PRP Records

Probable Primes Top 10000

(280932 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 ?
4001(10^110503-1)/9+5*10^99423+5*10^11079110503Makoto Morimoto09/2020
4002(10^110503-1)/9+7*(10^23617-1)/9*10^43443110503Makoto Morimoto09/2020
4003(10^110503-1)/9+8*(10^30251-1)/9*10^40126110503Makoto Morimoto09/2020
40043*(10^110503-1)/9+1*10^106036+1*10^4466110503Makoto Morimoto09/2020
40053*(10^110503-1)/9+1*10^58962+1*10^51540110503Makoto Morimoto09/2020
40063*(10^110503-1)/9+1*10^78213+1*10^32289110503Makoto Morimoto09/2020
40073*(10^110503-1)/9+2*10^76898+2*10^33604110503Makoto Morimoto09/2020
40083*(10^110503-1)/9-1*10^100802-1*10^9700110503Makoto Morimoto09/2020
40093*(10^110503-1)/9-1*10^76355-1*10^34147110503Makoto Morimoto09/2020
40103*(10^110503-1)/9-2*10^105704-2*10^4798110503Makoto Morimoto09/2020
40117*(10^110503-1)/9+1*(10^27685-1)/9*10^41409110503Makoto Morimoto09/2020
40127*(10^110503-1)/9+1*(10^91035-1)/9*10^9734110503Makoto Morimoto09/2020
40137*(10^110503-1)/9-1*(10^23717-1)/9*10^43393110503Makoto Morimoto09/2020
40147*(10^110503-1)/9-1*10^57906-1*10^52596110503Makoto Morimoto09/2020
40157*(10^110503-1)/9-1*10^72287-1*10^38215110503Makoto Morimoto09/2020
40167*(10^110503-1)/9-2*(10^53823-1)/9*10^28340110503Makoto Morimoto09/2020
40177*(10^110503-1)/9-2*(10^88659-1)/9*10^10922110503Makoto Morimoto09/2020
40187*(10^110503-1)/9-3*(10^79921-1)/9*10^15291110503Makoto Morimoto09/2020
40197*(10^110503-1)/9-3*10^60024-3*10^50478110503Makoto Morimoto09/2020
40207*(10^110503-1)/9-4*(10^103091-1)/9*10^3706110503Makoto Morimoto09/2020
40217*(10^110503-1)/9-4*10^103658-4*10^6844110503Makoto Morimoto09/2020
40227*(10^110503-1)/9-4*10^78188-4*10^32314110503Makoto Morimoto09/2020
40237*(10^110503-1)/9-5*(10^35035-1)/9*10^37734110503Makoto Morimoto09/2020
40247*(10^110503-1)/9-6*(10^67347-1)/9*10^21578110503Makoto Morimoto09/2020
40257*(10^110503-1)/9-6*10^60391-6*10^50111110503Makoto Morimoto09/2020
4026(10^110503-1)-4*(10^96247-1)/9*10^7128110503Makoto Morimoto09/2020
4027(10^110503-1)-4*10^74037-4*10^36465110503Makoto Morimoto09/2020
4028(10^110503-1)-4*10^77787-4*10^32715110503Makoto Morimoto09/2020
4029(10^110503-1)-4*10^91179-4*10^19323110503Makoto Morimoto09/2020
4030(10^110503-1)-5*(10^99143-1)/9*10^5680110503Makoto Morimoto09/2020
4031(10^110503-1)-7*(10^85075-1)/9*10^12714110503Makoto Morimoto09/2020
4032(10^110503-1)-7*10^100712-7*10^9790110503Makoto Morimoto09/2020
4033(10^110503-1)-7*10^76427-7*10^34075110503Makoto Morimoto09/2020
4034(10^110503-1)-7*10^90451-7*10^20051110503Makoto Morimoto09/2020
4035(10^110503-1)-8*10^106252-8*10^4250110503Makoto Morimoto09/2020
4036(11*10^110496+49)/3110497Robert Price07/2018
403725447^21958+21958^25447110481Hans Havermann11/2020
4038(31*2^366976+1)/7110472Lelio R Paula03/2014
40397*10^110468-23110469Robert Price07/2019
40402^366853+5711110434Lelio R Paula05/2017
4041(21181*2^366833+1)/3110432Lelio R Paula07/2014
40422^366816+315110423Lelio R Paula05/2017
40432^366775-2787037110411Enzo Doria03/2016
4044(112*10^110405-1)/3110407Serge Batalov12/2014
40452^366751+2797553110404Enzo Doria03/2016
404625276^23331+23331^25276110404Hans Havermann10/2020
40472^366748+255110403Lelio R Paula05/2017
40482^366738-2985110400Yves Minet09/2014
