PRP Records

Probable Primes Top 10000

(253476 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 ?
40012^328497-21693398888Enzo Doria05/2014
40022^328487+3276998885Lelio R Paula08/2016
40033^207250-11235898884Enzo Doria06/2014
400413^88754-9098867Lelio R Paula08/2016
40052^328406+70998861Lelio R Paula02/2013
4006(17*2^328413-1)/1617398860Lelio R Paula03/2014
40077^116976+7698857Lelio R Paula08/2016
40082^328335+115598839Lelio R Paula08/2016
4010(3*2^328311+1)/598832Lelio R Paula11/2013
4009287^40210+40210^28798832Norbert Schneider11/2014
4011(2^328284+9)/132598821Lelio R Paula10/2013
4012(21*2^328258+1)/212598814Lelio R Paula11/2013
401365^54491+4898788Lelio R Paula04/2016
40143^207042+9898785Lelio R Paula08/2016
40153^206977-11275698754Enzo Doria07/2014
40167^116846-5098747Lelio R Paula08/2016
40172^327967-2863598728Lelio R Paula08/2016
4018707^34642+34642^70798710Norbert Schneider12/2017
40196^126850-4798709Lelio R Paula08/2016
40208*6^126830-798694Lelio R Paula11/2014
402111^94770-27098693Enzo Doria08/2012
40222^327832+4398688Lelio R Paula12/2012
40232^327795+76198677Lelio R Paula02/2013
402410^98669+14741198670Patrick De Geest11/2016
402610^98669-9^(98669-1)98669Robert Price05/2016
402510^98669-10524998669Patrick De Geest11/2016
40272^327671-10980198639Enzo Doria04/2014
40285^141090-1498618Lelio R Paula08/2016
402920^75799+4798617Lelio R Paula08/2016
40302^327515-101798592Lelio R Paula08/2016
40316^126692+9768198586Mike Oakes04/2011
40322^327467-74198578Lelio R Paula08/2016
4033(2^327329+9)/1998535Lelio R Paula10/2013
40347^116577-6698519Lelio R Paula08/2016
4035(3*2^327250+1)/798512Lelio R Paula11/2013
4036(19*2^327192+1)/27598494Lelio R Paula11/2013
40372^327162-6694598486Lelio R Paula08/2016
40384*10^98472-398473Erik Branger11/2013
4039(6883*2^327047-1)/7798453Lelio R Paula05/2015
4040(71*10^98446+1)/998447Serge Batalov11/2010
404113^88363+9498432Lelio R Paula08/2016
404248^58543-47^5854398425Jean-Louis Charton11/2005
40436^126481+4198422Lelio R Paula08/2016
404478*10^98413-798415Robert Price05/2017
40457^116416+4698383Lelio R Paula08/2016
40467^116407-2498376Lelio R Paula07/2016
4047439^37228+37228^43998374Norbert Schneider08/2018
40492^326782-186067198372Enzo Doria03/2016
404817^79948+5898372Lelio R Paula08/2016
40503^206143-9898356Lelio R Paula08/2016
40518*5^140705+798350Lelio R Paula11/2014
40522^326585+1198312Lelio R Paula12/2012
40532^326582-45916198311Enzo Doria05/2015
4054(2^326548+9)/598301Lelio R Paula10/2013
40552^326538+7165998298Enzo Doria04/2016
405615^83575-5898292Lelio R Paula08/2016
405710^98288+398289Robert Price03/2011
405810^98288-11701798288Patrick De Geest11/2011
4059(44*10^98284-719)/998285Robert Price12/2017
40602^326421-279757398263Enzo Doria04/2016
40612^326401+1609598257Lelio R Paula07/2016
40627^116240-116240^798235Norbert Schneider05/2017
406317^79826-7898222Lelio R Paula08/2016
40642^326268-80998217Yves Minet04/2011
4065(418*10^98199+23)/998201Robert Price08/2017
406612*10^98198-798200Robert Price11/2017
406715^83496-7698199Lelio R Paula08/2016
4068(10223*2^326179+1)/612598190Lelio R Paula07/2014
40699*5^140471-498186Lelio R Paula11/2014
40702^326069-238398157Yves Minet10/2013
40712^325973+118598128Lelio R Paula07/2016
4072(25*2^325949-1)/1798121Lelio R Paula02/2014
40732^325945-184726998120Enzo Doria07/2015
40748*10^98111-6798112Robert Price10/2017
40752^325866+1598096Lelio R Paula12/2012
40762^325765+197430598066Enzo Doria06/2016
40772^325733-5869598056Lelio R Paula07/2016
40782^325717-364598051Lelio R Paula07/2016
4079(23*2^325583-1)/2198011Lelio R Paula02/2014
4080(7*10^98007-13)/398008Robert Price06/2016
40812^325512-45995997989Enzo Doria05/2015
4082(3^205354-8)/1797978Lelio R Paula09/2013
40832^325433+7681797966Enzo Doria05/2016
