PRP Records

Probable Primes Top 10000

(205873 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 ?
225192941#+(355049#)/(92941#)113830Makoto Morimoto10/2017
22522^378128-262977113828Enzo Doria05/2014
22532^378123-113215113827Enzo Doria07/2014
22546^146274-18893113824Enzo Doria03/2013
22552^378078+75113813Lelio R Paula03/2013
22562^377940+63113772Lelio R Paula03/2013
22572^377941-2785843113772Enzo Doria04/2016
22582^377810+1875109113733Enzo Doria09/2016
22592^377803-1838635113731Enzo Doria05/2015
22602^377799+52223113729Yves Minet08/2010
226111^109190-270113710Enzo Doria12/2012
22627*10^113693+9113694Robert Price09/2015
2263(2*10^113631+529)/9113631Robert Price01/2018
22642^377408-2798279113612Enzo Doria04/2016
22652^377222+93679113556Yves Minet02/2011
2266262147#+316847113552Makoto Morimoto02/2016
22672^377026-458903113497Enzo Doria04/2015
226835^73477-34^73477113454Robert Price05/2012
22692^376790+27113426Lelio R Paula03/2013
22702^376786-112701113424Enzo Doria06/2014
22712^376731+21113408Lelio R Paula03/2013
22722^376634+1871245113379Enzo Doria05/2016
2273(4^188318+17)/3113379Robert Price02/2017
22742^376576-344369113361Enzo Doria07/2015
2275(17*2^376526-1)/223113345Lelio R Paula03/2014
2276(27*2^376441-1)/811113319Lelio R Paula03/2014
22772^376128-21237113226Enzo Doria06/2013
22782^375638-1787171113079Enzo Doria03/2016
22792^375537+4847113048Yves Minet02/2011
2280(17^91837+16^91837)/33113000Robert Price08/2013
22815*F(270343)*(F(270343)+1)+1112997Serge Batalov04/2015
22822^375350-3221112992Yves Minet07/2011
2284(13*2^375306+1)/7112979Lelio R Paula03/2014
22832^375305+76757112979Enzo Doria05/2016
22852^375258+1874989112964Enzo Doria07/2016
2286(29^77237-1)/28112950Robert Price04/2012
22872^375154+74959112933Enzo Doria04/2016
22882^374993-2787163112885Enzo Doria11/2015
2289123^53970+2112793Lelio R Paula06/2013
2290p(22852)#/2+512112745Robert Price05/2017
22912^374441-21049112718Enzo Doria06/2013
2292(2^374321+1)/3112682H.&R. Lifchitz12/2000
2293(13^101089-1)/12112607Paul Bourdelais03/2010
22943^236011-8828112606Enzo Doria05/2014
229539^70666+2112435Lelio R Paula11/2013
2296(2^373350-7)/3112390Lelio R Paula03/2014
22972^373306-1840931112377Enzo Doria06/2015
22982^373117+1872107112320Enzo Doria05/2016
22992^373040+2792761112297Enzo Doria03/2016
2300EPrime(112280)112280Eric W. Weisstein10/2010
23012^372950+7112270Lelio R Paula03/2013
23022^372945+1872167112268Enzo Doria05/2016
23032^372695+72113112193Enzo Doria04/2016
23042^372689-2563112191Yves Minet07/2014
23052^372638-1859441112176Enzo Doria03/2016
23063^235074-113056112159Enzo Doria07/2014
2307(91*10^112098-1)/9112100Robert Price04/2015
23082^372310-85061112077Paul Bourdelais02/2012
2309(10^112067+53)/9112067Serge Batalov07/2015
231075^59760+2112054Lelio R Paula08/2013
23112^372108+74221112016Enzo Doria04/2016
23122^371970-459491111975Enzo Doria05/2015
231341^69427-40^69427111971Robert Price07/2012
2314(10^111902+71)/9111902Serge Batalov07/2015
23152^371440-112865111815Enzo Doria06/2014
23162^371426-459161111811Enzo Doria05/2015
23172^371276-461267111766Enzo Doria07/2015
23182^371098-113261111712Enzo Doria07/2014
2319(7*10^111706-61)/9111706Erik Branger01/2011
23202^371044+1869391111696Enzo Doria05/2016
232188^57416+87111645Norbert Schneider11/2015
23222^370829-109693111631Enzo Doria04/2014
232315^94906-2111619Lelio R Paula11/2013
23252^370643-37111575Yves Minet01/2012
2324(2^370655-5)/2439111575Lelio R Paula03/2014
23262^370610-3911111565Yves Minet04/2017
2327286^45405+45405^286111532Norbert Schneider04/2015
23284*5^159563-9111531Lelio R Paula11/2014
23292^370393-2797093111500Enzo Doria03/2016
2330(21*2^370382-1)/629111495Lelio R Paula03/2014
23312^370292-2791979111469Enzo Doria03/2016
23322^370177-461551111435Enzo Doria07/2015
2333109^54683-108111413Norbert Schneider02/2017