4049(23*2^366739+1)/74575110396Lelio R Paula03/2014
4050(2^366722+1314)/2110395Stefano Morozzi02/2021
40512^366716+1871791110393Enzo Doria05/2016
40522^366649+1871687110373Enzo Doria05/2016
40532^366629-351205110367Enzo Doria06/2015
40542^366558+1874479110345Enzo Doria06/2016
405525132^24581+24581^25132110345Hans Havermann10/2020
4056(2^366539+770)/2110339Stefano Morozzi09/2020
405726368^15285+15285^26368110331Hans Havermann10/2020
4058(23*10^110290+19)/3110291Robert Price07/2019
405918^87853-4409110280Enzo Doria03/2013
406028490^7419+7419^28490110267Hans Havermann11/2020
40612^366218-23110243Lelio R Paula02/2013
4062(21*2^366193-1)/197110235Lelio R Paula03/2014
40632^366178-343991110231Enzo Doria07/2015
406425777^18798+18798^25777110174Hans Havermann10/2020
40652^365944+1871341110161Enzo Doria05/2016
40662^365838-461267110129Enzo Doria07/2015
406730152^4491+4491^30152110126Hans Havermann11/2020
406810^110111-40001110111Robert Price01/2021
40692^365763-6555110106Lelio R Paula04/2017
4070(2^365689+2^182845+1)/511008311/2006
40712^365666-459161110077Enzo Doria05/2015
40723*10^110076-7110077Robert Price08/2015
407313^98785-72110041Lelio R Paula03/2017
4074(25^78707+1)/26110027Robert Price06/2013
4075(16*10^110014-73)/3110015Robert Price07/2020
4076(7*10^110006-151)/9110006Robert Price02/2018
40776^141361-7110001Lelio R Paula11/2014
407820^84536+81109984Lelio R Paula03/2017
40795*2^365347-9109982Lelio R Paula09/2014
40809*6^141303+7109957Lelio R Paula11/2014
408127635^9522+9522^27635109953Hans Havermann11/2020
408278^58099+77109929Norbert Schneider02/2015
40832*10^109928-7109929Robert Price10/2015
408430580^3933+3933^30580109927Hans Havermann11/2020
408526380^14689+14689^26380109926Hans Havermann11/2020
4086(2^365161+1130)/2109925Stefano Morozzi09/2020
4087(27*2^365137-1)/2021109916Lelio R Paula03/2014
4088(4441*29^75152-24)/7109905Curtis Bright05/2015
4089(2^365087+7)/6015109899Lelio R Paula01/2014
4090(2^365069+3774)/2109897Stefano Morozzi02/2021
409129652^5083+5083^29652109894Mark Rodenkirch10/2020
4092(2^365049+722)/2109891Stefano Morozzi09/2020
409318^87533-11109878Lelio R Paula04/2017
40942^364982-5109871Henri Lifchitz04/2006
40953*10^109861+59109862Robert Price08/2018
40965*10^109860-69109861Robert Price02/2021
40972^364936-1867979109857Enzo Doria04/2016
409827013^11652+11652^27013109846Hans Havermann10/2020
40992^364867-112087109836Enzo Doria06/2014
41004^182415-85061109825Mike Oakes06/2011
4101(2^364809+1034)/2109819Stefano Morozzi09/2020
410225708^18675+18675^25708109806Hans Havermann10/2020
4103(17^89227+16^89227)/33109788Robert Price08/2013
41042^364687-187109782Lelio R Paula01/2012
41052^364644+67109769Lelio R Paula01/2012
4106(9787*2^364625-1)/24947109763Lelio R Paula05/2015
4107(2^364616+5)/9109760Lelio R Paula01/2014
4108(55*10^109759+89)/9109760Robert Price03/2019
410912^101694+73109747Lelio R Paula03/2017
411013^98518-66109744Lelio R Paula03/2017
41112^364478-113261109719Enzo Doria07/2014
4112(2^364513+1)/(3*44290516579)109719Gord Palameta08/2018
4113(24737*2^364454+1)/3109716Lelio R Paula07/2014
411427814^8777+8777^27814109681Hans Havermann10/2020
4115(62*10^109673+1)/9109674Serge Batalov11/2010
41163^229824+340109654Lelio R Paula03/2017