40845*10^97963+8197964Robert Price08/2017
40852^325390-10906197953Enzo Doria04/2014
408613^87921+2497940Lelio R Paula08/2016
4087961^32831-960^3283197926Jean-Louis Charton02/2011
40882^325215+1290997900Lelio R Paula07/2016
40897*10^97874-6997875Robert Price01/2017
4091(17^79537+5^79537)/2297865Robert Price06/2013
409015^83212+2297865Lelio R Paula08/2016
40922^325087-10905797861Enzo Doria04/2014
40932^325074+187065797858Enzo Doria05/2016
40952^325066-211197855Yves Minet08/2013
4094CopelandErdos(97855)97855Eric W. Weisstein10/2015
409618^77944-8997841Lelio R Paula07/2016
4097119^47136+11897833Norbert Schneider09/2018
40986^125720-1766397830Enzo Doria02/2013
40992^324972-206997827Yves Minet05/2013
41002^324958-469197823Yves Minet05/2019
41012^324944-278831997818Enzo Doria03/2016
41034*10^97799-997800Erik Branger11/2013
41022^324882+57729457597800Lelio R Paula09/2016
41042^324863-186792197794Enzo Doria04/2016
41056^125662-1847397785Enzo Doria03/2013
410612^90604+1197779Lelio R Paula07/2016
41075^139830+2497737Lelio R Paula04/2016
41082^324612+115597718Lelio R Paula07/2016
410919^76404-4497702Lelio R Paula07/2016
41102^324505-298397686Yves Minet04/2011
4111(144^45259+1)/14597684Paul Bourdelais08/2019
4112(31*2^324496-1)/4597683Lelio R Paula02/2014
41136^125488-1784397649Enzo Doria02/2013
41147^115515-297622Lelio R Paula09/2013
4115(89^50069-1)/8897603Paul Bourdelais08/2017
41166^125418-597595Lelio R Paula11/2014
41172^324076+115597557Lelio R Paula07/2016
4118(2^324074+9)/1397555Lelio R Paula10/2013
4119(55459*2^323993+1)/2197536Lelio R Paula07/2014
412013^87557-12^8755797534Jean-Louis Charton12/2008
41212^323946+7393997518Enzo Doria04/2016
41222^323937+186694797515Enzo Doria03/2016
41236^125290-1853397495Enzo Doria03/2013
41242^323845+10197488Lelio R Paula12/2012
412518^77662+6597487Lelio R Paula07/2016
41262^323772+7677197466Enzo Doria05/2016
41272^323765-11221397463Enzo Doria06/2014
41282^323720-655597450Lelio R Paula07/2016
41292^323694-186040197442Enzo Doria03/2016
413020^74886+397429Lelio R Paula06/2016
41323*10^97399+7397400Robert Price04/2016
41317^115252-5097400Lelio R Paula07/2016
4133224737#+39358197389Nicolas PALAU12/2016
4134(26*10^97353+31)/397354Robert Price07/2016
413561^54517-60^5451797331Jean-Louis Charton09/2005
4136(38*10^97329+187)/997330Robert Price11/2017
4137p(19982)#/2-102497293Robert Price09/2017
41386^125021-8597286Lelio R Paula08/2016
41392^323164-4735597283Lelio R Paula07/2016
4140(3^203902+4)/3605101515797276Lelio R Paula09/2013
41412^323054-655597249Lelio R Paula07/2016
41429*10^97247-2997248Robert Price05/2017
4143(31*10^97242+41)/997243Robert Price04/2015
4144GoldenRatioPrime[97241]97241Eric W. Weisstein06/2009
414512^90098-4197233Lelio R Paula07/2016
41462^322928-21692997212Enzo Doria05/2014
4147(7*2^322896-1)/5797201Lelio R Paula02/2014
4148(2^322897+5)/314610748997193Lelio R Paula10/2013
41492^322725+7576197150Enzo Doria04/2016
4150(13*2^322686+1)/11997138Lelio R Paula11/2013
4151(41*10^97085+373)/997086Robert Price04/2017
41522^322413+7797056Lelio R Paula12/2012
41532^322406+17797054Lelio R Paula12/2012
4154(14*10^97044+31)/997045Robert Price02/2015
41552^322302+25525597023Lelio R Paula07/2016
41562^322196-11309396991Enzo Doria07/2014
41572^322000-186146996932Enzo Doria03/2016
41582^321971-11274796923Enzo Doria06/2014
415911^93062-9296915Lelio R Paula06/2016
4160(11*2^321841-7)/1596884Renaud Lifchitz03/2011
41613^203051+3496880Lelio R Paula05/2016
41622*10^96867-5196868Robert Price11/2017
4163(64*10^96863-1)/2796864Serge Batalov05/2010
41642^321716-278693996847Enzo Doria03/2016
41652^321701-11305396842Enzo Doria07/2014
41662^321700-2863596842Lelio R Paula06/2016
4167(5*2^321691-1)/2796838Lelio R Paula02/2014
41686^124433-12443396828Robert Price01/2014
