PRP Records

Probable Primes Top 10000

(172751 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 ?
2001(27*2^376441-1)/811113319Lelio R Paula03/2014
20022^376128-21237113226Enzo Doria06/2013
20032^375638-1787171113079Enzo Doria03/2016
20042^375537+4847113048Yves Minet02/2011
2005(17^91837+16^91837)/33113000Robert Price08/2013
20065*F(270343)*(F(270343)+1)+1112997Serge Batalov04/2015
20072^375350-3221112992Yves Minet07/2011
2008(13*2^375306+1)/7112979Lelio R Paula03/2014
20092^375305+76757112979Enzo Doria05/2016
20102^375258+1874989112964Enzo Doria07/2016
2011(29^77237-1)/28112950Robert Price04/2012
20122^375154+74959112933Enzo Doria04/2016
20132^374993-2787163112885Enzo Doria11/2015
2014123^53970+2112793Lelio R Paula06/2013
20152^374441-21049112718Enzo Doria06/2013
2016(2^374321+1)/3112682H.&R. Lifchitz12/2000
2017(13^101089-1)/12112607Paul Bourdelais03/2010
20183^236011-8828112606Enzo Doria05/2014
201939^70666+2112435Lelio R Paula11/2013
2020(2^373350-7)/3112390Lelio R Paula03/2014
20212^373306-1840931112377Enzo Doria06/2015
20222^373117+1872107112320Enzo Doria05/2016
20232^373040+2792761112297Enzo Doria03/2016
2024EPrime(112280)112280Eric W. Weisstein10/2010
20252^372950+7112270Lelio R Paula03/2013
20262^372945+1872167112268Enzo Doria05/2016
20272^372695+72113112193Enzo Doria04/2016
20282^372689-2563112191Yves Minet07/2014
20292^372638-1859441112176Enzo Doria03/2016
20303^235074-113056112159Enzo Doria07/2014
2031(91*10^112098-1)/9112100Robert Price04/2015
20322^372310-85061112077Paul Bourdelais02/2012
2033(10^112067+53)/9112067Serge Batalov07/2015
203475^59760+2112054Lelio R Paula08/2013
20352^372108+74221112016Enzo Doria04/2016
20362^371970-459491111975Enzo Doria05/2015
203741^69427-40^69427111971Robert Price07/2012
2038(10^111902+71)/9111902Serge Batalov07/2015
20392^371440-112865111815Enzo Doria06/2014
20402^371426-459161111811Enzo Doria05/2015
20412^371276-461267111766Enzo Doria07/2015
20422^371098-113261111712Enzo Doria07/2014
2043(7*10^111706-61)/9111706Erik Branger01/2011
20442^371044+1869391111696Enzo Doria05/2016
204588^57416+87111645Norbert Schneider11/2015
20462^370829-109693111631Enzo Doria04/2014
204715^94906-2111619Lelio R Paula11/2013
20492^370643-37111575Yves Minet01/2012
2048(2^370655-5)/2439111575Lelio R Paula03/2014
2050286^45405+45405^286111532Norbert Schneider04/2015
20514*5^159563-9111531Lelio R Paula11/2014
20522^370393-2797093111500Enzo Doria03/2016
2053(21*2^370382-1)/629111495Lelio R Paula03/2014
20542^370292-2791979111469Enzo Doria03/2016
20552^370177-461551111435Enzo Doria07/2015
2056109^54683-108111413Norbert Schneider02/2017
2057numbpart(10^10+76282)111391Serge Batalov04/2015
20582^369974+733111374Lelio R Paula05/2013
20592^369915-286267111356Enzo Doria07/2015
20607*10^111325+3111326Robert Price08/2015
206151^65176+2111293Lelio R Paula08/2013
20622^369643-1865767111274Enzo Doria03/2016
2063L(532277)111240Renaud Lifchitz03/2004
20642^369354-3413111187Yves Minet12/2016
20652^369296-27111170Lelio R Paula02/2013
20662^369239-109837111153Enzo Doria05/2014
20672^369224-291839111148Enzo Doria07/2015
20682^369216+2798881111146Enzo Doria04/2016
206910^111111+163849111112Patrick De Geest03/2017
207010^111111-312911111111Patrick De Geest03/2017
20712^369092-216923111108Enzo Doria05/2014
20722^369081-55111105Lelio R Paula02/2013
207388^57124-87111077Norbert Schneider11/2015
20742^368980+753111075Lelio R Paula05/2013
20752^368946-3623111064Yves Minet03/2017
20764^184463-3^184463111058Jean-Louis Charton12/2004
2077(4*10^111032-7)/3111033Ray Chandler04/2011
20782^368641-460303110972Enzo Doria06/2015
20792^368619-109087110966Enzo Doria04/2014
20803*2^368489+7110927Lelio R Paula09/2014
2081(9179*2^368330-1)/35110881Lelio R Paula05/2015
2082(34*10^110882-7)/9/13/29/1019374319110871Makoto Morimoto05/2016
20832^368048+25110794Lelio R Paula02/2013
