PRP Records

Probable Primes Top 10000

(172742 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 ?
30016^127858+4799493Lelio R Paula08/2016
30025^142337+4899490Lelio R Paula08/2016
30037^117724-2099489Lelio R Paula08/2016
3004(29*10^99474-17)/399475Erik Branger09/2014
3005(9*2^330407-1)/799463Lelio R Paula03/2014
3006(68*10^99441+7)/399443Robert Price03/2016
300746^59791-45^5979199418Jean-Louis Charton01/2013
3008(2*10^99408+529)/999408Robert Price01/2017
300953^57646-299398Lelio R Paula09/2013
30102^330165+187002599390Enzo Doria05/2016
30112^330142-15599383Lelio R Paula12/2012
30122^330088-11525999367Enzo Doria06/2015
3013(746*10^99303+1)/999305Robert Price02/2017
30143^208107+4099293Lelio R Paula08/2016
3015(5*2^329833-1)/36999288Lelio R Paula02/2014
30168*3^208093+599287Lelio R Paula08/2014
30175^142043+5699284Lelio R Paula08/2016
301822*10^99275+799277Robert Price04/2016
30192^329778+187618999274Enzo Doria07/2016
3020(10^99239-13)/399239Robert Price02/2017
30213^207987+6299236Lelio R Paula08/2016
30222^329638+4999231Lelio R Paula12/2012
30237^117413-1899226Lelio R Paula08/2016
30242^329586-45890399216Enzo Doria04/2015
30252^329553+10199206Lelio R Paula12/2012
30262^329551-11289799205Enzo Doria06/2014
3027(3^207925+7)/5099204Lelio R Paula09/2013
30286^127458-1799399182Enzo Doria03/2013
3029(46*10^99143-1)/999144Robert Price12/2014
303018^78968-306599127Enzo Doria03/2013
30312^329259+18999117Lelio R Paula12/2012
30328*10^99113+3999114Robert Price01/2017
30336^127364+7799109Lelio R Paula08/2016
30346^127285+1399047Lelio R Paula08/2016
30352^329007+7328399041Enzo Doria04/2016
30365*3^207543-899024Lelio R Paula08/2014
30372^328885+14999005Lelio R Paula12/2012
3038(2^328879-9)/11999001Lelio R Paula10/2013
30395^141618+5498987Lelio R Paula08/2016
3040(21*2^328809-1)/770998979Lelio R Paula03/2014
30412^328794-279760198977Enzo Doria04/2016
30426^127176+598963Lelio R Paula11/2014
30432^328700-10970998949Enzo Doria04/2014
304446711!2-2^4671198916Robert Price09/2015
30459*7^117037+498909Lelio R Paula11/2014
3046(10^98890+149)/398890Serge Batalov12/2014
30472^328497-21693398888Enzo Doria05/2014
30482^328487+3276998885Lelio R Paula08/2016
30493^207250-11235898884Enzo Doria06/2014
305013^88754-9098867Lelio R Paula08/2016
30512^328406+70998861Lelio R Paula02/2013
3052(17*2^328413-1)/1617398860Lelio R Paula03/2014
30537^116976+7698857Lelio R Paula08/2016
30542^328335+115598839Lelio R Paula08/2016
3055(3*2^328311+1)/598832Lelio R Paula11/2013
3056287^40210+40210^28798832Norbert Schneider11/2014
3057(2^328284+9)/132598821Lelio R Paula10/2013
3058(21*2^328258+1)/212598814Lelio R Paula11/2013
305965^54491+4898788Lelio R Paula04/2016
30603^207042+9898785Lelio R Paula08/2016
30613^206977-11275698754Enzo Doria07/2014
30627^116846-5098747Lelio R Paula08/2016
30632^327967-2863598728Lelio R Paula08/2016
30646^126850-4798709Lelio R Paula08/2016
30658*6^126830-798694Lelio R Paula11/2014
306611^94770-27098693Enzo Doria08/2012
30672^327832+4398688Lelio R Paula12/2012
30682^327795+76198677Lelio R Paula02/2013
306910^98669+14741198670Patrick De Geest11/2016
307110^98669-9^(98669-1)98669Robert Price05/2016
307010^98669-10524998669Patrick De Geest11/2016
30722^327671-10980198639Enzo Doria04/2014
30735^141090-1498618Lelio R Paula08/2016
307420^75799+4798617Lelio R Paula08/2016
30752^327515-101798592Lelio R Paula08/2016
30766^126692+9768198586Mike Oakes04/2011
30772^327467-74198578Lelio R Paula08/2016
3078(2^327329+9)/1998535Lelio R Paula10/2013
30797^116577-6698519Lelio R Paula08/2016
3080(3*2^327250+1)/798512Lelio R Paula11/2013
3081(19*2^327192+1)/27598494Lelio R Paula11/2013
30822^327162-6694598486Lelio R Paula08/2016
30834*10^98472-398473Erik Branger11/2013
