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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
3751127^47012+12698905Norbert Schneider01/2019
3752(10^98890+149)/398890Serge Batalov12/2014
375322775^21978+21978^2277598889Hans Havermann08/2017
37542^328497-21693398888Enzo Doria05/2014
37552^328487+3276998885Lelio R Paula08/2016
37563^207250-11235898884Enzo Doria06/2014
375713^88754-9098867Lelio R Paula08/2016
37582^328406+70998861Lelio R Paula02/2013
3759(17*2^328413-1)/1617398860Lelio R Paula03/2014
37607^116976+7698857Lelio R Paula08/2016
37612^328335+115598839Lelio R Paula08/2016
3763(3*2^328311+1)/598832Lelio R Paula11/2013
3762287^40210+40210^28798832Norbert Schneider11/2014
3764(2^328284+9)/132598821Lelio R Paula10/2013
3765(21*2^328258+1)/212598814Lelio R Paula11/2013
376665^54491+4898788Lelio R Paula04/2016
37673^207042+9898785Lelio R Paula08/2016
37683^206977-11275698754Enzo Doria07/2014
37697^116846-5098747Lelio R Paula08/2016
37702^327967-2863598728Lelio R Paula08/2016
3771707^34642+34642^70798710Norbert Schneider12/2017
37726^126850-4798709Lelio R Paula08/2016
37738*6^126830-798694Lelio R Paula11/2014
377411^94770-27098693Enzo Doria08/2012
37752^327832+4398688Lelio R Paula12/2012
37762^327795+76198677Lelio R Paula02/2013
377710^98669+14741198670Patrick De Geest11/2016
377910^98669-9^(98669-1)98669Robert Price05/2016
377810^98669-10524998669Patrick De Geest11/2016
37802^327671-10980198639Enzo Doria04/2014
37815^141090-1498618Lelio R Paula08/2016
378220^75799+4798617Lelio R Paula08/2016
37832^327515-101798592Lelio R Paula08/2016
37846^126692+9768198586Mike Oakes04/2011
37852^327467-74198578Lelio R Paula08/2016
3786(2^327329+9)/1998535Lelio R Paula10/2013
37877^116577-6698519Lelio R Paula08/2016
3788(3*2^327250+1)/798512Lelio R Paula11/2013
3789(19*2^327192+1)/27598494Lelio R Paula11/2013
37902^327162-6694598486Lelio R Paula08/2016
37914*10^98472-398473Erik Branger11/2013
3792(6883*2^327047-1)/7798453Lelio R Paula05/2015
3793(71*10^98446+1)/998447Serge Batalov11/2010
379413^88363+9498432Lelio R Paula08/2016
379548^58543-47^5854398425Jean-Louis Charton11/2005
37966^126481+4198422Lelio R Paula08/2016
379778*10^98413-798415Robert Price05/2017
37987^116416+4698383Lelio R Paula08/2016
37997^116407-2498376Lelio R Paula07/2016
3800439^37228+37228^43998374Norbert Schneider08/2018
38012^326782-186067198372Enzo Doria03/2016
380217^79948+5898372Lelio R Paula08/2016
38033^206143-9898356Lelio R Paula08/2016
38048*5^140705+798350Lelio R Paula11/2014
38052^326585+1198312Lelio R Paula12/2012
38062^326582-45916198311Enzo Doria05/2015
3807(2^326548+9)/598301Lelio R Paula10/2013
38082^326538+7165998298Enzo Doria04/2016
380915^83575-5898292Lelio R Paula08/2016
381010^98288+398289Robert Price03/2011
381110^98288-11701798288Patrick De Geest11/2011
3812(44*10^98284-719)/998285Robert Price12/2017
38132^326421-279757398263Enzo Doria04/2016
38142^326401+1609598257Lelio R Paula07/2016
38157^116240-116240^798235Norbert Schneider05/2017
381617^79826-7898222Lelio R Paula08/2016
38172^326268-80998217Yves Minet04/2011
3818(418*10^98199+23)/998201Robert Price08/2017
381912*10^98198-798200Robert Price11/2017
382015^83496-7698199Lelio R Paula08/2016
3821(10223*2^326179+1)/612598190Lelio R Paula07/2014
38229*5^140471-498186Lelio R Paula11/2014
38232^326069-238398157Yves Minet10/2013
38242^325973+118598128Lelio R Paula07/2016
3825(25*2^325949-1)/1798121Lelio R Paula02/2014
38262^325945-184726998120Enzo Doria07/2015
38278*10^98111-6798112Robert Price10/2017
38282^325866+1598096Lelio R Paula12/2012
38292^325765+197430598066Enzo Doria06/2016
38302^325733-5869598056Lelio R Paula07/2016
38312^325717-364598051Lelio R Paula07/2016
3832(23*2^325583-1)/2198011Lelio R Paula02/2014
3833(7*10^98007-13)/398008Robert Price06/2016