208469^60239-2110771Lelio R Paula10/2013
2085(23*2^367952+1)/15717110762Lelio R Paula03/2014
20862^367924-69110757Lelio R Paula02/2013
20872^367709-109723110692Enzo Doria04/2014
2088(3*2^367644-1)/107110671Lelio R Paula03/2014
2089(23*2^367398+1)/57963110595Lelio R Paula03/2014
20902^367215+1879223110543Enzo Doria09/2016
20912^367141+41110521Lelio R Paula02/2013
2092(31*2^366976+1)/7110472Lelio R Paula03/2014
2093(21181*2^366833+1)/3110432Lelio R Paula07/2014
20942^366775-2787037110411Enzo Doria03/2016
2095(112*10^110405-1)/3110407Serge Batalov12/2014
20962^366751+2797553110404Enzo Doria03/2016
20972^366738-2985110400Yves Minet09/2014
2098(23*2^366739+1)/74575110396Lelio R Paula03/2014
20992^366716+1871791110393Enzo Doria05/2016
21002^366649+1871687110373Enzo Doria05/2016
21012^366629-351205110367Enzo Doria06/2015
21022^366558+1874479110345Enzo Doria06/2016
210318^87853-4409110280Enzo Doria03/2013
21042^366218-23110243Lelio R Paula02/2013
2105(21*2^366193-1)/197110235Lelio R Paula03/2014
21062^366178-343991110231Enzo Doria07/2015
21072^365944+1871341110161Enzo Doria05/2016
21082^365838-461267110129Enzo Doria07/2015
2109(2^365689+2^182845+1)/511008311/2006
21102^365666-459161110077Enzo Doria05/2015
21113*10^110076-7110077Robert Price08/2015
211213^98785-72110041Lelio R Paula03/2017
2113(25^78707+1)/26110027Robert Price06/2013
21146^141361-7110001Lelio R Paula11/2014
211520^84536+81109984Lelio R Paula03/2017
21165*2^365347-9109982Lelio R Paula09/2014
21179*6^141303+7109957Lelio R Paula11/2014
211878^58099+77109929Norbert Schneider02/2015
21192*10^109928-7109929Robert Price10/2015
2120(27*2^365137-1)/2021109916Lelio R Paula03/2014
2121(4441*29^75152-24)/7109905Curtis Bright05/2015
2122(2^365087+7)/6015109899Lelio R Paula01/2014
212318^87533-11109878Lelio R Paula04/2017
21242^364982-5109871Henri Lifchitz04/2006
21252^364936-1867979109857Enzo Doria04/2016
21262^364867-112087109836Enzo Doria06/2014
21274^182415-85061109825Mike Oakes06/2011
2128(17^89227+16^89227)/33109788Robert Price08/2013
21292^364687-187109782Lelio R Paula01/2012
21302^364644+67109769Lelio R Paula01/2012
2131(9787*2^364625-1)/24947109763Lelio R Paula05/2015
2132(2^364616+5)/9109760Lelio R Paula01/2014
213312^101694+73109747Lelio R Paula03/2017
213413^98518-66109744Lelio R Paula03/2017
21352^364478-113261109719Enzo Doria07/2014
2136(24737*2^364454+1)/3109716Lelio R Paula07/2014
2137(62*10^109673+1)/9109674Serge Batalov11/2010
21383^229824+340109654Lelio R Paula03/2017
21392^364169-112813109626Enzo Doria06/2014
214010^109615+21109616Lelio R Paula03/2017
214110^109615-456267109615Patrick De Geest03/2017
21422^364094-113109604Lelio R Paula01/2012
2143(4^182026+11)/3109591Robert Price02/2017
21442^364041-6883109588Lelio R Paula09/2011
214512^101545+11109586Lelio R Paula03/2017
21462^363842-2787101109528Enzo Doria03/2016
2147(22699*2^363782+1)/763109511Lelio R Paula07/2014
21482^363769+5711109506Lelio R Paula04/2017
2149(31*2^363748+1)/49109499Lelio R Paula03/2014
2150p(22245)#/2-8109462Robert Price01/2017
21512^363556+55109442Lelio R Paula01/2012
2152(55459*2^363411+1)/81109401Lelio R Paula07/2014
21532^363406+1871569109397Enzo Doria05/2016
2154(2^363349+7)/9109378Lelio R Paula01/2014
21553^229236+100109374Lelio R Paula03/2017
21562^363268-58695109355Lelio R Paula04/2017
21572^363191-112321109332Enzo Doria06/2014
21582^363120+3109311Donovan Johnson04/2006
2159(10^109297-1)/9109297Paul Bourdelais, Harvey Dubner04/2007
21602^363042-114641109287Enzo Doria04/2015
21612^363020-112793109280Enzo Doria06/2014
2162(67607*2^362695+1)/70499109183Lelio R Paula07/2014
2163(9*2^362644+1)/5109167Lelio R Paula03/2014
21645^156181+38109166Lelio R Paula02/2017
21653^228750+68109142Lelio R Paula03/2017
2166(10223*2^362376+1)/9109090Lelio R Paula07/2014
216765^60167-64^60167109078Robert Price08/2013