3084(6883*2^327047-1)/7798453Lelio R Paula05/2015
3085(71*10^98446+1)/998447Serge Batalov11/2010
308613^88363+9498432Lelio R Paula08/2016
308748^58543-47^5854398425Jean-Louis Charton11/2005
30886^126481+4198422Lelio R Paula08/2016
30897^116416+4698383Lelio R Paula08/2016
30907^116407-2498376Lelio R Paula07/2016
30922^326782-186067198372Enzo Doria03/2016
309117^79948+5898372Lelio R Paula08/2016
30933^206143-9898356Lelio R Paula08/2016
30948*5^140705+798350Lelio R Paula11/2014
30952^326585+1198312Lelio R Paula12/2012
30962^326582-45916198311Enzo Doria05/2015
3097(2^326548+9)/598301Lelio R Paula10/2013
30982^326538+7165998298Enzo Doria04/2016
309915^83575-5898292Lelio R Paula08/2016
310010^98288+398289Robert Price03/2011
310110^98288-11701798288Patrick De Geest11/2011
31022^326421-279757398263Enzo Doria04/2016
31032^326401+1609598257Lelio R Paula07/2016
310417^79826-7898222Lelio R Paula08/2016
31052^326268-80998217Yves Minet04/2011
310615^83496-7698199Lelio R Paula08/2016
3107(10223*2^326179+1)/612598190Lelio R Paula07/2014
31089*5^140471-498186Lelio R Paula11/2014
31092^326069-238398157Yves Minet10/2013
31102^325973+118598128Lelio R Paula07/2016
3111(25*2^325949-1)/1798121Lelio R Paula02/2014
31122^325945-184726998120Enzo Doria07/2015
31132^325866+1598096Lelio R Paula12/2012
31142^325765+197430598066Enzo Doria06/2016
31152^325733-5869598056Lelio R Paula07/2016
31162^325717-364598051Lelio R Paula07/2016
3117(23*2^325583-1)/2198011Lelio R Paula02/2014
3118(7*10^98007-13)/398008Robert Price06/2016
31192^325512-45995997989Enzo Doria05/2015
3120(3^205354-8)/1797978Lelio R Paula09/2013
31212^325433+7681797966Enzo Doria05/2016
31222^325390-10906197953Enzo Doria04/2014
312313^87921+2497940Lelio R Paula08/2016
3124961^32831-960^3283197926Jean-Louis Charton02/2011
31252^325215+1290997900Lelio R Paula07/2016
31267*10^97874-6997875Robert Price01/2017
3127(17^79537+5^79537)/2297865Robert Price06/2013
312815^83212+2297865Lelio R Paula08/2016
31292^325087-10905797861Enzo Doria04/2014
31302^325074+187065797858Enzo Doria05/2016
31322^325066-211197855Yves Minet08/2013
3131CopelandErdos(97855)97855Eric W. Weisstein10/2015
313318^77944-8997841Lelio R Paula07/2016
31346^125720-1766397830Enzo Doria02/2013
31352^324972-206997827Yves Minet05/2013
31362^324944-278831997818Enzo Doria03/2016
31384*10^97799-997800Erik Branger11/2013
31372^324882+57729457597800Lelio R Paula09/2016
31392^324863-186792197794Enzo Doria04/2016
31406^125662-1847397785Enzo Doria03/2013
314112^90604+1197779Lelio R Paula07/2016
31425^139830+2497737Lelio R Paula04/2016
31432^324612+115597718Lelio R Paula07/2016
314419^76404-4497702Lelio R Paula07/2016
31452^324505-298397686Yves Minet04/2011
3146(31*2^324496-1)/4597683Lelio R Paula02/2014
31476^125488-1784397649Enzo Doria02/2013
31487^115515-297622Lelio R Paula09/2013
31496^125418-597595Lelio R Paula11/2014
31502^324076+115597557Lelio R Paula07/2016
3151(2^324074+9)/1397555Lelio R Paula10/2013
3152(55459*2^323993+1)/2197536Lelio R Paula07/2014
315313^87557-12^8755797534Jean-Louis Charton12/2008
31542^323946+7393997518Enzo Doria04/2016
31552^323937+186694797515Enzo Doria03/2016
31566^125290-1853397495Enzo Doria03/2013
31572^323845+10197488Lelio R Paula12/2012
315818^77662+6597487Lelio R Paula07/2016
31592^323772+7677197466Enzo Doria05/2016
31602^323765-11221397463Enzo Doria06/2014
31612^323720-655597450Lelio R Paula07/2016
31622^323694-186040197442Enzo Doria03/2016
316320^74886+397429Lelio R Paula06/2016
31653*10^97399+7397400Robert Price04/2016
31647^115252-5097400Lelio R Paula07/2016
3166224737#+39358197389Nicolas PALAU12/2016
3167(26*10^97353+31)/397354Robert Price07/2016
316861^54517-60^5451797331Jean-Louis Charton09/2005
31696^125021-8597286Lelio R Paula08/2016
31702^323164-4735597283Lelio R Paula07/2016
