PRP Records

Probable Primes Top 10000

(212140 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 ?
22512^383560-455115464Yves Minet03/2012
2252(2^383544+5)/3115458Lelio R Paula03/2014
225389^59221-88^59221115445Robert Price06/2015
22542^383347+1869413115399Enzo Doria05/2016
2255(2^383130-7)/131793115329Lelio R Paula03/2014
2256(12^106859+1)/13115320Paul Bourdelais02/2010
22572^383039+1869509115307Enzo Doria05/2016
2258(13*2^382968+1)/7115286Lelio R Paula04/2014
22592^382633+73697115185Enzo Doria04/2016
22602^382509-113593115147Enzo Doria08/2014
22612^382502-2791721115145Enzo Doria03/2016
22629^120590-120590115073Robert Price03/2014
22632^382198+9115054Lelio R Paula03/2013
22642^381883-59197114959Enzo Doria10/2015
22662^381806-4481114936Yves Minet07/2011
22652^381808-1851507114936Enzo Doria08/2015
22672^381774-112373114926Enzo Doria06/2014
22682^381555-109051114860Enzo Doria04/2014
22692^381546-113501114857Enzo Doria08/2014
22702^381360-110429114801Enzo Doria05/2014
2271(66^63079+1)/67114774Paul Bourdelais09/2017
22722^381252-115079114769Enzo Doria06/2015
22732^381209-29323114756Enzo Doria07/2015
2274569^41651-568^41651114754Jean-Louis Charton11/2009
22752^381201+1873205114753Enzo Doria06/2016
22762^380974-112991114685Enzo Doria07/2014
227788^58949-87114626Norbert Schneider11/2015
22782^380700+91114603Lelio R Paula03/2013
228010^114575+3^114576114576Mike Oakes09/2010
227910^114575+66561114576Patrick De Geest02/2017
228110^114575-581081114575Patrick De Geest02/2017
22822^380587-115315114569Enzo Doria06/2015
22832^380513-216925114546Enzo Doria05/2014
22842^380451-1840087114528Enzo Doria06/2015
2285(15*2^380388-1)/539114507Lelio R Paula04/2014
22862^380279-461347114476Enzo Doria07/2015
22872^380021+1871147114398Enzo Doria05/2016
22882^380005+1869707114393Enzo Doria05/2016
22892^379958-113297114379Enzo Doria07/2014
22902^379881-109105114356Enzo Doria04/2014
2291(21*2^379857-1)/13114349Lelio R Paula03/2014
2292(4*10^114340+83)/3114341Robert Price02/2018
2293(4*10^114296+149)/9114296Robert Price04/2018
229488^58773-87114284Norbert Schneider11/2015
22952^379529-2790283114250Enzo Doria03/2016
22962^379522+1869115114248Enzo Doria05/2016
2297(145*10^114226-1)/9114228Serge Batalov12/2014
22982^379317-115033114186Enzo Doria06/2015
2299(17*2^379246-1)/17407114162Lelio R Paula03/2014
2300(4*10^114076+143)/3114077Robert Price03/2018
23012*10^113941+9113942Dmitry Domanov11/2010
23022^378272-16565113872Enzo Doria04/2013
23032^378217-109075113855Enzo Doria04/2014
23042^378198+67113849Lelio R Paula03/2013
23052^378173-3249113842Yves Minet12/2014
2306(2^378155-5)/6597113833Lelio R Paula03/2014
230792941#+(355049#)/(92941#)113830Makoto Morimoto10/2017
23082^378128-262977113828Enzo Doria05/2014
23092^378123-113215113827Enzo Doria07/2014
23106^146274-18893113824Enzo Doria03/2013
23112^378078+75113813Lelio R Paula03/2013
23122^377940+63113772Lelio R Paula03/2013
23132^377941-2785843113772Enzo Doria04/2016
23142^377810+1875109113733Enzo Doria09/2016
23152^377803-1838635113731Enzo Doria05/2015
23162^377799+52223113729Yves Minet08/2010
231711^109190-270113710Enzo Doria12/2012
23187*10^113693+9113694Robert Price09/2015
2319(2*10^113631+529)/9113631Robert Price01/2018
23202^377408-2798279113612Enzo Doria04/2016
23212^377222+93679113556Yves Minet02/2011
2322262147#+316847113552Makoto Morimoto02/2016
23232^377026-458903113497Enzo Doria04/2015
232435^73477-34^73477113454Robert Price05/2012
23252^376790+27113426Lelio R Paula03/2013
23262^376786-112701113424Enzo Doria06/2014
23272^376731+21113408Lelio R Paula03/2013
23282^376634+1871245113379Enzo Doria05/2016
2329(4^188318+17)/3113379Robert Price02/2017
23302^376576-344369113361Enzo Doria07/2015
2331(17*2^376526-1)/223113345Lelio R Paula03/2014
2332(27*2^376441-1)/811113319Lelio R Paula03/2014
23332^376128-21237113226Enzo Doria06/2013
