PRP Records

Probable Primes Top 10000

(173006 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 ?
15012^442430-2791721133185Enzo Doria03/2016
1502(13*2^442428-1)/309133183Lelio R Paula07/2015
1503(25*2^442379-1)/71133169Lelio R Paula07/2015
1504(2^441799+78557)/5132995Lelio R Paula07/2015
15052^441781-2787883132990Enzo Doria03/2016
1506(3*2^441685+1)/749132959Lelio R Paula07/2015
15072^441521-113575132912Enzo Doria08/2014
15082^441330+1871959132854Enzo Doria05/2016
15092^441063+383132774Lelio R Paula06/2012
15102^440846+1870909132708Enzo Doria05/2016
15112^440656-113489132651Enzo Doria08/2014
1512numbpart(14180123587)132646Serge Batalov04/2017
1513(2^440399-1)/(16210820281161978209*31518475633*880799)132538Dario Alpern01/2015
1514(38^83891+1)/39132529Robert Price09/2013
151547^79201-46^79201132432Robert Price10/2012
15162^439897-113653132423Enzo Doria08/2014
1517(5*2^439822+1)/9132400Lelio R Paula06/2015
1518(112*10^132337-1)/3132339Serge Batalov12/2014
15192^439576-113247132326Enzo Doria07/2014
15202^439497-29143132302Enzo Doria07/2015
15212^439409-114193132276Enzo Doria12/2014
15229*10^132148-7132149Robert Price09/2015
15232^438845+1870217132106Enzo Doria05/2016
15242^438789+87855132089Lelio R Paula01/2016
15252^438774-2786411132085Enzo Doria03/2016
15262^438755-1848205132079Enzo Doria07/2015
15272^438739-112087132074Enzo Doria06/2014
1528L(631181)131910Henri Lifchitz09/2008
1529(3*2^438121+1)/4308193883131879Lelio R Paula06/2015
15302^438079-1863877131875Enzo Doria03/2016
1531(2^438067+5)/329131869Lelio R Paula06/2015
15322^437908-113855131824Enzo Doria09/2014
15332^437884-286349131817Enzo Doria07/2015
15343^276062-112292131716Enzo Doria07/2014
15352^437343+75953131654Enzo Doria04/2016
153635^85243-34^85243131621Robert Price05/2012
15372^436451+1884713131385Enzo Doria03/2017
15382^436365+35131359Robert Price11/2015
15392^436300+1866871131340Enzo Doria03/2016
1540(23*2^435891-1)/699131215Lelio R Paula07/2015
1541(11*2^435879+1)/3337131211Lelio R Paula06/2015
1543(2^435808+1)/641/6700417131182Lelio R Paula02/2012
1542(2^435808+1)/4294967297131182Serge Batalov12/2016
15442^435773+1875557131181Enzo Doria06/2016
15452^435612-2789939131133Enzo Doria12/2015
154666^72047-65^72047131093Robert Price09/2013
15472^435468+75631131089Enzo Doria04/2016
154837^83588-2131083Lelio R Paula08/2015
1549(4^217720+11)/3131081Robert Price02/2017
15502^435202-113193131009Enzo Doria07/2014
15512^434835-111937130899Enzo Doria05/2014
15522^434685+72257130854Enzo Doria04/2016
15532^434539-29317130810Enzo Doria07/2015
15542^434469-114259130789Enzo Doria01/2015
15552^434246+33130722Robert Price11/2015
15562^433744-114419130570Enzo Doria02/2015
15572^433708+1869451130560Enzo Doria05/2016
1558(29*2^433547-1)/27130511Lelio R Paula06/2015
15594*10^130480+9130481Robert Price05/2015
1560(23*2^433449-1)/75130481Lelio R Paula06/2015
1561(23*2^433334-1)/3731130445Lelio R Paula06/2015
15622^433023-113497130353Enzo Doria08/2014
15632^433002+1179379130347Enzo Doria06/2016
15642^432974+19130339Robert Price08/2015
1565(2^432457-1)/1672739247834685086279697130159Tony Prest / Never Odd Or Even09/2013
1566(2^216089*(2^216091-1)-339)/25130098Makoto Morimoto03/2017
1567((2^216091+1066)^2+(2^216091+1066)+41)/47/2069130095Makoto Morimoto05/2016
156897^65480-2130094Lelio R Paula05/2017
15692^432117-113215130081Enzo Doria07/2014
15702^431804+72511129986Enzo Doria04/2016
1571(3^272141-3^136071+1)/7129844Serge Batalov03/2014
1572(9*2^431141+1)/17129787Lelio R Paula06/2015
1573(29*2^430881-1)/21129709Lelio R Paula06/2015
15742^430807+1869563129686Enzo Doria05/2016
15752^430721-21429129660Enzo Doria07/2013
15762^430415-276271129568Enzo Doria07/2015
15772^430142-2791721129486Enzo Doria03/2016
15782^429568-21017129313Enzo Doria07/2013
15792^429194-112685129201Enzo Doria06/2014
15802^429145-2780449129186Enzo Doria04/2016
15812^428892-113453129110Enzo Doria07/2014