4117(2*10^109645-71)/3109645Robert Price12/2017
41182^364169-112813109626Enzo Doria06/2014
411928822^6359+6359^28822109622Hans Havermann11/2020
412010^109615+21109616Lelio R Paula03/2017
412110^109615-456267109615Patrick De Geest03/2017
41222^364094-113109604Lelio R Paula01/2012
412325251^21898+21898^25251109600Hans Havermann11/2020
4124(4^182026+11)/3109591Robert Price02/2017
41252^364041-6883109588Lelio R Paula09/2011
412612^101545+11109586Lelio R Paula03/2017
412726536^13475+13475^26536109582Hans Havermann11/2020
41282^363842-2787101109528Enzo Doria03/2016
4129(2^363812+3570)/2109519Stefano Morozzi09/2020
4130(22699*2^363782+1)/763109511Lelio R Paula07/2014
41312^363769+5711109506Lelio R Paula04/2017
4132(31*2^363748+1)/49109499Lelio R Paula03/2014
4133p(22245)#/2-8109462Robert Price01/2017
41342^363556+55109442Lelio R Paula01/2012
4135(2^363437+1682)/2109406Stefano Morozzi09/2020
4136(55459*2^363411+1)/81109401Lelio R Paula07/2014
41372^363406+1871569109397Enzo Doria05/2016
4138(2^363370+1338)/2109385Stefano Morozzi02/2021
4139(2^363349+7)/9109378Lelio R Paula01/2014
41403^229236+100109374Lelio R Paula03/2017
4141(2^363315+3258)/2109369Stefano Morozzi02/2021
41422^363268-58695109355Lelio R Paula04/2017
41432^363191-112321109332Enzo Doria06/2014
414426231^14718+14718^26231109327Hans Havermann10/2020
414525461^19672+19672^25461109326Hans Havermann10/2020
41464*10^109316-63109317Robert Price10/2018
41472^363120+3109311Donovan Johnson04/2006
4148(10^109297-1)/9109297Paul Bourdelais, Harvey Dubner04/2007
41492^363042-114641109287Enzo Doria04/2015
41502^363020-112793109280Enzo Doria06/2014
4151(85*10^109253+203)/9109254Robert Price09/2020
415224990^23431+23431^24990109202Hans Havermann10/2020
4153(2^362746+3738)/2109198Stefano Morozzi09/2020
4154(2^362716+1282)/2109189Stefano Morozzi01/2021
4155(67607*2^362695+1)/70499109183Lelio R Paula07/2014
415625060^22737+22737^25060109180Hans Havermann10/2020
4157(9*2^362644+1)/5109167Lelio R Paula03/2014
41585^156181+38109166Lelio R Paula02/2017
4159(2^362623+3618)/2109161Stefano Morozzi09/2020
416025138^21993+21993^25138109157Hans Havermann10/2020
41614*10^109142+91109143Robert Price08/2018
41633^228750+68109142Lelio R Paula03/2017
4162(2^362561+786)/2109142Stefano Morozzi09/2020
41642*10^109100-49109101Robert Price09/2020
4165(10223*2^362376+1)/9109090Lelio R Paula07/2014
416665^60167-64^60167109078Robert Price08/2013
41677*3^228589-2109066Lelio R Paula09/2014
416824874^24243+24243^24874109063Hans Havermann11/2020
4169(17*10^109059-161)/9109060Robert Price02/2021
417029158^5495+5495^29158109050Hans Havermann11/2020
4171(78557*2^362188+1)/189109033Lelio R Paula07/2014
41722*7^129008+9109025Lelio R Paula11/2014
417388*10^109022+7109024Robert Price03/2020
417428194^7337+7337^28194108985Hans Havermann10/2020
4175(5*10^108960+91)/3108961Robert Price04/2018
41762^361957+76367108960Enzo Doria05/2016
41772^361873-1411108935Yves Minet01/2013
4178(24737*2^361857+1)/35108933Lelio R Paula07/2014
4179115^52842-114108892Norbert Schneider07/2018
418013^97745-24108883Lelio R Paula03/2017
4181(2^361696+2562)/2108882Stefano Morozzi09/2020
418217^88475+8108864Lelio R Paula04/2017
41832^361567+51108843Lelio R Paula01/2012
41842^361563-109501108842Enzo Doria04/2014
