PRP Records

Probable Primes Top 10000

(180278 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 ?
20012^381806-4481114936Yves Minet07/2011
20022^381774-112373114926Enzo Doria06/2014
20032^381555-109051114860Enzo Doria04/2014
20042^381546-113501114857Enzo Doria08/2014
20052^381360-110429114801Enzo Doria05/2014
20062^381252-115079114769Enzo Doria06/2015
20072^381209-29323114756Enzo Doria07/2015
2008569^41651-568^41651114754Jean-Louis Charton11/2009
20092^381201+1873205114753Enzo Doria06/2016
20102^380974-112991114685Enzo Doria07/2014
201188^58949-87114626Norbert Schneider11/2015
20122^380700+91114603Lelio R Paula03/2013
201410^114575+3^114576114576Mike Oakes09/2010
201310^114575+66561114576Patrick De Geest02/2017
201510^114575-581081114575Patrick De Geest02/2017
20162^380587-115315114569Enzo Doria06/2015
20172^380513-216925114546Enzo Doria05/2014
20182^380451-1840087114528Enzo Doria06/2015
2019(15*2^380388-1)/539114507Lelio R Paula04/2014
20202^380279-461347114476Enzo Doria07/2015
20212^380021+1871147114398Enzo Doria05/2016
20222^380005+1869707114393Enzo Doria05/2016
20232^379958-113297114379Enzo Doria07/2014
20242^379881-109105114356Enzo Doria04/2014
2025(21*2^379857-1)/13114349Lelio R Paula03/2014
202688^58773-87114284Norbert Schneider11/2015
20272^379529-2790283114250Enzo Doria03/2016
20282^379522+1869115114248Enzo Doria05/2016
2029(145*10^114226-1)/9114228Serge Batalov12/2014
20302^379317-115033114186Enzo Doria06/2015
2031(17*2^379246-1)/17407114162Lelio R Paula03/2014
20322*10^113941+9113942Dmitry Domanov11/2010
20332^378272-16565113872Enzo Doria04/2013
20342^378217-109075113855Enzo Doria04/2014
20352^378198+67113849Lelio R Paula03/2013
20362^378173-3249113842Yves Minet12/2014
2037(2^378155-5)/6597113833Lelio R Paula03/2014
20382^378128-262977113828Enzo Doria05/2014
20392^378123-113215113827Enzo Doria07/2014
20406^146274-18893113824Enzo Doria03/2013
20412^378078+75113813Lelio R Paula03/2013
20422^377940+63113772Lelio R Paula03/2013
20432^377941-2785843113772Enzo Doria04/2016
20442^377810+1875109113733Enzo Doria09/2016
20452^377803-1838635113731Enzo Doria05/2015
20462^377799+52223113729Yves Minet08/2010
204711^109190-270113710Enzo Doria12/2012
20487*10^113693+9113694Robert Price09/2015
20492^377408-2798279113612Enzo Doria04/2016
20502^377222+93679113556Yves Minet02/2011
2051262147#+316847113552Makoto Morimoto02/2016
20522^377026-458903113497Enzo Doria04/2015
205335^73477-34^73477113454Robert Price05/2012
20542^376790+27113426Lelio R Paula03/2013
20552^376786-112701113424Enzo Doria06/2014
20562^376731+21113408Lelio R Paula03/2013
20582^376634+1871245113379Enzo Doria05/2016
2057(4^188318+17)/3113379Robert Price02/2017
20592^376576-344369113361Enzo Doria07/2015
2060(17*2^376526-1)/223113345Lelio R Paula03/2014
2061(27*2^376441-1)/811113319Lelio R Paula03/2014
20622^376128-21237113226Enzo Doria06/2013
20632^375638-1787171113079Enzo Doria03/2016
20642^375537+4847113048Yves Minet02/2011
2065(17^91837+16^91837)/33113000Robert Price08/2013
20665*F(270343)*(F(270343)+1)+1112997Serge Batalov04/2015
20672^375350-3221112992Yves Minet07/2011
2068(13*2^375306+1)/7112979Lelio R Paula03/2014
20692^375305+76757112979Enzo Doria05/2016
20702^375258+1874989112964Enzo Doria07/2016
2071(29^77237-1)/28112950Robert Price04/2012
20722^375154+74959112933Enzo Doria04/2016
20732^374993-2787163112885Enzo Doria11/2015
2074123^53970+2112793Lelio R Paula06/2013
2075p(22852)#/2+512112745Robert Price05/2017
20762^374441-21049112718Enzo Doria06/2013
2077(2^374321+1)/3112682H.&R. Lifchitz12/2000
2078(13^101089-1)/12112607Paul Bourdelais03/2010
20793^236011-8828112606Enzo Doria05/2014
208039^70666+2112435Lelio R Paula11/2013
2081(2^373350-7)/3112390Lelio R Paula03/2014
20822^373306-1840931112377Enzo Doria06/2015
20832^373117+1872107112320Enzo Doria05/2016
