PRP Records

Probable Primes Top 10000

(173006 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 ?
200111^109190-270113710Enzo Doria12/2012
20027*10^113693+9113694Robert Price09/2015
20032^377408-2798279113612Enzo Doria04/2016
20042^377222+93679113556Yves Minet02/2011
2005262147#+316847113552Makoto Morimoto02/2016
20062^377026-458903113497Enzo Doria04/2015
200735^73477-34^73477113454Robert Price05/2012
20082^376790+27113426Lelio R Paula03/2013
20092^376786-112701113424Enzo Doria06/2014
20102^376731+21113408Lelio R Paula03/2013
20112^376634+1871245113379Enzo Doria05/2016
2012(4^188318+17)/3113379Robert Price02/2017
20132^376576-344369113361Enzo Doria07/2015
2014(17*2^376526-1)/223113345Lelio R Paula03/2014
2015(27*2^376441-1)/811113319Lelio R Paula03/2014
20162^376128-21237113226Enzo Doria06/2013
20172^375638-1787171113079Enzo Doria03/2016
20182^375537+4847113048Yves Minet02/2011
2019(17^91837+16^91837)/33113000Robert Price08/2013
20205*F(270343)*(F(270343)+1)+1112997Serge Batalov04/2015
20212^375350-3221112992Yves Minet07/2011
2022(13*2^375306+1)/7112979Lelio R Paula03/2014
20232^375305+76757112979Enzo Doria05/2016
20242^375258+1874989112964Enzo Doria07/2016
2025(29^77237-1)/28112950Robert Price04/2012
20262^375154+74959112933Enzo Doria04/2016
20272^374993-2787163112885Enzo Doria11/2015
2028123^53970+2112793Lelio R Paula06/2013
2029p(22852)#/2+512112745Robert Price05/2017
20302^374441-21049112718Enzo Doria06/2013
2031(2^374321+1)/3112682H.&R. Lifchitz12/2000
2032(13^101089-1)/12112607Paul Bourdelais03/2010
20333^236011-8828112606Enzo Doria05/2014
203439^70666+2112435Lelio R Paula11/2013
2035(2^373350-7)/3112390Lelio R Paula03/2014
20362^373306-1840931112377Enzo Doria06/2015
20372^373117+1872107112320Enzo Doria05/2016
20382^373040+2792761112297Enzo Doria03/2016
2039EPrime(112280)112280Eric W. Weisstein10/2010
20402^372950+7112270Lelio R Paula03/2013
20412^372945+1872167112268Enzo Doria05/2016
20422^372695+72113112193Enzo Doria04/2016
20432^372689-2563112191Yves Minet07/2014
20442^372638-1859441112176Enzo Doria03/2016
20453^235074-113056112159Enzo Doria07/2014
2046(91*10^112098-1)/9112100Robert Price04/2015
20472^372310-85061112077Paul Bourdelais02/2012
2048(10^112067+53)/9112067Serge Batalov07/2015
204975^59760+2112054Lelio R Paula08/2013
20502^372108+74221112016Enzo Doria04/2016
20512^371970-459491111975Enzo Doria05/2015
205241^69427-40^69427111971Robert Price07/2012
2053(10^111902+71)/9111902Serge Batalov07/2015
20542^371440-112865111815Enzo Doria06/2014
20552^371426-459161111811Enzo Doria05/2015
20562^371276-461267111766Enzo Doria07/2015
20572^371098-113261111712Enzo Doria07/2014
2058(7*10^111706-61)/9111706Erik Branger01/2011
20592^371044+1869391111696Enzo Doria05/2016
206088^57416+87111645Norbert Schneider11/2015
20612^370829-109693111631Enzo Doria04/2014
206215^94906-2111619Lelio R Paula11/2013
20632^370643-37111575Yves Minet01/2012
2064(2^370655-5)/2439111575Lelio R Paula03/2014
20652^370610-3911111565Yves Minet04/2017
2066286^45405+45405^286111532Norbert Schneider04/2015
20674*5^159563-9111531Lelio R Paula11/2014
20682^370393-2797093111500Enzo Doria03/2016
2069(21*2^370382-1)/629111495Lelio R Paula03/2014
20702^370292-2791979111469Enzo Doria03/2016
20712^370177-461551111435Enzo Doria07/2015
2072109^54683-108111413Norbert Schneider02/2017
2073numbpart(10^10+76282)111391Serge Batalov04/2015
20742^369974+733111374Lelio R Paula05/2013
20752^369915-286267111356Enzo Doria07/2015
20762^369855-1615111338Lelio R Paula05/2017
20777*10^111325+3111326Robert Price08/2015
207851^65176+2111293Lelio R Paula08/2013
20792^369643-1865767111274Enzo Doria03/2016
20802^369603+885111262Lelio R Paula05/2017
2081L(532277)111240Renaud Lifchitz03/2004
20822^369392+29835111199Lelio R Paula05/2017
20832^369354-3413111187Yves Minet12/2016
