016
1977(10^120782+29)/3120782Serge Batalov12/2014
19782^401215-1657120778Yves Minet07/2014
19792^401159+53120761Lelio R Paula10/2013
19802^401031-113047120723Enzo Doria07/2014
1981(29*2^400909-1)/303120685Lelio R Paula04/2014
19822^400571-15120584Lelio R Paula10/2013
1983(10^120574+359)/9120574Serge Batalov12/2014
19842^400424-216413120540Enzo Doria04/2013
1985(17*2^400200-1)/587120471Lelio R Paula05/2014
19862^400166+1874899120462Enzo Doria06/2016
1987(3*2^400045-1)/865120424Lelio R Paula04/2014
19882^399966+73759120402Enzo Doria04/2016
1989(112*10^120395-1)/3120397Serge Batalov12/2014
19902^399918-95120388Lelio R Paula04/2013
19912^399792-1849259120350Enzo Doria08/2015
19929*10^120342-7120343Robert Price09/2015
19932^399526-1861721120270Enzo Doria11/2015
1994(10^(2*60126+1)+36*10^60126-1)/9120253Robert Price10/2015
19952^399322-2798111120208Enzo Doria04/2016
199672^64693-71^64693120157Robert Price03/2014
19972^399111-28489120145Enzo Doria08/2015
19992^398877+105120074Donovan Johnson01/2006
1998(101*10^120072-87)/7120074Hans Havermann02/2015
2000(88^61751+1)/89120072Paul Bourdelais09/2017


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 20 2018 10:36 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!