2334numbpart(10^10+76282)111391Serge Batalov04/2015
23352^369974+733111374Lelio R Paula05/2013
23362^369915-286267111356Enzo Doria07/2015
23372^369855-1615111338Lelio R Paula05/2017
23387*10^111325+3111326Robert Price08/2015
233951^65176+2111293Lelio R Paula08/2013
23402^369643-1865767111274Enzo Doria03/2016
23412^369603+885111262Lelio R Paula05/2017
2342L(532277)111240Renaud Lifchitz03/2004
2343105^55033-2111233Lelio R Paula10/2017
23442^369392+29835111199Lelio R Paula05/2017
23452^369354-3413111187Yves Minet12/2016
23462^369296-27111170Lelio R Paula02/2013
23472^369239-109837111153Enzo Doria05/2014
23482^369224-291839111148Enzo Doria07/2015
23492^369216+2798881111146Enzo Doria04/2016
235010^111111+163849111112Patrick De Geest03/2017
235110^111111-312911111111Patrick De Geest03/2017
23522^369092-216923111108Enzo Doria05/2014
23532^369081-55111105Lelio R Paula02/2013
235488^57124-87111077Norbert Schneider11/2015
23552^368980+753111075Lelio R Paula05/2013
23562^368946-3623111064Yves Minet03/2017
23572^368929+29835111059Lelio R Paula05/2017
23584^184463-3^184463111058Jean-Louis Charton12/2004
2359111^54298+110111057Norbert Schneider04/2017
2360(4*10^111032-7)/3111033Ray Chandler04/2011
23612^368641-460303110972Enzo Doria06/2015
23622^368619-109087110966Enzo Doria04/2014
23633*2^368489+7110927Lelio R Paula09/2014
236497411!4-2110913Robert Price07/2017
2365(9179*2^368330-1)/35110881Lelio R Paula05/2015
2366(34*10^110882-7)/9/13/29/1019374319110871Makoto Morimoto05/2016
23672^368050-64875110795Lelio R Paula05/2017
23682^368048+25110794Lelio R Paula02/2013
236969^60239-2110771Lelio R Paula10/2013
2370(23*2^367952+1)/15717110762Lelio R Paula03/2014
23712^367924-69110757Lelio R Paula02/2013
23722^367709-109723110692Enzo Doria04/2014
2373(3*2^367644-1)/107110671Lelio R Paula03/2014
2374(23*2^367398+1)/57963110595Lelio R Paula03/2014
23752^367215+1879223110543Enzo Doria09/2016
23762^367141+41110521Lelio R Paula02/2013
23772^367126+29835110516Lelio R Paula05/2017
2378(31*2^366976+1)/7110472Lelio R Paula03/2014
23792^366853+5711110434Lelio R Paula05/2017
2380(21181*2^366833+1)/3110432Lelio R Paula07/2014
23812^366816+315110423Lelio R Paula05/2017
23822^366775-2787037110411Enzo Doria03/2016
2383(112*10^110405-1)/3110407Serge Batalov12/2014
23842^366751+2797553110404Enzo Doria03/2016
23852^366748+255110403Lelio R Paula05/2017
23862^366738-2985110400Yves Minet09/2014
2387(23*2^366739+1)/74575110396Lelio R Paula03/2014
23882^366716+1871791110393Enzo Doria05/2016
23892^366649+1871687110373Enzo Doria05/2016
23902^366629-351205110367Enzo Doria06/2015
23912^366558+1874479110345Enzo Doria06/2016
239218^87853-4409110280Enzo Doria03/2013
23932^366218-23110243Lelio R Paula02/2013
2394(21*2^366193-1)/197110235Lelio R Paula03/2014
23952^366178-343991110231Enzo Doria07/2015
23962^365944+1871341110161Enzo Doria05/2016
23972^365838-461267110129Enzo Doria07/2015
23982^365763-6555110106Lelio R Paula04/2017
2399(2^365689+2^182845+1)/511008311/2006
24002^365666-459161110077Enzo Doria05/2015
24013*10^110076-7110077Robert Price08/2015
240213^98785-72110041Lelio R Paula03/2017
2403(25^78707+1)/26110027Robert Price06/2013
2404(7*10^110006-151)/9110006Robert Price02/2018
24056^141361-7110001Lelio R Paula11/2014
240620^84536+81109984Lelio R Paula03/2017
24075*2^365347-9109982Lelio R Paula09/2014
24089*6^141303+7109957Lelio R Paula11/2014
240978^58099+77109929Norbert Schneider02/2015
24102*10^109928-7109929Robert Price10/2015
2411(27*2^365137-1)/2021109916Lelio R Paula03/2014
2412(4441*29^75152-24)/7109905Curtis Bright05/2015
2413(2^365087+7)/6015109899Lelio R Paula01/2014
241418^87533-11109878Lelio R Paula04/2017
24152^364982-5109871Henri Lifchitz04/2006
24162^364936-1867979109857Enzo Doria04/2016
24172^364867-112087109836Enzo Doria06/2014
24184^182415-85061109825Mike Oakes06/2011