21687*3^228589-2109066Lelio R Paula09/2014
2169(78557*2^362188+1)/189109033Lelio R Paula07/2014
21702*7^129008+9109025Lelio R Paula11/2014
21712^361957+76367108960Enzo Doria05/2016
21722^361873-1411108935Yves Minet01/2013
2173(24737*2^361857+1)/35108933Lelio R Paula07/2014
217413^97745-24108883Lelio R Paula03/2017
217517^88475+8108864Lelio R Paula04/2017
21762^361567+51108843Lelio R Paula01/2012
21772^361563-109501108842Enzo Doria04/2014
217812^100852+83108838Lelio R Paula03/2017
21792^361497+767108822Lelio R Paula01/2012
21802^361280-112349108757Enzo Doria06/2014
21812^361271-5955108754Lelio R Paula04/2017
218212^100757+19108736Lelio R Paula03/2017
2183(19^85009-5^85009)/14108705Robert Price07/2013
2184(11*2^361027+1)/40463108677Lelio R Paula03/2014
21852^360973+1299108664Lelio R Paula04/2017
21862^360959-109101108660Enzo Doria04/2014
21876*5^155454+7108659Lelio R Paula11/2014
218810^108656+79108657Lelio R Paula02/2017
218910^108656-50001108656Patrick De Geest03/2017
21902^360918-35108648Lelio R Paula01/2012
2191(11*2^360886-1)/7108638Lelio R Paula03/2014
21922^360706-458903108584Enzo Doria04/2015
21932^360641-113185108564Enzo Doria07/2014
21942^360618+75019108557Enzo Doria04/2016
21953*5^155286+2108541Lelio R Paula11/2014
21967^128422+4108530Lelio R Paula11/2014
21977^128421-80108529Lelio R Paula03/2017
21982^360497+53807108521Yves Minet07/2010
21992^360366+1459108481Lelio R Paula09/2011
22002^360364-1499108481Yves Minet05/2013
22014*10^108412+9108413Robert Price05/2015
22022^360093-351103108399Enzo Doria06/2015
22032^360042+723108384Lelio R Paula01/2012
220485^56164-2108364Lelio R Paula10/2013
22052^359937-29323108352Enzo Doria07/2015
22062^359898-19997108341Enzo Doria06/2013
22072*5^154948-7108305Lelio R Paula11/2014
220810^108303+13108304Lelio R Paula02/2017
220910^108303-207959108303Patrick De Geest03/2017
22102^359730+753108290Lelio R Paula12/2011
22112^359650-19797108266Enzo Doria06/2013
221291^55259-90^55259108255Robert Price07/2015
22133^226845+68108233Lelio R Paula03/2017
22145^154822-12866108216Enzo Doria05/2014
2215(9*2^359480+1)/5108215Lelio R Paula03/2014
22162^359454-177108207Lelio R Paula12/2011
22176^139022-59108181Lelio R Paula02/2017
22182^359352-179108176Lelio R Paula12/2011
22192^359338-1858781108172Enzo Doria04/2016
222012^100230-97108167Lelio R Paula03/2017
2221(25*2^359297-1)/137108159Lelio R Paula03/2014
2222(2^359262-509203)/9108148Lelio R Paula12/2013
2223(3^226648-8)/352715633108131Lelio R Paula12/2013
22246^138956-59108129Lelio R Paula02/2017
22252^359184+30285108126Lelio R Paula04/2017
222613^97059+10108119Lelio R Paula03/2017
22272^359137-81108112Lelio R Paula12/2011
2229(15185*2^359105-1)/567108103Lelio R Paula05/2015
22282^359110-11655108103Lelio R Paula04/2017
22308*6^138875+5108067Lelio R Paula11/2014
22312^358987-216919108066Enzo Doria05/2014
223239^67918-67918^39108062Norbert Schneider02/2017
22332^358785-16933108006Enzo Doria05/2013
2234(2^358783+5)/33383108000Lelio R Paula12/2013
22356^138770-77107985Lelio R Paula02/2017
2236(2^358727-1017)/94178479107980Lelio R Paula12/2013
223710^107976+19107977Lelio R Paula02/2017
223810^107976-202103107976Patrick De Geest03/2017
22392^358684+75781107975Enzo Doria04/2016
224099^54094+2107952Lelio R Paula06/2013
2241(2^358583-9)/391107942Lelio R Paula12/2013
22422^358538+55107931Lelio R Paula12/2011
22432^358517-109009107925Enzo Doria03/2014
22443^226159+104107906Lelio R Paula03/2017
22452^358310-11655107863Lelio R Paula03/2017
22462^358275-112987107852Enzo Doria07/2014
22472^358233-20005107839Enzo Doria06/2013
22482^358194+175107828Lelio R Paula12/2011
2249107^53125-106107812Norbert Schneider12/2016
22503^225922-2107793Lelio R Paula10/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 24 2017 22:44 (Time in France)

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