PRP Records

Probable Primes Top 10000

(205869 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 ?
1751(11*2^435879+1)/3337131211Lelio R Paula06/2015
1753(2^435808+1)/641/6700417131182Lelio R Paula02/2012
1752(2^435808+1)/4294967297131182Serge Batalov12/2016
17542^435773+1875557131181Enzo Doria06/2016
17552^435612-2789939131133Enzo Doria12/2015
175666^72047-65^72047131093Robert Price09/2013
1757(5*10^131090+37)/3131091Robert Price03/2018
17582^435468+75631131089Enzo Doria04/2016
175937^83588-2131083Lelio R Paula08/2015
1760(4^217720+11)/3131081Robert Price02/2017
17612^435202-113193131009Enzo Doria07/2014
1762floor((sqrt(5)-1)/2*10^130911)130911Serge Batalov06/2017
17632^434835-111937130899Enzo Doria05/2014
17642^434685+72257130854Enzo Doria04/2016
1765(7*10^130825+113)/3130826Robert Price02/2018
17662^434539-29317130810Enzo Doria07/2015
17672^434469-114259130789Enzo Doria01/2015
17682^434246+33130722Robert Price11/2015
17692^433911-91130621Lelio R Paula06/2017
17702^433744-114419130570Enzo Doria02/2015
17712^433708+1869451130560Enzo Doria05/2016
17722^433710+93130560Lelio R Paula06/2017
1773(29*2^433547-1)/27130511Lelio R Paula06/2015
17744*10^130480+9130481Robert Price05/2015
1775(23*2^433449-1)/75130481Lelio R Paula06/2015
1776(23*2^433334-1)/3731130445Lelio R Paula06/2015
17772^433023-113497130353Enzo Doria08/2014
17782^433002+1179379130347Enzo Doria06/2016
17792^432974+19130339Robert Price08/2015
1780(2^432457-1)/1672739247834685086279697130159Tony Prest / Never Odd Or Even09/2013
17812^432217+41130111Lelio R Paula06/2017
1782(2^216089*(2^216091-1)-339)/25130098Makoto Morimoto03/2017
1783((2^216091+1066)^2+(2^216091+1066)+41)/47/2069130095Makoto Morimoto05/2016
178497^65480-2130094Lelio R Paula05/2017
17852^432117-113215130081Enzo Doria07/2014
17862^431804+72511129986Enzo Doria04/2016
1787(3^272141-3^136071+1)/7129844Serge Batalov03/2014
1788(9*2^431141+1)/17129787Lelio R Paula06/2015
1789(29*2^430881-1)/21129709Lelio R Paula06/2015
17902^430807+1869563129686Enzo Doria05/2016
17912^430721-21429129660Enzo Doria07/2013
17922^430415-276271129568Enzo Doria07/2015
17932^430142-2791721129486Enzo Doria03/2016
17942^429568-21017129313Enzo Doria07/2013
17952^429194-112685129201Enzo Doria06/2014
17962^429145-2780449129186Enzo Doria04/2016
17972^428892-113453129110Enzo Doria07/2014
1798(11*2^428881-7)/15129106Renaud Lifchitz03/2011
17992^428727-113959129060Enzo Doria10/2014
1800(7*2^428725-1)/13129059Lelio R Paula05/2014
1801(10^129051-31)/3129051Serge Batalov12/2014
18022^428564+71161129011Enzo Doria04/2016
18032^428502-113285128992Enzo Doria07/2014
18042^428421-21373128968Enzo Doria06/2013
1805L(616787)128901Henri Lifchitz09/2008
180691^65772-2128851Lelio R Paula05/2017
18072^428022+43128848Lelio R Paula05/2017
18082^427999-459397128841Enzo Doria05/2015
18092^427993+76847128839Enzo Doria05/2016
18102^427824-1851507128788Enzo Doria08/2015
18112^427807-21469128783Enzo Doria07/2013