41692^321631+6996821Lelio R Paula12/2012
4170(13*2^321606+1)/11996813Lelio R Paula11/2013
4171(46*10^96798-1)/996799Serge Batalov10/2014
4172(59*10^96798+31)/996799Robert Price09/2015
4173223319#+23122396790Makoto Morimoto02/2016
41742^321519-2863596787Lelio R Paula06/2016
41752^321487-186723796778Enzo Doria03/2016
41762^321461-6396770Lelio R Paula12/2012
41772^321439+12396763Lelio R Paula12/2012
41782^321434+70996762Lelio R Paula02/2013
417914^84413+8996749Lelio R Paula07/2016
4180(28*10^96743+71)/996744Serge Batalov12/2008
418113^86847+9696743Lelio R Paula06/2016
41829*2^321336-796733Lelio R Paula08/2014
4183(209*10^96722-17)/396724Robert Price05/2017
41842^321237-461596702Yves Minet05/2019
41852^321187-115996687Yves Minet11/2012
41862^321182-185008196686Enzo Doria08/2015
41872^321116-11282996666Enzo Doria06/2014
41882^321108-10949996664Enzo Doria04/2014
41892^321098+279385996661Enzo Doria03/2016
41902^321057+409796648Lelio R Paula06/2016
4191(4435*29^66081-4)/796640Curtis Bright05/2015
4192p(19849)#/2-6496581Robert Price04/2017
41932^320817+18996576Lelio R Paula12/2012
41942^320816-468596576Yves Minet05/2019
4195(361*10^96567-163)/996569Robert Price10/2017
41962^320788-11032796567Enzo Doria05/2014
41972^320764+79396560Lelio R Paula02/2013
4198(9179*2^320652-1)/22196528Lelio R Paula05/2015
41992^320616-7879596516Lelio R Paula03/2016
42002^320612-46193996514Enzo Doria07/2015
42015*2^320431+796461Lelio R Paula08/2014
420219^75431-9096458Lelio R Paula06/2016
4203(2^320370+3)/6796440Lelio R Paula10/2013
42042^320309+187147796423Enzo Doria05/2016
4205tau(809^6028)96410Nik Lygeros / Olivier Rozier / LR team10/2013
4206(21*2^320252-1)/189596404Lelio R Paula02/2014
42072^320232-17396400Lelio R Paula12/2012
4208175^42975-296395Lelio R Paula10/2017
420910^96377+19991196378Patrick De Geest12/2016
421010^96377-2000196377Robert Price11/2016
42112^320124-279044996367Enzo Doria03/2016
42122^320043-10877596343Enzo Doria04/2014
421310^96338+42493996339Patrick De Geest03/2016
421410^96338-928196338Robert Price09/2015
4215(3*2^320008+1)/796332Lelio R Paula09/2013
42162^319838+425796281Lelio R Paula03/2016
42172^319830-1699596279Lelio R Paula03/2016
42186^123713+14396268Lelio R Paula05/2016
4219(28*10^96265-97)/396266Robert Price07/2016
4220103^47825-10296264Norbert Schneider10/2016
42212^319713-8196244Lelio R Paula11/2012
4222(55459*2^319706+1)/2016796242Lelio R Paula07/2014
422312^89153-4396213Lelio R Paula06/2016
4224(2*10^96195-59)/396195Robert Price05/2017
42252^319545+14796193Lelio R Paula11/2012
4226(50^56597+1)/5196155Robert Price03/2014
4227(41*10^96137-59)/996138Robert Price10/2017
42282^319353-11034396135Enzo Doria05/2014
422911^92309-4296130Lelio R Paula05/2016
423014^83869-13^8386996125Jean-Louis Charton01/2009
4231(7*10^96112+143)/396113Robert Price04/2016
42322^319237+6583596100Lelio R Paula03/2016
42332^319194-184196087Yves Minet03/2013
423420^73847-3196078Lelio R Paula05/2016
423550^56543-4996065Norbert Schneider09/2018
42362^319107-10955596061Enzo Doria04/2014
4237(3*2^319114-1)/262796060Lelio R Paula02/2014
42382^319098-11215796059Enzo Doria06/2014
423915^81673+9496055Lelio R Paula07/2016
42402^319074+187174996051Enzo Doria05/2016
42412^319007-11211196031Enzo Doria06/2014
42422^318946-142196013Yves Minet01/2013
42432^318834-11041195979Enzo Doria05/2014
42442^318831-196595978Lelio R Paula03/2016
4245(5*10^95976+7)/395977Erik Branger03/2014
42465*3^201089-895945Lelio R Paula08/2014
42472^318711-13995942Lelio R Paula11/2012
42482^318635-116795919Lelio R Paula03/2016
424915^81555+1695917Lelio R Paula07/2016
4250(37*10^95895+377)/995896Robert Price10/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 25 2019 15:53 (Time in France)

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