20842^369296-27111170Lelio R Paula02/2013
20852^369239-109837111153Enzo Doria05/2014
20862^369224-291839111148Enzo Doria07/2015
20872^369216+2798881111146Enzo Doria04/2016
208810^111111+163849111112Patrick De Geest03/2017
208910^111111-312911111111Patrick De Geest03/2017
20902^369092-216923111108Enzo Doria05/2014
20912^369081-55111105Lelio R Paula02/2013
209288^57124-87111077Norbert Schneider11/2015
20932^368980+753111075Lelio R Paula05/2013
20942^368946-3623111064Yves Minet03/2017
20952^368929+29835111059Lelio R Paula05/2017
20964^184463-3^184463111058Jean-Louis Charton12/2004
2097111^54298+110111057Norbert Schneider04/2017
2098(4*10^111032-7)/3111033Ray Chandler04/2011
20992^368641-460303110972Enzo Doria06/2015
21002^368619-109087110966Enzo Doria04/2014
21013*2^368489+7110927Lelio R Paula09/2014
2102(9179*2^368330-1)/35110881Lelio R Paula05/2015
2103(34*10^110882-7)/9/13/29/1019374319110871Makoto Morimoto05/2016
21042^368050-64875110795Lelio R Paula05/2017
21052^368048+25110794Lelio R Paula02/2013
210669^60239-2110771Lelio R Paula10/2013
2107(23*2^367952+1)/15717110762Lelio R Paula03/2014
21082^367924-69110757Lelio R Paula02/2013
21092^367709-109723110692Enzo Doria04/2014
2110(3*2^367644-1)/107110671Lelio R Paula03/2014
2111(23*2^367398+1)/57963110595Lelio R Paula03/2014
21122^367215+1879223110543Enzo Doria09/2016
21132^367141+41110521Lelio R Paula02/2013
21142^367126+29835110516Lelio R Paula05/2017
2115(31*2^366976+1)/7110472Lelio R Paula03/2014
21162^366853+5711110434Lelio R Paula05/2017
2117(21181*2^366833+1)/3110432Lelio R Paula07/2014
21182^366816+315110423Lelio R Paula05/2017
21192^366775-2787037110411Enzo Doria03/2016
2120(112*10^110405-1)/3110407Serge Batalov12/2014
21212^366751+2797553110404Enzo Doria03/2016
21222^366748+255110403Lelio R Paula05/2017
21232^366738-2985110400Yves Minet09/2014
2124(23*2^366739+1)/74575110396Lelio R Paula03/2014
21252^366716+1871791110393Enzo Doria05/2016
21262^366649+1871687110373Enzo Doria05/2016
21272^366629-351205110367Enzo Doria06/2015
21282^366558+1874479110345Enzo Doria06/2016
212918^87853-4409110280Enzo Doria03/2013
21302^366218-23110243Lelio R Paula02/2013
2131(21*2^366193-1)/197110235Lelio R Paula03/2014
21322^366178-343991110231Enzo Doria07/2015
21332^365944+1871341110161Enzo Doria05/2016
21342^365838-461267110129Enzo Doria07/2015
21352^365763-6555110106Lelio R Paula04/2017
2136(2^365689+2^182845+1)/511008311/2006
21372^365666-459161110077Enzo Doria05/2015
21383*10^110076-7110077Robert Price08/2015
213913^98785-72110041Lelio R Paula03/2017
2140(25^78707+1)/26110027Robert Price06/2013
21416^141361-7110001Lelio R Paula11/2014
214220^84536+81109984Lelio R Paula03/2017
21435*2^365347-9109982Lelio R Paula09/2014
21449*6^141303+7109957Lelio R Paula11/2014
214578^58099+77109929Norbert Schneider02/2015
21462*10^109928-7109929Robert Price10/2015
2147(27*2^365137-1)/2021109916Lelio R Paula03/2014
2148(4441*29^75152-24)/7109905Curtis Bright05/2015
2149(2^365087+7)/6015109899Lelio R Paula01/2014
215018^87533-11109878Lelio R Paula04/2017
21512^364982-5109871Henri Lifchitz04/2006
21522^364936-1867979109857Enzo Doria04/2016
21532^364867-112087109836Enzo Doria06/2014
21544^182415-85061109825Mike Oakes06/2011
2155(17^89227+16^89227)/33109788Robert Price08/2013
21562^364687-187109782Lelio R Paula01/2012
21572^364644+67109769Lelio R Paula01/2012
2158(9787*2^364625-1)/24947109763Lelio R Paula05/2015
2159(2^364616+5)/9109760Lelio R Paula01/2014
216012^101694+73109747Lelio R Paula03/2017
216113^98518-66109744Lelio R Paula03/2017
21622^364478-113261109719Enzo Doria07/2014
2163(24737*2^364454+1)/3109716Lelio R Paula07/2014
2164(62*10^109673+1)/9109674Serge Batalov11/2010
21653^229824+340109654Lelio R Paula03/2017
21662^364169-112813109626Enzo Doria06/2014
216710^109615+21109616Lelio R Paula03/2017
216810^109615-456267109615Patrick De Geest03/2017
