PRP Records

Probable Primes Top 10000

(172213 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 ?
30015*3^207543-899024Lelio R Paula08/2014
30022^328885+14999005Lelio R Paula12/2012
3003(2^328879-9)/11999001Lelio R Paula10/2013
30045^141618+5498987Lelio R Paula08/2016
3005(21*2^328809-1)/770998979Lelio R Paula03/2014
30062^328794-279760198977Enzo Doria04/2016
30076^127176+598963Lelio R Paula11/2014
30082^328700-10970998949Enzo Doria04/2014
300946711!2-2^4671198916Robert Price09/2015
30109*7^117037+498909Lelio R Paula11/2014
3011(10^98890+149)/398890Serge Batalov12/2014
30122^328497-21693398888Enzo Doria05/2014
30132^328487+3276998885Lelio R Paula08/2016
30143^207250-11235898884Enzo Doria06/2014
301513^88754-9098867Lelio R Paula08/2016
30162^328406+70998861Lelio R Paula02/2013
3017(17*2^328413-1)/1617398860Lelio R Paula03/2014
30187^116976+7698857Lelio R Paula08/2016
30192^328335+115598839Lelio R Paula08/2016
3021(3*2^328311+1)/598832Lelio R Paula11/2013
3020287^40210+40210^28798832Norbert Schneider11/2014
3022(2^328284+9)/132598821Lelio R Paula10/2013
3023(21*2^328258+1)/212598814Lelio R Paula11/2013
302465^54491+4898788Lelio R Paula04/2016
30253^207042+9898785Lelio R Paula08/2016
30263^206977-11275698754Enzo Doria07/2014
30277^116846-5098747Lelio R Paula08/2016
30282^327967-2863598728Lelio R Paula08/2016
30296^126850-4798709Lelio R Paula08/2016
30308*6^126830-798694Lelio R Paula11/2014
303111^94770-27098693Enzo Doria08/2012
30322^327832+4398688Lelio R Paula12/2012
30332^327795+76198677Lelio R Paula02/2013
303410^98669+14741198670Patrick De Geest11/2016
303610^98669-9^(98669-1)98669Robert Price05/2016
303510^98669-10524998669Patrick De Geest11/2016
30372^327671-10980198639Enzo Doria04/2014
30385^141090-1498618Lelio R Paula08/2016
303920^75799+4798617Lelio R Paula08/2016
30402^327515-101798592Lelio R Paula08/2016
30416^126692+9768198586Mike Oakes04/2011
30422^327467-74198578Lelio R Paula08/2016
3043(2^327329+9)/1998535Lelio R Paula10/2013
30447^116577-6698519Lelio R Paula08/2016
3045(3*2^327250+1)/798512Lelio R Paula11/2013
3046(19*2^327192+1)/27598494Lelio R Paula11/2013
30472^327162-6694598486Lelio R Paula08/2016
30484*10^98472-398473Erik Branger11/2013
3049(6883*2^327047-1)/7798453Lelio R Paula05/2015
3050(71*10^98446+1)/998447Serge Batalov11/2010
305113^88363+9498432Lelio R Paula08/2016
305248^58543-47^5854398425Jean-Louis Charton11/2005
30536^126481+4198422Lelio R Paula08/2016
30547^116416+4698383Lelio R Paula08/2016
30557^116407-2498376Lelio R Paula07/2016
30572^326782-186067198372Enzo Doria03/2016
305617^79948+5898372Lelio R Paula08/2016
30583^206143-9898356Lelio R Paula08/2016
30598*5^140705+798350Lelio R Paula11/2014
30602^326585+1198312Lelio R Paula12/2012
30612^326582-45916198311Enzo Doria05/2015
3062(2^326548+9)/598301Lelio R Paula10/2013
30632^326538+7165998298Enzo Doria04/2016
306415^83575-5898292Lelio R Paula08/2016
306510^98288+398289Robert Price03/2011
306610^98288-11701798288Patrick De Geest11/2011
30672^326421-279757398263Enzo Doria04/2016
30682^326401+1609598257Lelio R Paula07/2016
306917^79826-7898222Lelio R Paula08/2016
30702^326268-80998217Yves Minet04/2011
307115^83496-7698199Lelio R Paula08/2016
3072(10223*2^326179+1)/612598190Lelio R Paula07/2014
30739*5^140471-498186Lelio R Paula11/2014
30742^326069-238398157Yves Minet10/2013
30752^325973+118598128Lelio R Paula07/2016
3076(25*2^325949-1)/1798121Lelio R Paula02/2014
30772^325945-184726998120Enzo Doria07/2015
30782^325866+1598096Lelio R Paula12/2012
30792^325765+197430598066Enzo Doria06/2016
30802^325733-5869598056Lelio R Paula07/2016
30812^325717-364598051Lelio R Paula07/2016
3082(23*2^325583-1)/2198011Lelio R Paula02/2014
3083(7*10^98007-13)/398008Robert Price06/2016
30842^325512-45995997989Enzo Doria05/2015