20842^373040+2792761112297Enzo Doria03/2016
2085EPrime(112280)112280Eric W. Weisstein10/2010
20862^372950+7112270Lelio R Paula03/2013
20872^372945+1872167112268Enzo Doria05/2016
20882^372695+72113112193Enzo Doria04/2016
20892^372689-2563112191Yves Minet07/2014
20902^372638-1859441112176Enzo Doria03/2016
20913^235074-113056112159Enzo Doria07/2014
2092(91*10^112098-1)/9112100Robert Price04/2015
20932^372310-85061112077Paul Bourdelais02/2012
2094(10^112067+53)/9112067Serge Batalov07/2015
209575^59760+2112054Lelio R Paula08/2013
20962^372108+74221112016Enzo Doria04/2016
20972^371970-459491111975Enzo Doria05/2015
209841^69427-40^69427111971Robert Price07/2012
2099(10^111902+71)/9111902Serge Batalov07/2015
21002^371440-112865111815Enzo Doria06/2014
21012^371426-459161111811Enzo Doria05/2015
21022^371276-461267111766Enzo Doria07/2015
21032^371098-113261111712Enzo Doria07/2014
2104(7*10^111706-61)/9111706Erik Branger01/2011
21052^371044+1869391111696Enzo Doria05/2016
210688^57416+87111645Norbert Schneider11/2015
21072^370829-109693111631Enzo Doria04/2014
210815^94906-2111619Lelio R Paula11/2013
21102^370643-37111575Yves Minet01/2012
2109(2^370655-5)/2439111575Lelio R Paula03/2014
21112^370610-3911111565Yves Minet04/2017
2112286^45405+45405^286111532Norbert Schneider04/2015
21134*5^159563-9111531Lelio R Paula11/2014
21142^370393-2797093111500Enzo Doria03/2016
2115(21*2^370382-1)/629111495Lelio R Paula03/2014
21162^370292-2791979111469Enzo Doria03/2016
21172^370177-461551111435Enzo Doria07/2015
2118109^54683-108111413Norbert Schneider02/2017
2119numbpart(10^10+76282)111391Serge Batalov04/2015
21202^369974+733111374Lelio R Paula05/2013
21212^369915-286267111356Enzo Doria07/2015
21222^369855-1615111338Lelio R Paula05/2017
21237*10^111325+3111326Robert Price08/2015
212451^65176+2111293Lelio R Paula08/2013
21252^369643-1865767111274Enzo Doria03/2016
21262^369603+885111262Lelio R Paula05/2017
2127L(532277)111240Renaud Lifchitz03/2004
21282^369392+29835111199Lelio R Paula05/2017
21292^369354-3413111187Yves Minet12/2016
21302^369296-27111170Lelio R Paula02/2013
21312^369239-109837111153Enzo Doria05/2014
21322^369224-291839111148Enzo Doria07/2015
21332^369216+2798881111146Enzo Doria04/2016
213410^111111+163849111112Patrick De Geest03/2017
213510^111111-312911111111Patrick De Geest03/2017
21362^369092-216923111108Enzo Doria05/2014
21372^369081-55111105Lelio R Paula02/2013
213888^57124-87111077Norbert Schneider11/2015
21392^368980+753111075Lelio R Paula05/2013
21402^368946-3623111064Yves Minet03/2017
21412^368929+29835111059Lelio R Paula05/2017
21424^184463-3^184463111058Jean-Louis Charton12/2004
2143111^54298+110111057Norbert Schneider04/2017
2144(4*10^111032-7)/3111033Ray Chandler04/2011
21452^368641-460303110972Enzo Doria06/2015
21462^368619-109087110966Enzo Doria04/2014
21473*2^368489+7110927Lelio R Paula09/2014
214897411!4-2110913Robert Price07/2017
2149(9179*2^368330-1)/35110881Lelio R Paula05/2015
2150(34*10^110882-7)/9/13/29/1019374319110871Makoto Morimoto05/2016
21512^368050-64875110795Lelio R Paula05/2017
21522^368048+25110794Lelio R Paula02/2013
215369^60239-2110771Lelio R Paula10/2013
2154(23*2^367952+1)/15717110762Lelio R Paula03/2014
21552^367924-69110757Lelio R Paula02/2013
21562^367709-109723110692Enzo Doria04/2014
2157(3*2^367644-1)/107110671Lelio R Paula03/2014
2158(23*2^367398+1)/57963110595Lelio R Paula03/2014
21592^367215+1879223110543Enzo Doria09/2016
21602^367141+41110521Lelio R Paula02/2013
21612^367126+29835110516Lelio R Paula05/2017
2162(31*2^366976+1)/7110472Lelio R Paula03/2014
21632^366853+5711110434Lelio R Paula05/2017
2164(21181*2^366833+1)/3110432Lelio R Paula07/2014
21652^366816+315110423Lelio R Paula05/2017
21662^366775-2787037110411Enzo Doria03/2016
2167(112*10^110405-1)/3110407Serge Batalov12/2014
21682^366751+2797553110404Enzo Doria03/2016