38342^325512-45995997989Enzo Doria05/2015
3835(3^205354-8)/1797978Lelio R Paula09/2013
38362^325433+7681797966Enzo Doria05/2016
38375*10^97963+8197964Robert Price08/2017
38382^325390-10906197953Enzo Doria04/2014
383913^87921+2497940Lelio R Paula08/2016
3840961^32831-960^3283197926Jean-Louis Charton02/2011
38412^325215+1290997900Lelio R Paula07/2016
38427*10^97874-6997875Robert Price01/2017
3844(17^79537+5^79537)/2297865Robert Price06/2013
384315^83212+2297865Lelio R Paula08/2016
38452^325087-10905797861Enzo Doria04/2014
38462^325074+187065797858Enzo Doria05/2016
38472^325066-211197855Yves Minet08/2013
3848CopelandErdos(97855)97855Eric W. Weisstein10/2015
384918^77944-8997841Lelio R Paula07/2016
3850119^47136+11897833Norbert Schneider09/2018
38516^125720-1766397830Enzo Doria02/2013
38522^324972-206997827Yves Minet05/2013
38532^324944-278831997818Enzo Doria03/2016
38554*10^97799-997800Erik Branger11/2013
38542^324882+57729457597800Lelio R Paula09/2016
38562^324863-186792197794Enzo Doria04/2016
38576^125662-1847397785Enzo Doria03/2013
385812^90604+1197779Lelio R Paula07/2016
38595^139830+2497737Lelio R Paula04/2016
38602^324612+115597718Lelio R Paula07/2016
386119^76404-4497702Lelio R Paula07/2016
38622^324505-298397686Yves Minet04/2011
3863(31*2^324496-1)/4597683Lelio R Paula02/2014
38646^125488-1784397649Enzo Doria02/2013
38657^115515-297622Lelio R Paula09/2013
3866(89^50069-1)/8897603Paul Bourdelais08/2017
38676^125418-597595Lelio R Paula11/2014
38682^324076+115597557Lelio R Paula07/2016
3869(2^324074+9)/1397555Lelio R Paula10/2013
3870(55459*2^323993+1)/2197536Lelio R Paula07/2014
387113^87557-12^8755797534Jean-Louis Charton12/2008
38722^323946+7393997518Enzo Doria04/2016
38732^323937+186694797515Enzo Doria03/2016
38746^125290-1853397495Enzo Doria03/2013
38752^323845+10197488Lelio R Paula12/2012
387618^77662+6597487Lelio R Paula07/2016
38772^323772+7677197466Enzo Doria05/2016
38782^323765-11221397463Enzo Doria06/2014
38792^323720-655597450Lelio R Paula07/2016
38802^323694-186040197442Enzo Doria03/2016
388120^74886+397429Lelio R Paula06/2016
38833*10^97399+7397400Robert Price04/2016
38827^115252-5097400Lelio R Paula07/2016
3884224737#+39358197389Nicolas PALAU12/2016
3885(26*10^97353+31)/397354Robert Price07/2016
388661^54517-60^5451797331Jean-Louis Charton09/2005
3887(38*10^97329+187)/997330Robert Price11/2017
3888p(19982)#/2-102497293Robert Price09/2017
38896^125021-8597286Lelio R Paula08/2016
38902^323164-4735597283Lelio R Paula07/2016
3891(3^203902+4)/3605101515797276Lelio R Paula09/2013
38922^323054-655597249Lelio R Paula07/2016
38939*10^97247-2997248Robert Price05/2017
3894(31*10^97242+41)/997243Robert Price04/2015
3895GoldenRatioPrime[97241]97241Eric W. Weisstein06/2009
389612^90098-4197233Lelio R Paula07/2016
38972^322928-21692997212Enzo Doria05/2014
3898(7*2^322896-1)/5797201Lelio R Paula02/2014
3899(2^322897+5)/314610748997193Lelio R Paula10/2013
39002^322725+7576197150Enzo Doria04/2016
3901(13*2^322686+1)/11997138Lelio R Paula11/2013
3902(41*10^97085+373)/997086Robert Price04/2017
39032^322413+7797056Lelio R Paula12/2012
39042^322406+17797054Lelio R Paula12/2012
3905(14*10^97044+31)/997045Robert Price02/2015
39062^322302+25525597023Lelio R Paula07/2016
39072^322196-11309396991Enzo Doria07/2014
39082^322000-186146996932Enzo Doria03/2016
39092^321971-11274796923Enzo Doria06/2014
391011^93062-9296915Lelio R Paula06/2016
3911(11*2^321841-7)/1596884Renaud Lifchitz03/2011
39123^203051+3496880Lelio R Paula05/2016
39132*10^96867-5196868Robert Price11/2017
3914(64*10^96863-1)/2796864Serge Batalov05/2010
39152^321716-278693996847Enzo Doria03/2016
39162^321701-11305396842Enzo Doria07/2014
39172^321700-2863596842Lelio R Paula06/2016
3918(5*2^321691-1)/2796838Lelio R Paula02/2014