1582(11*2^428881-7)/15129106Renaud Lifchitz03/2011
15832^428727-113959129060Enzo Doria10/2014
1584(7*2^428725-1)/13129059Lelio R Paula05/2014
1585(10^129051-31)/3129051Serge Batalov12/2014
15862^428564+71161129011Enzo Doria04/2016
15872^428502-113285128992Enzo Doria07/2014
15882^428421-21373128968Enzo Doria06/2013
1589L(616787)128901Henri Lifchitz09/2008
159091^65772-2128851Lelio R Paula05/2017
15912^427999-459397128841Enzo Doria05/2015
15922^427993+76847128839Enzo Doria05/2016
15932^427824-1851507128788Enzo Doria08/2015
15942^427807-21469128783Enzo Doria07/2013
159511^123594-240128710Enzo Doria09/2012
15962^427504-21503128692Enzo Doria07/2013
15972^427269-113635128621Enzo Doria08/2014
15982^427130+1877569128579Enzo Doria08/2016
15992^427016-115349128545Enzo Doria07/2015
16002^426889-112879128507Enzo Doria06/2014
16012^426804+1869931128481Enzo Doria05/2016
16022^426750+77635128465Enzo Doria05/2016
1603(15*2^426398-1)/11128359Lelio R Paula05/2014
16042^426352+74971128345Enzo Doria04/2016
16052^426300-1863689128330Enzo Doria03/2016
16062^426293+1881017128327Enzo Doria11/2016
16072^426043+35128252Robert Price11/2015
16082^425808-459959128181Enzo Doria06/2015
16092^425627-113605128127Enzo Doria08/2014
161018565^30002-30002^18565128070Norbert Schneider01/2015
1611(2^425287-9)/2737128021Lelio R Paula05/2015
1612(3*2^425233-1)/25128007Lelio R Paula05/2014
16132^425205+4911128000Marek Hubal02/2017
16142^425118-113663127974Enzo Doria08/2014
16152^425061+1869761127957Enzo Doria05/2016
16162^424918-21141127914Enzo Doria07/2013
16172^424864-29489127897Enzo Doria08/2015
1618(97*10^127858-1)/3127860Serge Batalov12/2014
16192^424632-2786639127827Enzo Doria03/2016
16202^424577-113755127811Enzo Doria09/2014
1621(7*2^424512-1)/3127792Lelio R Paula05/2014
162211^122629-720127705Enzo Doria11/2012
16232^423696-21429127546Enzo Doria07/2013
16242^423664-1864559127536Enzo Doria03/2016
16253^267267-4127519Henri Lifchitz10/2014
1626(19^99689+5^99689)/24127477Robert Price09/2013
1627(21*2^423372+1)/101127447Lelio R Paula05/2014
16282^423328-21537127435Enzo Doria07/2013
1629(2^423165-7)/25127384Lelio R Paula05/2015
1630(F(5)^182099-F(4)^182099)/F(3)127282Wayne Halsdorf08/2013
1631(234483*27^88884-145)/26127230Curtis Bright05/2015
16322^422515-114997127190Enzo Doria06/2015
16335*10^127179-3127180Robert Price07/2015
16342^421860-113285126993Enzo Doria07/2014
1635(2^421827-7)/11126982Lelio R Paula05/2015
163611^121910-840126957Enzo Doria12/2012
1637331^50339-10004126846Enzo Doria07/2012
16382^421363-2790757126843Enzo Doria03/2016
1639(106*10^126839-1)/3126841Serge Batalov12/2014
1640(7*2^421243+1)/39126807Lelio R Paula05/2014
16412^421161-286183126783Enzo Doria06/2015
16422^420939-113935126716Enzo Doria10/2014
16432^420741-113659126656Enzo Doria08/2014
16442^420694-21126642Lelio R Paula05/2017
1645(31*2^420556+1)/7126601Lelio R Paula05/2014
16462^420424-59189126561Enzo Doria10/2015
16472^420126+71893126471Enzo Doria04/2016
16482^419866+1877059126393Enzo Doria07/2016
1649F(604711)126377Henri Lifchitz02/2005
16502^419757+72707126360Enzo Doria04/2016
16512^419720-21569126349Enzo Doria07/2013
16522^419637+29126324Henri Lifchitz02/2006
16532^419612+1876741126316Enzo Doria07/2016
16542^419520+2793271126289Enzo Doria03/2016
1655(2^419447-5)/369126264Lelio R Paula05/2014
16562^419328-1859939126231Enzo Doria03/2016
16572^419282-1851507126217Enzo Doria08/2015
16582^419251+1866143126208Enzo Doria03/2016
165911^121185+2126202Robert Price05/2014
1660(23*2^419036-1)/1393126141Lelio R Paula05/2014
16612^418851+23126087Robert Price09/2015
1662(2^418849-9)/2681126083Lelio R Paula05/2014
16632^418829+167126081Lelio R Paula01/2012
1664(31*2^418782-1)/75891126063Lelio R Paula05/2014
1665(19*2^418754-1)/15126058Lelio R Paula05/2014
16662^418319-109501125927Enzo Doria04/2014
16672^418316-112373125926Enzo Doria06/2014