3085(3^205354-8)/1797978Lelio R Paula09/2013
30862^325433+7681797966Enzo Doria05/2016
30872^325390-10906197953Enzo Doria04/2014
308813^87921+2497940Lelio R Paula08/2016
3089961^32831-960^3283197926Jean-Louis Charton02/2011
30902^325215+1290997900Lelio R Paula07/2016
30917*10^97874-6997875Robert Price01/2017
3093(17^79537+5^79537)/2297865Robert Price06/2013
309215^83212+2297865Lelio R Paula08/2016
30942^325087-10905797861Enzo Doria04/2014
30952^325074+187065797858Enzo Doria05/2016
30972^325066-211197855Yves Minet08/2013
3096CopelandErdos(97855)97855Eric W. Weisstein10/2015
309818^77944-8997841Lelio R Paula07/2016
30996^125720-1766397830Enzo Doria02/2013
31002^324972-206997827Yves Minet05/2013
31012^324944-278831997818Enzo Doria03/2016
31034*10^97799-997800Erik Branger11/2013
31022^324882+57729457597800Lelio R Paula09/2016
31042^324863-186792197794Enzo Doria04/2016
31056^125662-1847397785Enzo Doria03/2013
310612^90604+1197779Lelio R Paula07/2016
31075^139830+2497737Lelio R Paula04/2016
31082^324612+115597718Lelio R Paula07/2016
310919^76404-4497702Lelio R Paula07/2016
31102^324505-298397686Yves Minet04/2011
3111(31*2^324496-1)/4597683Lelio R Paula02/2014
31126^125488-1784397649Enzo Doria02/2013
31137^115515-297622Lelio R Paula09/2013
31146^125418-597595Lelio R Paula11/2014
31152^324076+115597557Lelio R Paula07/2016
3116(2^324074+9)/1397555Lelio R Paula10/2013
3117(55459*2^323993+1)/2197536Lelio R Paula07/2014
311813^87557-12^8755797534Jean-Louis Charton12/2008
31192^323946+7393997518Enzo Doria04/2016
31202^323937+186694797515Enzo Doria03/2016
31216^125290-1853397495Enzo Doria03/2013
31222^323845+10197488Lelio R Paula12/2012
312318^77662+6597487Lelio R Paula07/2016
31242^323772+7677197466Enzo Doria05/2016
31252^323765-11221397463Enzo Doria06/2014
31262^323720-655597450Lelio R Paula07/2016
31272^323694-186040197442Enzo Doria03/2016
312820^74886+397429Lelio R Paula06/2016
31303*10^97399+7397400Robert Price04/2016
31297^115252-5097400Lelio R Paula07/2016
3131224737#+39358197389Nicolas PALAU12/2016
3132(26*10^97353+31)/397354Robert Price07/2016
313361^54517-60^5451797331Jean-Louis Charton09/2005
31346^125021-8597286Lelio R Paula08/2016
31352^323164-4735597283Lelio R Paula07/2016
3136(3^203902+4)/3605101515797276Lelio R Paula09/2013
31372^323054-655597249Lelio R Paula07/2016
3138(31*10^97242+41)/997243Robert Price04/2015
3139GoldenRatioPrime[97241]97241Eric W. Weisstein06/2009
314012^90098-4197233Lelio R Paula07/2016
31412^322928-21692997212Enzo Doria05/2014
3142(7*2^322896-1)/5797201Lelio R Paula02/2014
3143(2^322897+5)/314610748997193Lelio R Paula10/2013
31442^322725+7576197150Enzo Doria04/2016
3145(13*2^322686+1)/11997138Lelio R Paula11/2013
31462^322413+7797056Lelio R Paula12/2012
31472^322406+17797054Lelio R Paula12/2012
3148(14*10^97044+31)/997045Robert Price02/2015
31492^322302+25525597023Lelio R Paula07/2016
31502^322196-11309396991Enzo Doria07/2014
31512^322000-186146996932Enzo Doria03/2016
31522^321971-11274796923Enzo Doria06/2014
315311^93062-9296915Lelio R Paula06/2016
3154(11*2^321841-7)/1596884Renaud Lifchitz03/2011
31553^203051+3496880Lelio R Paula05/2016
3156(64*10^96863-1)/2796864Serge Batalov05/2010
31572^321716-278693996847Enzo Doria03/2016
31582^321701-11305396842Enzo Doria07/2014
31592^321700-2863596842Lelio R Paula06/2016
3160(5*2^321691-1)/2796838Lelio R Paula02/2014
31616^124433-12443396828Robert Price01/2014
31622^321631+6996821Lelio R Paula12/2012
3163(13*2^321606+1)/11996813Lelio R Paula11/2013
3164(46*10^96798-1)/996799Serge Batalov10/2014
3165(59*10^96798+31)/996799Robert Price09/2015
3166223319#+23122396790Makoto Morimoto02/2016
31672^321519-2863596787Lelio R Paula06/2016
31682^321487-186723796778Enzo Doria03/2016