2419(17^89227+16^89227)/33109788Robert Price08/2013
24202^364687-187109782Lelio R Paula01/2012
24212^364644+67109769Lelio R Paula01/2012
2422(9787*2^364625-1)/24947109763Lelio R Paula05/2015
2423(2^364616+5)/9109760Lelio R Paula01/2014
242412^101694+73109747Lelio R Paula03/2017
242513^98518-66109744Lelio R Paula03/2017
24262^364478-113261109719Enzo Doria07/2014
2427(24737*2^364454+1)/3109716Lelio R Paula07/2014
2428(62*10^109673+1)/9109674Serge Batalov11/2010
24293^229824+340109654Lelio R Paula03/2017
2430(2*10^109645-71)/3109645Robert Price12/2017
24312^364169-112813109626Enzo Doria06/2014
243210^109615+21109616Lelio R Paula03/2017
243310^109615-456267109615Patrick De Geest03/2017
24342^364094-113109604Lelio R Paula01/2012
2435(4^182026+11)/3109591Robert Price02/2017
24362^364041-6883109588Lelio R Paula09/2011
243712^101545+11109586Lelio R Paula03/2017
24382^363842-2787101109528Enzo Doria03/2016
2439(22699*2^363782+1)/763109511Lelio R Paula07/2014
24402^363769+5711109506Lelio R Paula04/2017
2441(31*2^363748+1)/49109499Lelio R Paula03/2014
2442p(22245)#/2-8109462Robert Price01/2017
24432^363556+55109442Lelio R Paula01/2012
2444(55459*2^363411+1)/81109401Lelio R Paula07/2014
24452^363406+1871569109397Enzo Doria05/2016
2446(2^363349+7)/9109378Lelio R Paula01/2014
24473^229236+100109374Lelio R Paula03/2017
24482^363268-58695109355Lelio R Paula04/2017
24492^363191-112321109332Enzo Doria06/2014
24502^363120+3109311Donovan Johnson04/2006
2451(10^109297-1)/9109297Paul Bourdelais, Harvey Dubner04/2007
24522^363042-114641109287Enzo Doria04/2015
24532^363020-112793109280Enzo Doria06/2014
2454(67607*2^362695+1)/70499109183Lelio R Paula07/2014
2455(9*2^362644+1)/5109167Lelio R Paula03/2014
24565^156181+38109166Lelio R Paula02/2017
24573^228750+68109142Lelio R Paula03/2017
2458(10223*2^362376+1)/9109090Lelio R Paula07/2014
245965^60167-64^60167109078Robert Price08/2013
24607*3^228589-2109066Lelio R Paula09/2014
2461(78557*2^362188+1)/189109033Lelio R Paula07/2014
24622*7^129008+9109025Lelio R Paula11/2014
24632^361957+76367108960Enzo Doria05/2016
24642^361873-1411108935Yves Minet01/2013
2465(24737*2^361857+1)/35108933Lelio R Paula07/2014
246613^97745-24108883Lelio R Paula03/2017
246717^88475+8108864Lelio R Paula04/2017
24682^361567+51108843Lelio R Paula01/2012
24692^361563-109501108842Enzo Doria04/2014
247012^100852+83108838Lelio R Paula03/2017
24712^361497+767108822Lelio R Paula01/2012
24722^361280-112349108757Enzo Doria06/2014
24732^361271-5955108754Lelio R Paula04/2017
247412^100757+19108736Lelio R Paula03/2017
247514^94849-61108710Lelio R Paula05/2017
2476(19^85009-5^85009)/14108705Robert Price07/2013
2477(11*2^361027+1)/40463108677Lelio R Paula03/2014
24782^360973+1299108664Lelio R Paula04/2017
24792^360959-109101108660Enzo Doria04/2014
24806*5^155454+7108659Lelio R Paula11/2014
248110^108656+79108657Lelio R Paula02/2017
248210^108656-50001108656Patrick De Geest03/2017
24832^360918-35108648Lelio R Paula01/2012
2484(11*2^360886-1)/7108638Lelio R Paula03/2014
24852^360706-458903108584Enzo Doria04/2015
24862^360641-113185108564Enzo Doria07/2014
24872^360618+75019108557Enzo Doria04/2016
2488(14*10^108545-221)/9108546Robert Price04/2018
24893*5^155286+2108541Lelio R Paula11/2014
24907^128422+4108530Lelio R Paula11/2014
24917^128421-80108529Lelio R Paula03/2017
24922^360497+53807108521Yves Minet07/2010
24932^360366+1459108481Lelio R Paula09/2011
24942^360364-1499108481Yves Minet05/2013
249514^94642-23108472Lelio R Paula05/2017
24964*10^108412+9108413Robert Price05/2015
24972^360093-351103108399Enzo Doria06/2015
24982^360042+723108384Lelio R Paula01/2012
249985^56164-2108364Lelio R Paula10/2013
25002^359937-29323108352Enzo Doria07/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 24 2018 23:03 (Time in France)

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