181211^123594-240128710Enzo Doria09/2012
18132^427504-21503128692Enzo Doria07/2013
18142^427420+91128667Lelio R Paula05/2017
18152^427269-113635128621Enzo Doria08/2014
18162^427130+1877569128579Enzo Doria08/2016
18172^427016-115349128545Enzo Doria07/2015
1818(4*10^128510+137)/3128511Robert Price03/2018
18192^426889-112879128507Enzo Doria06/2014
18202^426804+1869931128481Enzo Doria05/2016
18212^426750+77635128465Enzo Doria05/2016
18222^426425-91128367Lelio R Paula05/2017
1823(15*2^426398-1)/11128359Lelio R Paula05/2014
18242^426352+74971128345Enzo Doria04/2016
18252^426300-1863689128330Enzo Doria03/2016
18262^426293+1881017128327Enzo Doria11/2016
18272^426043+35128252Robert Price11/2015
1828(4*10^128244-19)/3128245Robert Price03/2018
18292^425808-459959128181Enzo Doria06/2015
18302^425627-113605128127Enzo Doria08/2014
183118565^30002-30002^18565128070Norbert Schneider01/2015
1832(2^425287-9)/2737128021Lelio R Paula05/2015
1833(3*2^425233-1)/25128007Lelio R Paula05/2014
18342^425205+4911128000Marek Hubal02/2017
18352^425118-113663127974Enzo Doria08/2014
18362^425061+1869761127957Enzo Doria05/2016
18372^424918-21141127914Enzo Doria07/2013
18382^424864-29489127897Enzo Doria08/2015
1839(97*10^127858-1)/3127860Serge Batalov12/2014
18402^424632-2786639127827Enzo Doria03/2016
18412^424577-113755127811Enzo Doria09/2014
1842(7*2^424512-1)/3127792Lelio R Paula05/2014
184311^122629-720127705Enzo Doria11/2012
18442^423696-21429127546Enzo Doria07/2013
18452^423664-1864559127536Enzo Doria03/2016
18463^267267-4127519Henri Lifchitz10/2014
1847(19^99689+5^99689)/24127477Robert Price09/2013
1848(21*2^423372+1)/101127447Lelio R Paula05/2014
18492^423328-21537127435Enzo Doria07/2013
1850(2^423165-7)/25127384Lelio R Paula05/2015
1851(F(5)^182099-F(4)^182099)/F(3)127282Wayne Halsdorf08/2013
1852(234483*27^88884-145)/26127230Curtis Bright05/2015
18532^422515-114997127190Enzo Doria06/2015
18545*10^127179-3127180Robert Price07/2015
1855-516776642557847117490*Bern(37960)/34256837217082767928421792453127042Thomas Ritschel06/2017
1856(78^67141-1)/77127036Paul Bourdelais09/2017
18572^421860-113285126993Enzo Doria07/2014
1858(2^421827-7)/11126982Lelio R Paula05/2015
185911^121910-840126957Enzo Doria12/2012
1860(71^68539+1)/72126882Paul Bourdelais09/2017
1861(5*10^126871-119)/3126872Robert Price03/2018
1862331^50339-10004126846Enzo Doria07/2012
18632^421363-2790757126843Enzo Doria03/2016
1864(106*10^126839-1)/3126841Serge Batalov12/2014
1865(7*2^421243+1)/39126807Lelio R Paula05/2014
18662^421161-286183126783Enzo Doria06/2015
18672^420939-113935126716Enzo Doria10/2014
1868177^56363-2126703Lelio R Paula10/2017
18692^420741-113659126656Enzo Doria08/2014
18702^420694-21126642Lelio R Paula05/2017
1871(13*10^126638+437)/9126639Robert Price04/2018
1872(31*2^420556+1)/7126601Lelio R Paula05/2014
18732^420424-59189126561Enzo Doria10/2015
18742^420126+71893126471Enzo Doria04/2016
