PRP Records

Probable Primes Top 10000

(252538 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 (> 50000) Who ? When ?
25012^378128-262977113828Enzo Doria05/2014
25022^378123-113215113827Enzo Doria07/2014
25036^146274-18893113824Enzo Doria03/2013
25042^378078+75113813Lelio R Paula03/2013
25052^377940+63113772Lelio R Paula03/2013
25062^377941-2785843113772Enzo Doria04/2016
25072^377810+1875109113733Enzo Doria09/2016
25082^377803-1838635113731Enzo Doria05/2015
25092^377799+52223113729Yves Minet08/2010
251011^109190-270113710Enzo Doria12/2012
25117*10^113693+9113694Robert Price09/2015
25124*10^113658+49113659Robert Price01/2019
2513(2*10^113631+529)/9113631Robert Price01/2018
25142^377408-2798279113612Enzo Doria04/2016
25155*10^113586+57113587Robert Price12/2018
25162^377222+93679113556Yves Minet02/2011
2517262147#+316847113552Makoto Morimoto02/2016
25182^377026-458903113497Enzo Doria04/2015
251935^73477-34^73477113454Robert Price05/2012
25202^376790+27113426Lelio R Paula03/2013
25212^376786-112701113424Enzo Doria06/2014
25222^376731+21113408Lelio R Paula03/2013
25242^376634+1871245113379Enzo Doria05/2016
2523(4^188318+17)/3113379Robert Price02/2017
25252^376576-344369113361Enzo Doria07/2015
2526(17*2^376526-1)/223113345Lelio R Paula03/2014
2527(27*2^376441-1)/811113319Lelio R Paula03/2014
25282^376128-21237113226Enzo Doria06/2013
25295*10^113224-81113225Robert Price01/2019
25302^375638-1787171113079Enzo Doria03/2016
25312^375537+4847113048Yves Minet02/2011
2532(17^91837+16^91837)/33113000Robert Price08/2013
25335*F(270343)*(F(270343)+1)+1112997Serge Batalov04/2015
25342^375350-3221112992Yves Minet07/2011
2535(13*2^375306+1)/7112979Lelio R Paula03/2014
25362^375305+76757112979Enzo Doria05/2016
25372^375258+1874989112964Enzo Doria07/2016
2538(29^77237-1)/28112950Robert Price04/2012
25392^375154+74959112933Enzo Doria04/2016
25402^374993-2787163112885Enzo Doria11/2015
2541123^53970+2112793Lelio R Paula06/2013
2542p(22852)#/2+512112745Robert Price05/2017
2543(11*10^112742-131)/3112743Robert Price09/2018
25442^374441-21049112718Enzo Doria06/2013
2545(2^374321+1)/3112682H.&R. Lifchitz12/2000
2546(13^101089-1)/12112607Paul Bourdelais03/2010
25473^236011-8828112606Enzo Doria05/2014
254839^70666+2112435Lelio R Paula11/2013
2549(2^373350-7)/3112390Lelio R Paula03/2014
25502^373306-1840931112377Enzo Doria06/2015
25512^373117+1872107112320Enzo Doria05/2016
25522^373040+2792761112297Enzo Doria03/2016
2553EPrime(112280)112280Eric W. Weisstein10/2010
25542^372950+7112270Lelio R Paula03/2013
25552^372945+1872167112268Enzo Doria05/2016
25562^372695+72113112193Enzo Doria04/2016
25572^372689-2563112191Yves Minet07/2014
25582^372638-1859441112176Enzo Doria03/2016
25593^235074-113056112159Enzo Doria07/2014
2560(91*10^112098-1)/9112100Robert Price04/2015
25612^372310-85061112077Paul Bourdelais02/2012
2562(10^112067+53)/9112067Serge Batalov07/2015
256375^59760+2112054Lelio R Paula08/2013
25642^372108+74221112016Enzo Doria04/2016
2565215^48018+48018^215112000Norbert Schneider10/2018
25662^371970-459491111975Enzo Doria05/2015
256741^69427-40^69427111971Robert Price07/2012
2568(10^111902+71)/9111902Serge Batalov07/2015
25692^371440-112865111815Enzo Doria06/2014
25702^371426-459161111811Enzo Doria05/2015
25712^371276-461267111766Enzo Doria07/2015
25722^371098-113261111712Enzo Doria07/2014
2573(7*10^111706-61)/9111706Erik Branger01/2011
25742^371044+1869391111696Enzo Doria05/2016
257588^57416+87111645Norbert Schneider11/2015
25762^370829-109693111631Enzo Doria04/2014
257715^94906-2111619Lelio R Paula11/2013
25792^370643-37111575Yves Minet01/2012
2578(2^370655-5)/2439111575Lelio R Paula03/2014
25802^370610-3911111565Yves Minet04/2017
2581286^45405+45405^286111532Norbert Schneider04/2015
25824*5^159563-9111531Lelio R Paula11/2014
2583(4^185225+23)/3111517Robert Price10/2018
25842^370393-2797093111500Enzo Doria03/2016