21692^364094-113109604Lelio R Paula01/2012
2170(4^182026+11)/3109591Robert Price02/2017
21712^364041-6883109588Lelio R Paula09/2011
217212^101545+11109586Lelio R Paula03/2017
21732^363842-2787101109528Enzo Doria03/2016
2174(22699*2^363782+1)/763109511Lelio R Paula07/2014
21752^363769+5711109506Lelio R Paula04/2017
2176(31*2^363748+1)/49109499Lelio R Paula03/2014
2177p(22245)#/2-8109462Robert Price01/2017
21782^363556+55109442Lelio R Paula01/2012
2179(55459*2^363411+1)/81109401Lelio R Paula07/2014
21802^363406+1871569109397Enzo Doria05/2016
2181(2^363349+7)/9109378Lelio R Paula01/2014
21823^229236+100109374Lelio R Paula03/2017
21832^363268-58695109355Lelio R Paula04/2017
21842^363191-112321109332Enzo Doria06/2014
21852^363120+3109311Donovan Johnson04/2006
2186(10^109297-1)/9109297Paul Bourdelais, Harvey Dubner04/2007
21872^363042-114641109287Enzo Doria04/2015
21882^363020-112793109280Enzo Doria06/2014
2189(67607*2^362695+1)/70499109183Lelio R Paula07/2014
2190(9*2^362644+1)/5109167Lelio R Paula03/2014
21915^156181+38109166Lelio R Paula02/2017
21923^228750+68109142Lelio R Paula03/2017
2193(10223*2^362376+1)/9109090Lelio R Paula07/2014
219465^60167-64^60167109078Robert Price08/2013
21957*3^228589-2109066Lelio R Paula09/2014
2196(78557*2^362188+1)/189109033Lelio R Paula07/2014
21972*7^129008+9109025Lelio R Paula11/2014
21982^361957+76367108960Enzo Doria05/2016
21992^361873-1411108935Yves Minet01/2013
2200(24737*2^361857+1)/35108933Lelio R Paula07/2014
220113^97745-24108883Lelio R Paula03/2017
220217^88475+8108864Lelio R Paula04/2017
22032^361567+51108843Lelio R Paula01/2012
22042^361563-109501108842Enzo Doria04/2014
220512^100852+83108838Lelio R Paula03/2017
22062^361497+767108822Lelio R Paula01/2012
22072^361280-112349108757Enzo Doria06/2014
22082^361271-5955108754Lelio R Paula04/2017
220912^100757+19108736Lelio R Paula03/2017
221014^94849-61108710Lelio R Paula05/2017
2211(19^85009-5^85009)/14108705Robert Price07/2013
2212(11*2^361027+1)/40463108677Lelio R Paula03/2014
22132^360973+1299108664Lelio R Paula04/2017
22142^360959-109101108660Enzo Doria04/2014
22156*5^155454+7108659Lelio R Paula11/2014
221610^108656+79108657Lelio R Paula02/2017
221710^108656-50001108656Patrick De Geest03/2017
22182^360918-35108648Lelio R Paula01/2012
2219(11*2^360886-1)/7108638Lelio R Paula03/2014
22202^360706-458903108584Enzo Doria04/2015
22212^360641-113185108564Enzo Doria07/2014
22222^360618+75019108557Enzo Doria04/2016
22233*5^155286+2108541Lelio R Paula11/2014
22247^128422+4108530Lelio R Paula11/2014
22257^128421-80108529Lelio R Paula03/2017
22262^360497+53807108521Yves Minet07/2010
22272^360366+1459108481Lelio R Paula09/2011
22282^360364-1499108481Yves Minet05/2013
222914^94642-23108472Lelio R Paula05/2017
22304*10^108412+9108413Robert Price05/2015
22312^360093-351103108399Enzo Doria06/2015
22322^360042+723108384Lelio R Paula01/2012
223385^56164-2108364Lelio R Paula10/2013
22342^359937-29323108352Enzo Doria07/2015
22352^359898-19997108341Enzo Doria06/2013
22362*5^154948-7108305Lelio R Paula11/2014
223710^108303+13108304Lelio R Paula02/2017
223810^108303-207959108303Patrick De Geest03/2017
22392^359730+753108290Lelio R Paula12/2011
22402^359650-19797108266Enzo Doria06/2013
224191^55259-90^55259108255Robert Price07/2015
22423^226845+68108233Lelio R Paula03/2017
22435^154822-12866108216Enzo Doria05/2014
2244(9*2^359480+1)/5108215Lelio R Paula03/2014
22452^359454-177108207Lelio R Paula12/2011
22466^139022-59108181Lelio R Paula02/2017
22472^359352-179108176Lelio R Paula12/2011
22482^359338-1858781108172Enzo Doria04/2016
224912^100230-97108167Lelio R Paula03/2017
2250(25*2^359297-1)/137108159Lelio R Paula03/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 25 2017 10:58 (Time in France)

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