16682^417968+1869811125821Enzo Doria06/2016
16692^417902+63125802Lelio R Paula09/2015
1670(10^125792-91)/9125792Serge Batalov12/2014
16712^417704+77011125742Enzo Doria05/2016
1672(10^125706+149)/3125706Serge Batalov12/2014
16732^417419-115309125656Enzo Doria07/2015
16742^417300+77281125620Enzo Doria05/2016
16752^417095-1657125559Yves Minet07/2014
16762^416773-25125462Lelio R Paula09/2015
1677(11*2^416691+1)/43125436Lelio R Paula05/2014
1678(21*2^416566-1)/17125399Lelio R Paula05/2014
16792^416530+1870429125389Enzo Doria05/2016
16802^416490+1875109125376Enzo Doria09/2016
16812^416416-114929125354Enzo Doria05/2015
1682(172*10^125292-1)/9125294Serge Batalov12/2014
16832^416134+1865899125269Enzo Doria03/2016
1684(9*2^415992+1)/13560845125220Lelio R Paula05/2014
1685(23^91943-1)/22125201Robert Price01/2012
168643125^27010-106125185Enzo Doria08/2012
16872^415765-112603125158Enzo Doria06/2014
16882^415290-113591125015Enzo Doria08/2014
16892^415276-460919125011Enzo Doria06/2015
16902^415259+77243125006Enzo Doria05/2016
16912^415144-3683124971Yves Minet10/2011
16922^414874+79124890Lelio R Paula01/2015
1693(2^414765+7)/1389124854Lelio R Paula05/2014
16942^414618+79459124813Enzo Doria06/2016
16952^414432-1846709124757Enzo Doria07/2015
1696(13*2^414274-1)/153124708Lelio R Paula05/2014
16972^414032-5124637Henri Lifchitz07/2006
16982^414032+1872331124637Enzo Doria05/2016
169914120^30009-30009^14120124533Norbert Schneider02/2015
170064^68909-63^68909124463Robert Price07/2013
17012^413387+76253124442Enzo Doria04/2016
1702287117#+391613124424Nicolas PALAU01/2017
1703(27*2^413207-1)/108335124385Lelio R Paula05/2014
17042^412868-120599124286Paul Bourdelais02/2012
170545^75145-2124231Lelio R Paula08/2015
17062^412645-112213124219Enzo Doria06/2014
17072^412248+74611124100Enzo Doria04/2016
17082^412192-3329124083Yves Minet12/2014
1709(25*2^412191-1)/23124082Lelio R Paula05/2014
1710F(593689)124074Henri Lifchitz01/2005
1711(11*2^412161+1)/19124073Lelio R Paula05/2014
17122^411884-113279123990Enzo Doria07/2014
1713(2^411832+1)/257123972Lelio R Paula05/2014
17142^411790-1853531123962Enzo Doria08/2015
1715(5^177337+1)/6123953Paul Bourdelais11/2008
17162^411711-113257123938Enzo Doria07/2014
1717(23*2^411675-1)/3123928Lelio R Paula05/2014
17182^411325-351103123822Enzo Doria06/2015
17192^411052+1872481123739Enzo Doria05/2016
17202^410997+39123723Lelio R Paula05/2014
17212^410596-39123602Lelio R Paula05/2014
17222^410540-115079123585Enzo Doria06/2015
1723(3*2^410392-1)/9229123537Lelio R Paula05/2014
17242^410206-113081123485Enzo Doria07/2014
1725(25*2^410192+1)/10397123478Lelio R Paula04/2014
17262^409909-189123395Enzo Doria05/2014
17272^409896-109043123391Enzo Doria04/2014
17282^409890+75409123390Enzo Doria04/2016
1729F(590041)123311Henri Lifchitz01/2005
17302^409566-113501123292Enzo Doria08/2014
17312^409533+77747123282Enzo Doria05/2016
17322^409436-112799123253Enzo Doria06/2014
17332^409225+1873787123189Enzo Doria06/2016
17342^409174+73009123174Enzo Doria04/2016
17352^409058-112685123139Enzo Doria06/2014
17362^408778+77689123055Enzo Doria05/2016
17372^408690-75123028Lelio R Paula11/2013
17382^408574-2787341122994Enzo Doria03/2016
1739Phi(157825,10)122961Maksym Voznyy06/2015
1740(13*2^408283+1)/1665122904Lelio R Paula05/2014
1741(11*2^408100-1)/35122850Lelio R Paula04/2014
1742(2^407821-lucasV(1,2,407821)+1)/2122767Mike Oakes11/2016
1743(21*2^407604-1)/215122701Lelio R Paula04/2014
1744(21*2^407433-1)/13122650Lelio R Paula04/2014
1745(73*10^122592-1)/9122593Robert Price01/2015
17462^407179-112075122574Enzo Doria06/2014
1747(21*2^407131+1)/207517523122552Lelio R Paula04/2014
17482^407008-1867919122522Enzo Doria04/2016
174911^117642-300122512Enzo Doria10/2012
17502^406949+72197122504Enzo Doria04/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 25 2017 10:58 (Time in France)

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