3171(3^203902+4)/3605101515797276Lelio R Paula09/2013
31722^323054-655597249Lelio R Paula07/2016
3173(31*10^97242+41)/997243Robert Price04/2015
3174GoldenRatioPrime[97241]97241Eric W. Weisstein06/2009
317512^90098-4197233Lelio R Paula07/2016
31762^322928-21692997212Enzo Doria05/2014
3177(7*2^322896-1)/5797201Lelio R Paula02/2014
3178(2^322897+5)/314610748997193Lelio R Paula10/2013
31792^322725+7576197150Enzo Doria04/2016
3180(13*2^322686+1)/11997138Lelio R Paula11/2013
3181(41*10^97085+373)/997086Robert Price04/2017
31822^322413+7797056Lelio R Paula12/2012
31832^322406+17797054Lelio R Paula12/2012
3184(14*10^97044+31)/997045Robert Price02/2015
31852^322302+25525597023Lelio R Paula07/2016
31862^322196-11309396991Enzo Doria07/2014
31872^322000-186146996932Enzo Doria03/2016
31882^321971-11274796923Enzo Doria06/2014
318911^93062-9296915Lelio R Paula06/2016
3190(11*2^321841-7)/1596884Renaud Lifchitz03/2011
31913^203051+3496880Lelio R Paula05/2016
3192(64*10^96863-1)/2796864Serge Batalov05/2010
31932^321716-278693996847Enzo Doria03/2016
31942^321701-11305396842Enzo Doria07/2014
31952^321700-2863596842Lelio R Paula06/2016
3196(5*2^321691-1)/2796838Lelio R Paula02/2014
31976^124433-12443396828Robert Price01/2014
31982^321631+6996821Lelio R Paula12/2012
3199(13*2^321606+1)/11996813Lelio R Paula11/2013
3200(46*10^96798-1)/996799Serge Batalov10/2014
3201(59*10^96798+31)/996799Robert Price09/2015
3202223319#+23122396790Makoto Morimoto02/2016
32032^321519-2863596787Lelio R Paula06/2016
32042^321487-186723796778Enzo Doria03/2016
32052^321461-6396770Lelio R Paula12/2012
32062^321439+12396763Lelio R Paula12/2012
32072^321434+70996762Lelio R Paula02/2013
320814^84413+8996749Lelio R Paula07/2016
3209(28*10^96743+71)/996744Serge Batalov12/2008
321013^86847+9696743Lelio R Paula06/2016
32119*2^321336-796733Lelio R Paula08/2014
32122^321187-115996687Yves Minet11/2012
32132^321182-185008196686Enzo Doria08/2015
32142^321116-11282996666Enzo Doria06/2014
32152^321108-10949996664Enzo Doria04/2014
32162^321098+279385996661Enzo Doria03/2016
32172^321057+409796648Lelio R Paula06/2016
3218(4435*29^66081-4)/796640Curtis Bright05/2015
3219p(19849)#/2-6496581Robert Price04/2017
32202^320817+18996576Lelio R Paula12/2012
32212^320788-11032796567Enzo Doria05/2014
32222^320764+79396560Lelio R Paula02/2013
3223(9179*2^320652-1)/22196528Lelio R Paula05/2015
32242^320616-7879596516Lelio R Paula03/2016
32252^320612-46193996514Enzo Doria07/2015
32265*2^320431+796461Lelio R Paula08/2014
322719^75431-9096458Lelio R Paula06/2016
3228(2^320370+3)/6796440Lelio R Paula10/2013
32292^320309+187147796423Enzo Doria05/2016
3230tau(809^6028)96410Nik Lygeros / Olivier Rozier / LR team10/2013
3231(21*2^320252-1)/189596404Lelio R Paula02/2014
32322^320232-17396400Lelio R Paula12/2012
323310^96377+19991196378Patrick De Geest12/2016
323410^96377-2000196377Robert Price11/2016
32352^320124-279044996367Enzo Doria03/2016
32362^320043-10877596343Enzo Doria04/2014
323710^96338+42493996339Patrick De Geest03/2016
323810^96338-928196338Robert Price09/2015
3239(3*2^320008+1)/796332Lelio R Paula09/2013
32402^319838+425796281Lelio R Paula03/2016
32412^319830-1699596279Lelio R Paula03/2016
32426^123713+14396268Lelio R Paula05/2016
3243(28*10^96265-97)/396266Robert Price07/2016
3244103^47825-10296264Norbert Schneider10/2016
32452^319713-8196244Lelio R Paula11/2012
3246(55459*2^319706+1)/2016796242Lelio R Paula07/2014
324712^89153-4396213Lelio R Paula06/2016
32482^319545+14796193Lelio R Paula11/2012
3249(50^56597+1)/5196155Robert Price03/2014
32502^319353-11034396135Enzo Doria05/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 21 2017 08:01 (Time in France)

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