18752^419866+1877059126393Enzo Doria07/2016
1876F(604711)126377Henri Lifchitz02/2005
18772^419757+72707126360Enzo Doria04/2016
18782^419720-21569126349Enzo Doria07/2013
18792^419637+29126324Henri Lifchitz02/2006
18802^419612+1876741126316Enzo Doria07/2016
18812^419520+2793271126289Enzo Doria03/2016
1882(2^419447-5)/369126264Lelio R Paula05/2014
18832^419328-1859939126231Enzo Doria03/2016
18842^419282-1851507126217Enzo Doria08/2015
18852^419251+1866143126208Enzo Doria03/2016
188611^121185+2126202Robert Price05/2014
1887(23*2^419036-1)/1393126141Lelio R Paula05/2014
18882^418851+23126087Robert Price09/2015
1889(2^418849-9)/2681126083Lelio R Paula05/2014
18902^418829+167126081Lelio R Paula01/2012
1891(31*2^418782-1)/75891126063Lelio R Paula05/2014
1892(19*2^418754-1)/15126058Lelio R Paula05/2014
18932^418319-109501125927Enzo Doria04/2014
18942^418316-112373125926Enzo Doria06/2014
18952^417968+1869811125821Enzo Doria06/2016
18962^417902+63125802Lelio R Paula09/2015
1897(10^125792-91)/9125792Serge Batalov12/2014
18982^417704+77011125742Enzo Doria05/2016
1899(10^125706+149)/3125706Serge Batalov12/2014
19002^417419-115309125656Enzo Doria07/2015
19012^417300+77281125620Enzo Doria05/2016
19022^417095-1657125559Yves Minet07/2014
19032^416773-25125462Lelio R Paula09/2015
1904(289511#+292834)/(2^3*146417)125444Makoto Morimoto10/2017
1905(11*2^416691+1)/43125436Lelio R Paula05/2014
1906(21*2^416566-1)/17125399Lelio R Paula05/2014
19072^416530+1870429125389Enzo Doria05/2016
19082^416490+1875109125376Enzo Doria09/2016
19092^416416-114929125354Enzo Doria05/2015
1910(172*10^125292-1)/9125294Serge Batalov12/2014
19112^416134+1865899125269Enzo Doria03/2016
1912(9*2^415992+1)/13560845125220Lelio R Paula05/2014
1913(23^91943-1)/22125201Robert Price01/2012
191443125^27010-106125185Enzo Doria08/2012
19152^415765-112603125158Enzo Doria06/2014
19162^415290-113591125015Enzo Doria08/2014
19172^415276-460919125011Enzo Doria06/2015
19182^415259+77243125006Enzo Doria05/2016
19192^415144-3683124971Yves Minet10/2011
19202^414874+79124890Lelio R Paula01/2015
1921(2^414765+7)/1389124854Lelio R Paula05/2014
19222^414618+79459124813Enzo Doria06/2016
19232^414432-1846709124757Enzo Doria07/2015
19242*10^124751-51124752Robert Price04/2018
1925(13*2^414274-1)/153124708Lelio R Paula05/2014
19272^414032-5124637Henri Lifchitz07/2006
19262^414032+1872331124637Enzo Doria05/2016
192814120^30009-30009^14120124533Norbert Schneider02/2015
192964^68909-63^68909124463Robert Price07/2013
19302^413387+76253124442Enzo Doria04/2016
1931287117#+391613124424Nicolas PALAU01/2017
1932(4*10^124420+83)/3124421Robert Price02/2018
1933(27*2^413207-1)/108335124385Lelio R Paula05/2014
19342^412868-120599124286Paul Bourdelais02/2012
193545^75145-2124231Lelio R Paula08/2015
19362^412645-112213124219Enzo Doria06/2014
19372^412248+74611124100Enzo Doria04/2016
19382^412192-3329124083Yves Minet12/2014
1939(25*2^412191-1)/23124082Lelio R Paula05/2014