2585(21*2^370382-1)/629111495Lelio R Paula03/2014
25862^370292-2791979111469Enzo Doria03/2016
25872^370177-461551111435Enzo Doria07/2015
2588109^54683-108111413Norbert Schneider02/2017
2589numbpart(10^10+76282)111391Serge Batalov04/2015
25902^369974+733111374Lelio R Paula05/2013
2591121^53470+120111367Norbert Schneider10/2018
25922^369915-286267111356Enzo Doria07/2015
25932^369855-1615111338Lelio R Paula05/2017
25947*10^111325+3111326Robert Price08/2015
259551^65176+2111293Lelio R Paula08/2013
25962^369643-1865767111274Enzo Doria03/2016
25972^369603+885111262Lelio R Paula05/2017
2598L(532277)111240Renaud Lifchitz03/2004
2599105^55033-2111233Lelio R Paula10/2017
2600(35*10^111232-737)/9111233Robert Price07/2018
26012^369392+29835111199Lelio R Paula05/2017
26022^369354-3413111187Yves Minet12/2016
26032^369296-27111170Lelio R Paula02/2013
26042^369239-109837111153Enzo Doria05/2014
26052^369224-291839111148Enzo Doria07/2015
26062^369216+2798881111146Enzo Doria04/2016
260710^111111+163849111112Patrick De Geest03/2017
260810^111111-312911111111Patrick De Geest03/2017
26092^369092-216923111108Enzo Doria05/2014
26102^369081-55111105Lelio R Paula02/2013
261188^57124-87111077Norbert Schneider11/2015
26122^368980+753111075Lelio R Paula05/2013
26132^368946-3623111064Yves Minet03/2017
26142^368929+29835111059Lelio R Paula05/2017
26154^184463-3^184463111058Jean-Louis Charton12/2004
2616111^54298+110111057Norbert Schneider04/2017
2617(4*10^111032-7)/3111033Ray Chandler04/2011
26182^368641-460303110972Enzo Doria06/2015
26192^368619-109087110966Enzo Doria04/2014
26203*2^368489+7110927Lelio R Paula09/2014
2621(14*10^110922+61)/3110923Robert Price12/2018
262297411!4-2110913Robert Price07/2017
2623(9179*2^368330-1)/35110881Lelio R Paula05/2015
2624(34*10^110882-7)/9/13/29/1019374319110871Makoto Morimoto05/2016
26252^368050-64875110795Lelio R Paula05/2017
26262^368048+25110794Lelio R Paula02/2013
262769^60239-2110771Lelio R Paula10/2013
2628(23*2^367952+1)/15717110762Lelio R Paula03/2014
26292^367924-69110757Lelio R Paula02/2013
26302^367709-109723110692Enzo Doria04/2014
2631(3*2^367644-1)/107110671Lelio R Paula03/2014
2632(23*2^367398+1)/57963110595Lelio R Paula03/2014
26332^367215+1879223110543Enzo Doria09/2016
26342^367141+41110521Lelio R Paula02/2013
26352^367126+29835110516Lelio R Paula05/2017
2636(11*10^110496+49)/3110497Robert Price07/2018
2637(31*2^366976+1)/7110472Lelio R Paula03/2014
26382^366853+5711110434Lelio R Paula05/2017
2639(21181*2^366833+1)/3110432Lelio R Paula07/2014
26402^366816+315110423Lelio R Paula05/2017
26412^366775-2787037110411Enzo Doria03/2016
2642(112*10^110405-1)/3110407Serge Batalov12/2014
26432^366751+2797553110404Enzo Doria03/2016
26442^366748+255110403Lelio R Paula05/2017
26452^366738-2985110400Yves Minet09/2014
2646(23*2^366739+1)/74575110396Lelio R Paula03/2014
26472^366716+1871791110393Enzo Doria05/2016
26482^366649+1871687110373Enzo Doria05/2016
26492^366629-351205110367Enzo Doria06/2015
26502^366558+1874479110345Enzo Doria06/2016
265118^87853-4409110280Enzo Doria03/2013
26522^366218-23110243Lelio R Paula02/2013
2653(21*2^366193-1)/197110235Lelio R Paula03/2014
26542^366178-343991110231Enzo Doria07/2015
26552^365944+1871341110161Enzo Doria05/2016
26562^365838-461267110129Enzo Doria07/2015
26572^365763-6555110106Lelio R Paula04/2017
2658(2^365689+2^182845+1)/511008311/2006
26592^365666-459161110077Enzo Doria05/2015
26603*10^110076-7110077Robert Price08/2015
266113^98785-72110041Lelio R Paula03/2017
2662(25^78707+1)/26110027Robert Price06/2013
2663(7*10^110006-151)/9110006Robert Price02/2018
26646^141361-7110001Lelio R Paula11/2014
266520^84536+81109984Lelio R Paula03/2017
26665*2^365347-9109982Lelio R Paula09/2014
26679*6^141303+7109957Lelio R Paula11/2014
266878^58099+77109929Norbert Schneider02/2015
26692*10^109928-7109929Robert Price10/2015