418512^100852+83108838Lelio R Paula03/2017
41862^361497+767108822Lelio R Paula01/2012
418728019^7630+7630^28019108785Hans Havermann10/2020
418824723^24758-24758^24723108765Norbert Schneider11/2020
41892^361280-112349108757Enzo Doria06/2014
41902^361271-5955108754Lelio R Paula04/2017
419112^100757+19108736Lelio R Paula03/2017
419225368^19333+19333^25368108735Hans Havermann11/2020
4193(2^361195+3618)/2108731Stefano Morozzi09/2020
419414^94849-61108710Lelio R Paula05/2017
419527267^9700+9700^27267108708Hans Havermann11/2020
4196(19^85009-5^85009)/14108705Robert Price07/2013
419724832^23853+23853^24832108704Hans Havermann11/2020
419827502^8963+8963^27502108701Hans Havermann11/2020
419925807^16278+16278^25807108689Hans Havermann11/2020
4200(11*2^361027+1)/40463108677Lelio R Paula03/2014
42012^360973+1299108664Lelio R Paula04/2017
42022^360959-109101108660Enzo Doria04/2014
42036*5^155454+7108659Lelio R Paula11/2014
420410^108656+79108657Lelio R Paula02/2017
420510^108656-50001108656Patrick De Geest03/2017
42062^360918-35108648Lelio R Paula01/2012
4207(11*2^360886-1)/7108638Lelio R Paula03/2014
42083*10^108624-49108625Robert Price07/2018
4209(2^360831+666)/2108621Stefano Morozzi09/2020
4210(134*10^108610+7)/3108612Robert Price02/2020
42112*10^108609+29108610Robert Price02/2021
4212(2^360742+3222)/2108594Stefano Morozzi09/2020
42132^360706-458903108584Enzo Doria04/2015
421431112^3087+3087^31112108567Hans Havermann11/2020
42152^360641-113185108564Enzo Doria07/2014
42162^360618+75019108557Enzo Doria04/2016
4217(14*10^108545-221)/9108546Robert Price04/2018
4218(44*10^108544-233)/9108545Robert Price01/2019
42193*5^155286+2108541Lelio R Paula11/2014
42207^128422+4108530Lelio R Paula11/2014
42217^128421-80108529Lelio R Paula03/2017
42222^360497+53807108521Yves Minet07/2010
42232^360468-4559108512Yves Minet03/2019
4224(2^360451+578)/2108507Stefano Morozzi09/2020
42252^360366+1459108481Lelio R Paula09/2011
42262^360364-1499108481Yves Minet05/2013
422725662^16871+16871^25662108477Hans Havermann10/2020
422825009^21748+21748^25009108475Hans Havermann10/2020
422914^94642-23108472Lelio R Paula05/2017
4230(197*10^108446-11)/3108448Robert Price03/2020
4231(2^360229+1290)/2108440Stefano Morozzi01/2021
42324*10^108412+9108413Robert Price05/2015
4233(259*10^108409-1)/3108411Robert Price12/2020
4234(2^360122+1194)/2108408Stefano Morozzi09/2020
4235133^51042-132108406Norbert Schneider02/2019
42362^360093-351103108399Enzo Doria06/2015
42372^360042+723108384Lelio R Paula01/2012
423885^56164-2108364Lelio R Paula10/2013
42392^359937-29323108352Enzo Doria07/2015
4240(2^359922+1762)/2108348Stefano Morozzi09/2020
4241(2^359903+758)/2108342Stefano Morozzi09/2020
42422^359898-19997108341Enzo Doria06/2013
4243(2^359886+2122)/2108337Stefano Morozzi09/2020
42442*5^154948-7108305Lelio R Paula11/2014
424510^108303+13108304Lelio R Paula02/2017
424610^108303-207959108303Patrick De Geest03/2017
42477*10^108300+69108301Robert Price07/2019
42482^359730+753108290Lelio R Paula12/2011
4249(8*10^108273+13)/3108274Robert Price06/2018
42502^359650-19797108266Enzo Doria06/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 13 2021 12:02 (Time in France)

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