21692^366748+255110403Lelio R Paula05/2017
21702^366738-2985110400Yves Minet09/2014
2171(23*2^366739+1)/74575110396Lelio R Paula03/2014
21722^366716+1871791110393Enzo Doria05/2016
21732^366649+1871687110373Enzo Doria05/2016
21742^366629-351205110367Enzo Doria06/2015
21752^366558+1874479110345Enzo Doria06/2016
217618^87853-4409110280Enzo Doria03/2013
21772^366218-23110243Lelio R Paula02/2013
2178(21*2^366193-1)/197110235Lelio R Paula03/2014
21792^366178-343991110231Enzo Doria07/2015
21802^365944+1871341110161Enzo Doria05/2016
21812^365838-461267110129Enzo Doria07/2015
21822^365763-6555110106Lelio R Paula04/2017
2183(2^365689+2^182845+1)/511008311/2006
21842^365666-459161110077Enzo Doria05/2015
21853*10^110076-7110077Robert Price08/2015
218613^98785-72110041Lelio R Paula03/2017
2187(25^78707+1)/26110027Robert Price06/2013
21886^141361-7110001Lelio R Paula11/2014
218920^84536+81109984Lelio R Paula03/2017
21905*2^365347-9109982Lelio R Paula09/2014
21919*6^141303+7109957Lelio R Paula11/2014
219278^58099+77109929Norbert Schneider02/2015
21932*10^109928-7109929Robert Price10/2015
2194(27*2^365137-1)/2021109916Lelio R Paula03/2014
2195(4441*29^75152-24)/7109905Curtis Bright05/2015
2196(2^365087+7)/6015109899Lelio R Paula01/2014
219718^87533-11109878Lelio R Paula04/2017
21982^364982-5109871Henri Lifchitz04/2006
21992^364936-1867979109857Enzo Doria04/2016
22002^364867-112087109836Enzo Doria06/2014
22014^182415-85061109825Mike Oakes06/2011
2202(17^89227+16^89227)/33109788Robert Price08/2013
22032^364687-187109782Lelio R Paula01/2012
22042^364644+67109769Lelio R Paula01/2012
2205(9787*2^364625-1)/24947109763Lelio R Paula05/2015
2206(2^364616+5)/9109760Lelio R Paula01/2014
220712^101694+73109747Lelio R Paula03/2017
220813^98518-66109744Lelio R Paula03/2017
22092^364478-113261109719Enzo Doria07/2014
2210(24737*2^364454+1)/3109716Lelio R Paula07/2014
2211(62*10^109673+1)/9109674Serge Batalov11/2010
22123^229824+340109654Lelio R Paula03/2017
22132^364169-112813109626Enzo Doria06/2014
221410^109615+21109616Lelio R Paula03/2017
221510^109615-456267109615Patrick De Geest03/2017
22162^364094-113109604Lelio R Paula01/2012
2217(4^182026+11)/3109591Robert Price02/2017
22182^364041-6883109588Lelio R Paula09/2011
221912^101545+11109586Lelio R Paula03/2017
22202^363842-2787101109528Enzo Doria03/2016
2221(22699*2^363782+1)/763109511Lelio R Paula07/2014
22222^363769+5711109506Lelio R Paula04/2017
2223(31*2^363748+1)/49109499Lelio R Paula03/2014
2224p(22245)#/2-8109462Robert Price01/2017
22252^363556+55109442Lelio R Paula01/2012
2226(55459*2^363411+1)/81109401Lelio R Paula07/2014
22272^363406+1871569109397Enzo Doria05/2016
2228(2^363349+7)/9109378Lelio R Paula01/2014
22293^229236+100109374Lelio R Paula03/2017
22302^363268-58695109355Lelio R Paula04/2017
22312^363191-112321109332Enzo Doria06/2014
22322^363120+3109311Donovan Johnson04/2006
2233(10^109297-1)/9109297Paul Bourdelais, Harvey Dubner04/2007
22342^363042-114641109287Enzo Doria04/2015
22352^363020-112793109280Enzo Doria06/2014
2236(67607*2^362695+1)/70499109183Lelio R Paula07/2014
2237(9*2^362644+1)/5109167Lelio R Paula03/2014
22385^156181+38109166Lelio R Paula02/2017
22393^228750+68109142Lelio R Paula03/2017
2240(10223*2^362376+1)/9109090Lelio R Paula07/2014
224165^60167-64^60167109078Robert Price08/2013
22427*3^228589-2109066Lelio R Paula09/2014
2243(78557*2^362188+1)/189109033Lelio R Paula07/2014
22442*7^129008+9109025Lelio R Paula11/2014
22452^361957+76367108960Enzo Doria05/2016
22462^361873-1411108935Yves Minet01/2013
2247(24737*2^361857+1)/35108933Lelio R Paula07/2014
224813^97745-24108883Lelio R Paula03/2017
224917^88475+8108864Lelio R Paula04/2017
22502^361567+51108843Lelio R Paula01/2012


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 20 2017 08:36 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!