23342^375638-1787171113079Enzo Doria03/2016
23352^375537+4847113048Yves Minet02/2011
2336(17^91837+16^91837)/33113000Robert Price08/2013
23375*F(270343)*(F(270343)+1)+1112997Serge Batalov04/2015
23382^375350-3221112992Yves Minet07/2011
2339(13*2^375306+1)/7112979Lelio R Paula03/2014
23402^375305+76757112979Enzo Doria05/2016
23412^375258+1874989112964Enzo Doria07/2016
2342(29^77237-1)/28112950Robert Price04/2012
23432^375154+74959112933Enzo Doria04/2016
23442^374993-2787163112885Enzo Doria11/2015
2345123^53970+2112793Lelio R Paula06/2013
2346p(22852)#/2+512112745Robert Price05/2017
23472^374441-21049112718Enzo Doria06/2013
2348(2^374321+1)/3112682H.&R. Lifchitz12/2000
2349(13^101089-1)/12112607Paul Bourdelais03/2010
23503^236011-8828112606Enzo Doria05/2014
235139^70666+2112435Lelio R Paula11/2013
2352(2^373350-7)/3112390Lelio R Paula03/2014
23532^373306-1840931112377Enzo Doria06/2015
23542^373117+1872107112320Enzo Doria05/2016
23552^373040+2792761112297Enzo Doria03/2016
2356EPrime(112280)112280Eric W. Weisstein10/2010
23572^372950+7112270Lelio R Paula03/2013
23582^372945+1872167112268Enzo Doria05/2016
23592^372695+72113112193Enzo Doria04/2016
23602^372689-2563112191Yves Minet07/2014
23612^372638-1859441112176Enzo Doria03/2016
23623^235074-113056112159Enzo Doria07/2014
2363(91*10^112098-1)/9112100Robert Price04/2015
23642^372310-85061112077Paul Bourdelais02/2012
2365(10^112067+53)/9112067Serge Batalov07/2015
236675^59760+2112054Lelio R Paula08/2013
23672^372108+74221112016Enzo Doria04/2016
23682^371970-459491111975Enzo Doria05/2015
236941^69427-40^69427111971Robert Price07/2012
2370(10^111902+71)/9111902Serge Batalov07/2015
23712^371440-112865111815Enzo Doria06/2014
23722^371426-459161111811Enzo Doria05/2015
23732^371276-461267111766Enzo Doria07/2015
23742^371098-113261111712Enzo Doria07/2014
2375(7*10^111706-61)/9111706Erik Branger01/2011
23762^371044+1869391111696Enzo Doria05/2016
237788^57416+87111645Norbert Schneider11/2015
23782^370829-109693111631Enzo Doria04/2014
237915^94906-2111619Lelio R Paula11/2013
23802^370643-37111575Yves Minet01/2012
2381(2^370655-5)/2439111575Lelio R Paula03/2014
23822^370610-3911111565Yves Minet04/2017
2383286^45405+45405^286111532Norbert Schneider04/2015
23844*5^159563-9111531Lelio R Paula11/2014
23852^370393-2797093111500Enzo Doria03/2016
2386(21*2^370382-1)/629111495Lelio R Paula03/2014
23872^370292-2791979111469Enzo Doria03/2016
23882^370177-461551111435Enzo Doria07/2015
2389109^54683-108111413Norbert Schneider02/2017
2390numbpart(10^10+76282)111391Serge Batalov04/2015
23912^369974+733111374Lelio R Paula05/2013
23922^369915-286267111356Enzo Doria07/2015
23932^369855-1615111338Lelio R Paula05/2017
23947*10^111325+3111326Robert Price08/2015
239551^65176+2111293Lelio R Paula08/2013
23962^369643-1865767111274Enzo Doria03/2016
23972^369603+885111262Lelio R Paula05/2017
2398L(532277)111240Renaud Lifchitz03/2004
2399105^55033-2111233Lelio R Paula10/2017
24002^369392+29835111199Lelio R Paula05/2017
24012^369354-3413111187Yves Minet12/2016
24022^369296-27111170Lelio R Paula02/2013
24032^369239-109837111153Enzo Doria05/2014
24042^369224-291839111148Enzo Doria07/2015
24052^369216+2798881111146Enzo Doria04/2016
240610^111111+163849111112Patrick De Geest03/2017
240710^111111-312911111111Patrick De Geest03/2017
24082^369092-216923111108Enzo Doria05/2014
24092^369081-55111105Lelio R Paula02/2013
241088^57124-87111077Norbert Schneider11/2015
24112^368980+753111075Lelio R Paula05/2013
24122^368946-3623111064Yves Minet03/2017
24132^368929+29835111059Lelio R Paula05/2017
24144^184463-3^184463111058Jean-Louis Charton12/2004
2415111^54298+110111057Norbert Schneider04/2017
2416(4*10^111032-7)/3111033Ray Chandler04/2011
24172^368641-460303110972Enzo Doria06/2015
24182^368619-109087110966Enzo Doria04/2014
24193*2^368489+7110927Lelio R Paula09/2014