31692^321461-6396770Lelio R Paula12/2012
31702^321439+12396763Lelio R Paula12/2012
31712^321434+70996762Lelio R Paula02/2013
317214^84413+8996749Lelio R Paula07/2016
3173(28*10^96743+71)/996744Serge Batalov12/2008
317413^86847+9696743Lelio R Paula06/2016
31759*2^321336-796733Lelio R Paula08/2014
31762^321187-115996687Yves Minet11/2012
31772^321182-185008196686Enzo Doria08/2015
31782^321116-11282996666Enzo Doria06/2014
31792^321108-10949996664Enzo Doria04/2014
31802^321098+279385996661Enzo Doria03/2016
31812^321057+409796648Lelio R Paula06/2016
3182(4435*29^66081-4)/796640Curtis Bright05/2015
31832^320817+18996576Lelio R Paula12/2012
31842^320788-11032796567Enzo Doria05/2014
31852^320764+79396560Lelio R Paula02/2013
3186(9179*2^320652-1)/22196528Lelio R Paula05/2015
31872^320616-7879596516Lelio R Paula03/2016
31882^320612-46193996514Enzo Doria07/2015
31895*2^320431+796461Lelio R Paula08/2014
319019^75431-9096458Lelio R Paula06/2016
3191(2^320370+3)/6796440Lelio R Paula10/2013
31922^320309+187147796423Enzo Doria05/2016
3193tau(809^6028)96410Nik Lygeros / Olivier Rozier / LR team10/2013
3194(21*2^320252-1)/189596404Lelio R Paula02/2014
31952^320232-17396400Lelio R Paula12/2012
319610^96377+19991196378Patrick De Geest12/2016
319710^96377-2000196377Robert Price11/2016
31982^320124-279044996367Enzo Doria03/2016
31992^320043-10877596343Enzo Doria04/2014
320010^96338+42493996339Patrick De Geest03/2016
320110^96338-928196338Robert Price09/2015
3202(3*2^320008+1)/796332Lelio R Paula09/2013
32032^319838+425796281Lelio R Paula03/2016
32042^319830-1699596279Lelio R Paula03/2016
32056^123713+14396268Lelio R Paula05/2016
3206(28*10^96265-97)/396266Robert Price07/2016
3207103^47825-10296264Norbert Schneider10/2016
32082^319713-8196244Lelio R Paula11/2012
3209(55459*2^319706+1)/2016796242Lelio R Paula07/2014
321012^89153-4396213Lelio R Paula06/2016
32112^319545+14796193Lelio R Paula11/2012
3212(50^56597+1)/5196155Robert Price03/2014
32132^319353-11034396135Enzo Doria05/2014
321411^92309-4296130Lelio R Paula05/2016
321514^83869-13^8386996125Jean-Louis Charton01/2009
3216(7*10^96112+143)/396113Robert Price04/2016
32172^319237+6583596100Lelio R Paula03/2016
32182^319194-184196087Yves Minet03/2013
321920^73847-3196078Lelio R Paula05/2016
32202^319107-10955596061Enzo Doria04/2014
3221(3*2^319114-1)/262796060Lelio R Paula02/2014
32222^319098-11215796059Enzo Doria06/2014
322315^81673+9496055Lelio R Paula07/2016
32242^319074+187174996051Enzo Doria05/2016
32252^319007-11211196031Enzo Doria06/2014
32262^318946-142196013Yves Minet01/2013
32272^318834-11041195979Enzo Doria05/2014
32282^318831-196595978Lelio R Paula03/2016
3229(5*10^95976+7)/395977Erik Branger03/2014
32305*3^201089-895945Lelio R Paula08/2014
32312^318711-13995942Lelio R Paula11/2012
32322^318635-116795919Lelio R Paula03/2016
323315^81555+1695917Lelio R Paula07/2016
3234(22699*2^318527+1)/2195890Lelio R Paula07/2014
32352^318496-9730595877Lelio R Paula03/2016
32362^318466+1501595868Lelio R Paula03/2016
32376^123187-17312995859Mike Oakes04/2011
32382^318423-48795855Yves Minet03/2012
3239(10223*2^318350+1)/156395834Lelio R Paula07/2014
324045369!2+102495787Robert Price02/2015
32413^200758-8695786Lelio R Paula05/2016
3242(509203*2^317881-1)/5280595693Lelio R Paula04/2015
3243(11*10^95641-113)/395642Robert Price01/2017
3244(13*10^95588+11)/395589Robert Price05/2015
3245Phi(191188,10)/19118995587Maksym Voznyy11/2015
32463^200325+7095580Lelio R Paula05/2016
3247(25*10^95574-7)/995575Robert Price12/2014
3248(2^317485-3)/2131395569Lelio R Paula06/2013
32492^317464+3195567Lelio R Paula11/2012
32507^113073+8295558Lelio R Paula04/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 26 2017 17:51 (Time in France)

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