39196^124433-12443396828Robert Price01/2014
39202^321631+6996821Lelio R Paula12/2012
3921(13*2^321606+1)/11996813Lelio R Paula11/2013
3922(46*10^96798-1)/996799Serge Batalov10/2014
3923(59*10^96798+31)/996799Robert Price09/2015
3924223319#+23122396790Makoto Morimoto02/2016
39252^321519-2863596787Lelio R Paula06/2016
39262^321487-186723796778Enzo Doria03/2016
39272^321461-6396770Lelio R Paula12/2012
39282^321439+12396763Lelio R Paula12/2012
39292^321434+70996762Lelio R Paula02/2013
393014^84413+8996749Lelio R Paula07/2016
3931(28*10^96743+71)/996744Serge Batalov12/2008
393213^86847+9696743Lelio R Paula06/2016
39339*2^321336-796733Lelio R Paula08/2014
3934(209*10^96722-17)/396724Robert Price05/2017
39352^321187-115996687Yves Minet11/2012
39362^321182-185008196686Enzo Doria08/2015
39372^321116-11282996666Enzo Doria06/2014
39382^321108-10949996664Enzo Doria04/2014
39392^321098+279385996661Enzo Doria03/2016
39402^321057+409796648Lelio R Paula06/2016
3941(4435*29^66081-4)/796640Curtis Bright05/2015
3942p(19849)#/2-6496581Robert Price04/2017
39432^320817+18996576Lelio R Paula12/2012
3944(361*10^96567-163)/996569Robert Price10/2017
39452^320788-11032796567Enzo Doria05/2014
39462^320764+79396560Lelio R Paula02/2013
3947(9179*2^320652-1)/22196528Lelio R Paula05/2015
39482^320616-7879596516Lelio R Paula03/2016
39492^320612-46193996514Enzo Doria07/2015
39505*2^320431+796461Lelio R Paula08/2014
395119^75431-9096458Lelio R Paula06/2016
3952(2^320370+3)/6796440Lelio R Paula10/2013
39532^320309+187147796423Enzo Doria05/2016
3954tau(809^6028)96410Nik Lygeros / Olivier Rozier / LR team10/2013
3955(21*2^320252-1)/189596404Lelio R Paula02/2014
39562^320232-17396400Lelio R Paula12/2012
3957175^42975-296395Lelio R Paula10/2017
395810^96377+19991196378Patrick De Geest12/2016
395910^96377-2000196377Robert Price11/2016
39602^320124-279044996367Enzo Doria03/2016
39612^320043-10877596343Enzo Doria04/2014
396210^96338+42493996339Patrick De Geest03/2016
396310^96338-928196338Robert Price09/2015
3964(3*2^320008+1)/796332Lelio R Paula09/2013
39652^319838+425796281Lelio R Paula03/2016
39662^319830-1699596279Lelio R Paula03/2016
39676^123713+14396268Lelio R Paula05/2016
3968(28*10^96265-97)/396266Robert Price07/2016
3969103^47825-10296264Norbert Schneider10/2016
39702^319713-8196244Lelio R Paula11/2012
3971(55459*2^319706+1)/2016796242Lelio R Paula07/2014
397212^89153-4396213Lelio R Paula06/2016
3973(2*10^96195-59)/396195Robert Price05/2017
39742^319545+14796193Lelio R Paula11/2012
3975(50^56597+1)/5196155Robert Price03/2014
3976(41*10^96137-59)/996138Robert Price10/2017
39772^319353-11034396135Enzo Doria05/2014
397811^92309-4296130Lelio R Paula05/2016
397914^83869-13^8386996125Jean-Louis Charton01/2009
3980(7*10^96112+143)/396113Robert Price04/2016
39812^319237+6583596100Lelio R Paula03/2016
39822^319194-184196087Yves Minet03/2013
398320^73847-3196078Lelio R Paula05/2016
398450^56543-4996065Norbert Schneider09/2018
39852^319107-10955596061Enzo Doria04/2014
3986(3*2^319114-1)/262796060Lelio R Paula02/2014
39872^319098-11215796059Enzo Doria06/2014
398815^81673+9496055Lelio R Paula07/2016
39892^319074+187174996051Enzo Doria05/2016
39902^319007-11211196031Enzo Doria06/2014
39912^318946-142196013Yves Minet01/2013
39922^318834-11041195979Enzo Doria05/2014
39932^318831-196595978Lelio R Paula03/2016
3994(5*10^95976+7)/395977Erik Branger03/2014
39955*3^201089-895945Lelio R Paula08/2014
39962^318711-13995942Lelio R Paula11/2012
39972^318635-116795919Lelio R Paula03/2016
399815^81555+1695917Lelio R Paula07/2016
3999(37*10^95895+377)/995896Robert Price10/2017
4000(22699*2^318527+1)/2195890Lelio R Paula07/2014


Find by discoverer :


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

Go back
Valid XHTML 1.0!    Valid CSS!