242097411!4-2110913Robert Price07/2017
2421(9179*2^368330-1)/35110881Lelio R Paula05/2015
2422(34*10^110882-7)/9/13/29/1019374319110871Makoto Morimoto05/2016
24232^368050-64875110795Lelio R Paula05/2017
24242^368048+25110794Lelio R Paula02/2013
242569^60239-2110771Lelio R Paula10/2013
2426(23*2^367952+1)/15717110762Lelio R Paula03/2014
24272^367924-69110757Lelio R Paula02/2013
24282^367709-109723110692Enzo Doria04/2014
2429(3*2^367644-1)/107110671Lelio R Paula03/2014
2430(23*2^367398+1)/57963110595Lelio R Paula03/2014
24312^367215+1879223110543Enzo Doria09/2016
24322^367141+41110521Lelio R Paula02/2013
24332^367126+29835110516Lelio R Paula05/2017
2434(31*2^366976+1)/7110472Lelio R Paula03/2014
24352^366853+5711110434Lelio R Paula05/2017
2436(21181*2^366833+1)/3110432Lelio R Paula07/2014
24372^366816+315110423Lelio R Paula05/2017
24382^366775-2787037110411Enzo Doria03/2016
2439(112*10^110405-1)/3110407Serge Batalov12/2014
24402^366751+2797553110404Enzo Doria03/2016
24412^366748+255110403Lelio R Paula05/2017
24422^366738-2985110400Yves Minet09/2014
2443(23*2^366739+1)/74575110396Lelio R Paula03/2014
24442^366716+1871791110393Enzo Doria05/2016
24452^366649+1871687110373Enzo Doria05/2016
24462^366629-351205110367Enzo Doria06/2015
24472^366558+1874479110345Enzo Doria06/2016
244818^87853-4409110280Enzo Doria03/2013
24492^366218-23110243Lelio R Paula02/2013
2450(21*2^366193-1)/197110235Lelio R Paula03/2014
24512^366178-343991110231Enzo Doria07/2015
24522^365944+1871341110161Enzo Doria05/2016
24532^365838-461267110129Enzo Doria07/2015
24542^365763-6555110106Lelio R Paula04/2017
2455(2^365689+2^182845+1)/511008311/2006
24562^365666-459161110077Enzo Doria05/2015
24573*10^110076-7110077Robert Price08/2015
245813^98785-72110041Lelio R Paula03/2017
2459(25^78707+1)/26110027Robert Price06/2013
2460(7*10^110006-151)/9110006Robert Price02/2018
24616^141361-7110001Lelio R Paula11/2014
246220^84536+81109984Lelio R Paula03/2017
24635*2^365347-9109982Lelio R Paula09/2014
24649*6^141303+7109957Lelio R Paula11/2014
246578^58099+77109929Norbert Schneider02/2015
24662*10^109928-7109929Robert Price10/2015
2467(27*2^365137-1)/2021109916Lelio R Paula03/2014
2468(4441*29^75152-24)/7109905Curtis Bright05/2015
2469(2^365087+7)/6015109899Lelio R Paula01/2014
247018^87533-11109878Lelio R Paula04/2017
24712^364982-5109871Henri Lifchitz04/2006
24722^364936-1867979109857Enzo Doria04/2016
24732^364867-112087109836Enzo Doria06/2014
24744^182415-85061109825Mike Oakes06/2011
2475(17^89227+16^89227)/33109788Robert Price08/2013
24762^364687-187109782Lelio R Paula01/2012
24772^364644+67109769Lelio R Paula01/2012
2478(9787*2^364625-1)/24947109763Lelio R Paula05/2015
2479(2^364616+5)/9109760Lelio R Paula01/2014
248012^101694+73109747Lelio R Paula03/2017
248113^98518-66109744Lelio R Paula03/2017
24822^364478-113261109719Enzo Doria07/2014
2483(24737*2^364454+1)/3109716Lelio R Paula07/2014
2484(62*10^109673+1)/9109674Serge Batalov11/2010
24853^229824+340109654Lelio R Paula03/2017
2486(2*10^109645-71)/3109645Robert Price12/2017
24872^364169-112813109626Enzo Doria06/2014
248810^109615+21109616Lelio R Paula03/2017
248910^109615-456267109615Patrick De Geest03/2017
24902^364094-113109604Lelio R Paula01/2012
2491(4^182026+11)/3109591Robert Price02/2017
24922^364041-6883109588Lelio R Paula09/2011
249312^101545+11109586Lelio R Paula03/2017
24942^363842-2787101109528Enzo Doria03/2016
2495(22699*2^363782+1)/763109511Lelio R Paula07/2014
24962^363769+5711109506Lelio R Paula04/2017
2497(31*2^363748+1)/49109499Lelio R Paula03/2014
2498p(22245)#/2-8109462Robert Price01/2017
24992^363556+55109442Lelio R Paula01/2012
2500(55459*2^363411+1)/81109401Lelio R Paula07/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 20 2018 08:38 (Time in France)

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