1940F(593689)124074Henri Lifchitz01/2005
1941(11*2^412161+1)/19124073Lelio R Paula05/2014
19422^411884-113279123990Enzo Doria07/2014
1943(2^411832+1)/257123972Lelio R Paula05/2014
19442^411790-1853531123962Enzo Doria08/2015
1945(5^177337+1)/6123953Paul Bourdelais11/2008
19462^411711-113257123938Enzo Doria07/2014
1947(23*2^411675-1)/3123928Lelio R Paula05/2014
19482^411325-351103123822Enzo Doria06/2015
19492^411052+1872481123739Enzo Doria05/2016
19502^410997+39123723Lelio R Paula05/2014
19512^410596-39123602Lelio R Paula05/2014
19522^410540-115079123585Enzo Doria06/2015
1953(7*10^123563+107)/3123564Robert Price02/2018
1954(3*2^410392-1)/9229123537Lelio R Paula05/2014
19552^410206-113081123485Enzo Doria07/2014
1956(25*2^410192+1)/10397123478Lelio R Paula04/2014
19572^409909-189123395Enzo Doria05/2014
19582^409896-109043123391Enzo Doria04/2014
19592^409890+75409123390Enzo Doria04/2016
1960133^58076-2123345Lelio R Paula10/2017
1961F(590041)123311Henri Lifchitz01/2005
19622^409566-113501123292Enzo Doria08/2014
19632^409533+77747123282Enzo Doria05/2016
19642^409436-112799123253Enzo Doria06/2014
19652^409225+1873787123189Enzo Doria06/2016
19662^409174+73009123174Enzo Doria04/2016
19672^409058-112685123139Enzo Doria06/2014
19682^408778+77689123055Enzo Doria05/2016
19692^408690-75123028Lelio R Paula11/2013
19702^408574-2787341122994Enzo Doria03/2016
1971Phi(157825,10)122961Maksym Voznyy06/2015
1972(13*2^408283+1)/1665122904Lelio R Paula05/2014
1973(11*2^408100-1)/35122850Lelio R Paula04/2014
1974(2^407821-lucasV(1,2,407821)+1)/2122767Mike Oakes11/2016
1975(21*2^407604-1)/215122701Lelio R Paula04/2014
1976(21*2^407433-1)/13122650Lelio R Paula04/2014
1977(73*10^122592-1)/9122593Robert Price01/2015
19782^407179-112075122574Enzo Doria06/2014
1979(21*2^407131+1)/207517523122552Lelio R Paula04/2014
1980(66^67349+1)/67122543Paul Bourdelais09/2017
19812^407008-1867919122522Enzo Doria04/2016
198211^117642-300122512Enzo Doria10/2012
1983(F(3*97700+1)^2+L(3*97700+1)^2)/2122509Henri Lifchitz10/2017
19842^406949+72197122504Enzo Doria04/2016
19852^406826-65122467Lelio R Paula11/2013
19862^406821-2797363122466Enzo Doria04/2016
19872^406758-17122447Lelio R Paula11/2013
1988(30^82883-1)/29122427Robert Price12/2011
1989(2^406583-1)/813167122388Jens K. Andersen02/2009
199097^61575-2122336Lelio R Paula12/2014
19912^406298+2799109122308Enzo Doria04/2016
1992(27*2^406241-1)/10277122289Lelio R Paula04/2014
19932^406229-1849993122288Enzo Doria08/2015
19943*10^122274+7122275Robert Price07/2015
19952^406117+1876577122254Enzo Doria07/2016
19963^256199-2^256199122238Mike Oakes06/2005
19972^405992-78557122216Jorge Menendez03/2018
19982^405774+179149122151Enzo Doria06/2016
19992^405514-3311122072Yves Minet12/2014
20002^405514-115511122072Enzo Doria07/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 22 2018 09:48 (Time in France)

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