2670(27*2^365137-1)/2021109916Lelio R Paula03/2014
2671(4441*29^75152-24)/7109905Curtis Bright05/2015
2672(2^365087+7)/6015109899Lelio R Paula01/2014
267318^87533-11109878Lelio R Paula04/2017
26742^364982-5109871Henri Lifchitz04/2006
26753*10^109861+59109862Robert Price08/2018
26762^364936-1867979109857Enzo Doria04/2016
26772^364867-112087109836Enzo Doria06/2014
26784^182415-85061109825Mike Oakes06/2011
2679(17^89227+16^89227)/33109788Robert Price08/2013
26802^364687-187109782Lelio R Paula01/2012
26812^364644+67109769Lelio R Paula01/2012
2682(9787*2^364625-1)/24947109763Lelio R Paula05/2015
2683(2^364616+5)/9109760Lelio R Paula01/2014
268412^101694+73109747Lelio R Paula03/2017
268513^98518-66109744Lelio R Paula03/2017
26862^364478-113261109719Enzo Doria07/2014
2687(2^364513+1)/(3*44290516579)109719Gord Palameta08/2018
2688(24737*2^364454+1)/3109716Lelio R Paula07/2014
2689(62*10^109673+1)/9109674Serge Batalov11/2010
26903^229824+340109654Lelio R Paula03/2017
2691(2*10^109645-71)/3109645Robert Price12/2017
26922^364169-112813109626Enzo Doria06/2014
269310^109615+21109616Lelio R Paula03/2017
269410^109615-456267109615Patrick De Geest03/2017
26952^364094-113109604Lelio R Paula01/2012
2696(4^182026+11)/3109591Robert Price02/2017
26972^364041-6883109588Lelio R Paula09/2011
269812^101545+11109586Lelio R Paula03/2017
26992^363842-2787101109528Enzo Doria03/2016
2700(22699*2^363782+1)/763109511Lelio R Paula07/2014
27012^363769+5711109506Lelio R Paula04/2017
2702(31*2^363748+1)/49109499Lelio R Paula03/2014
2703p(22245)#/2-8109462Robert Price01/2017
27042^363556+55109442Lelio R Paula01/2012
2705(55459*2^363411+1)/81109401Lelio R Paula07/2014
27062^363406+1871569109397Enzo Doria05/2016
2707(2^363349+7)/9109378Lelio R Paula01/2014
27083^229236+100109374Lelio R Paula03/2017
27092^363268-58695109355Lelio R Paula04/2017
27102^363191-112321109332Enzo Doria06/2014
27114*10^109316-63109317Robert Price10/2018
27122^363120+3109311Donovan Johnson04/2006
2713(10^109297-1)/9109297Paul Bourdelais, Harvey Dubner04/2007
27142^363042-114641109287Enzo Doria04/2015
27152^363020-112793109280Enzo Doria06/2014
2716(67607*2^362695+1)/70499109183Lelio R Paula07/2014
2717(9*2^362644+1)/5109167Lelio R Paula03/2014
27185^156181+38109166Lelio R Paula02/2017
27194*10^109142+91109143Robert Price08/2018
27203^228750+68109142Lelio R Paula03/2017
2721(10223*2^362376+1)/9109090Lelio R Paula07/2014
272265^60167-64^60167109078Robert Price08/2013
27237*3^228589-2109066Lelio R Paula09/2014
2724(78557*2^362188+1)/189109033Lelio R Paula07/2014
27252*7^129008+9109025Lelio R Paula11/2014
2726(5*10^108960+91)/3108961Robert Price04/2018
27272^361957+76367108960Enzo Doria05/2016
27282^361873-1411108935Yves Minet01/2013
2729(24737*2^361857+1)/35108933Lelio R Paula07/2014
2730115^52842-114108892Norbert Schneider07/2018
273113^97745-24108883Lelio R Paula03/2017
273217^88475+8108864Lelio R Paula04/2017
27332^361567+51108843Lelio R Paula01/2012
27342^361563-109501108842Enzo Doria04/2014
273512^100852+83108838Lelio R Paula03/2017
27362^361497+767108822Lelio R Paula01/2012
27372^361280-112349108757Enzo Doria06/2014
27382^361271-5955108754Lelio R Paula04/2017
273912^100757+19108736Lelio R Paula03/2017
274014^94849-61108710Lelio R Paula05/2017
2741(19^85009-5^85009)/14108705Robert Price07/2013
2742(11*2^361027+1)/40463108677Lelio R Paula03/2014
27432^360973+1299108664Lelio R Paula04/2017
27442^360959-109101108660Enzo Doria04/2014
27456*5^155454+7108659Lelio R Paula11/2014
274610^108656+79108657Lelio R Paula02/2017
274710^108656-50001108656Patrick De Geest03/2017
27482^360918-35108648Lelio R Paula01/2012
2749(11*2^360886-1)/7108638Lelio R Paula03/2014
27503*10^108624-49108625Robert Price07/2018


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 14 2019 10:37 (Time in France)

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