PRP Records

Probable Primes Top 10000

(271067 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 ?
32522^370643-37111575Yves Minet01/2012
3251(2^370655-5)/2439111575Lelio R Paula03/2014
32532^370610-3911111565Yves Minet04/2017
3254286^45405+45405^286111532Norbert Schneider04/2015
32554*5^159563-9111531Lelio R Paula11/2014
3256(4^185225+23)/3111517Robert Price10/2018
32572^370393-2797093111500Enzo Doria03/2016
3258(21*2^370382-1)/629111495Lelio R Paula03/2014
3259(2^370371+554)/2111493Stefano Morozzi09/2020
32602^370292-2791979111469Enzo Doria03/2016
32612^370177-461551111435Enzo Doria07/2015
3262(2^370169+1706)/2111432Stefano Morozzi09/2020
3263109^54683-108111413Norbert Schneider02/2017
3264(2^370043+1010)/2111394Stefano Morozzi09/2020
3265numbpart(10^10+76282)111391Serge Batalov04/2015
32662^369974+733111374Lelio R Paula05/2013
3267121^53470+120111367Norbert Schneider10/2018
32682^369915-286267111356Enzo Doria07/2015
32692^369855-1615111338Lelio R Paula05/2017
32707*10^111325+3111326Robert Price08/2015
327151^65176+2111293Lelio R Paula08/2013
32722^369643-1865767111274Enzo Doria03/2016
32732^369603+885111262Lelio R Paula05/2017
3274L(532277)111240Renaud Lifchitz03/2004
3275105^55033-2111233Lelio R Paula10/2017
3276(35*10^111232-737)/9111233Robert Price07/2018
32779*10^111201-29111202Robert Price09/2019
32782^369392+29835111199Lelio R Paula05/2017
32793^233059+16111198Robert Price03/2020
32802^369354-3413111187Yves Minet12/2016
32812^369296-27111170Lelio R Paula02/2013
32822^369239-109837111153Enzo Doria05/2014
32832^369224-291839111148Enzo Doria07/2015
32842^369216+2798881111146Enzo Doria04/2016
328510^111111+163849111112Patrick De Geest03/2017
328610^111111-312911111111Patrick De Geest03/2017
32872^369092-216923111108Enzo Doria05/2014
32882^369081-55111105Lelio R Paula02/2013
3289(2^369047+3618)/2111094Stefano Morozzi09/2020
329088^57124-87111077Norbert Schneider11/2015
32912^368980+753111075Lelio R Paula05/2013
32922^368946-3623111064Yves Minet03/2017
32932^368929+29835111059Lelio R Paula05/2017
32944^184463-3^184463111058Jean-Louis Charton12/2004
3295111^54298+110111057Norbert Schneider04/2017
3296(4*10^111032-7)/3111033Ray Chandler04/2011
32972^368641-460303110972Enzo Doria06/2015
32982^368619-109087110966Enzo Doria04/2014
3299(74*10^110961+313)/9110962Robert Price06/2019
33003*2^368489+7110927Lelio R Paula09/2014
3301(14*10^110922+61)/3110923Robert Price12/2018
330297411!4-2110913Robert Price07/2017
3303(9179*2^368330-1)/35110881Lelio R Paula05/2015
3304(34*10^110882-7)/9/13/29/1019374319110871Makoto Morimoto05/2016
33052^368050-64875110795Lelio R Paula05/2017
33062^368048+25110794Lelio R Paula02/2013
330769^60239-2110771Lelio R Paula10/2013
3308(23*2^367952+1)/15717110762Lelio R Paula03/2014
33092^367924-69110757Lelio R Paula02/2013
33102^367709-109723110692Enzo Doria04/2014
3311(3*2^367644-1)/107110671Lelio R Paula03/2014
3312(2^367626+3514)/2110667Stefano Morozzi09/2020
3313(23*2^367398+1)/57963110595Lelio R Paula03/2014
3314140^51515-139110558Norbert Schneider04/2019
33152^367215+1879223110543Enzo Doria09/2016
33162^367141+41110521Lelio R Paula02/2013
33172^367126+29835110516Lelio R Paula05/2017
3332(10^110503-1)/9+2*(10^59183-1)/9*10^25660110503Makoto Morimoto09/2020
3331(10^110503-1)/9+2*(10^65511-1)/9*10^22496110503Makoto Morimoto09/2020
3330(10^110503-1)/9+2*10^108327+2*10^2175110503Makoto Morimoto09/2020
3329(10^110503-1)/9+2*10^66251+2*10^44251110503Makoto Morimoto09/2020
3328(10^110503-1)/9+3*(10^28813-1)/9*10^40845110503Makoto Morimoto09/2020
3327(10^110503-1)/9+3*(10^82573-1)/9*10^13965110503Makoto Morimoto09/2020
3326(10^110503-1)/9+4*(10^43305-1)/9*10^33599110503Makoto Morimoto09/2020
3325(10^110503-1)/9+5*10^70327+5*10^40175110503Makoto Morimoto09/2020
3318(10^110503-1)/9+5*10^99423+5*10^11079110503Makoto Morimoto09/2020
3319(10^110503-1)/9+7*(10^23617-1)/9*10^43443110503Makoto Morimoto09/2020
3320(10^110503-1)/9+8*(10^30251-1)/9*10^40126110503Makoto Morimoto09/2020
33213*(10^110503-1)/9+1*10^106036+1*10^4466110503Makoto Morimoto09/2020
33223*(10^110503-1)/9+1*10^58962+1*10^51540110503Makoto Morimoto09/2020
33233*(10^110503-1)/9+1*10^78213+1*10^32289110503Makoto Morimoto09/2020
33243*(10^110503-1)/9+2*10^76898+2*10^33604110503Makoto Morimoto09/2020
33343*(10^110503-1)/9-1*10^100802-1*10^9700110503Makoto Morimoto09/2020
33353*(10^110503-1)/9-1*10^76355-1*10^34147110503Makoto Morimoto09/2020
33363*(10^110503-1)/9-2*10^105704-2*10^4798110503Makoto Morimoto09/2020
33507*(10^110503-1)/9+1*(10^27685-1)/9*10^41409110503Makoto Morimoto09/2020
33517*(10^110503-1)/9+1*(10^91035-1)/9*10^9734110503Makoto Morimoto09/2020
33527*(10^110503-1)/9-1*(10^23717-1)/9*10^43393110503Makoto Morimoto09/2020
33537*(10^110503-1)/9-1*10^57906-1*10^52596110503Makoto Morimoto09/2020
33547*(10^110503-1)/9-1*10^72287-1*10^38215110503Makoto Morimoto09/2020
33557*(10^110503-1)/9-2*(10^53823-1)/9*10^28340110503Makoto Morimoto09/2020
33567*(10^110503-1)/9-2*(10^88659-1)/9*10^10922110503Makoto Morimoto09/2020
33577*(10^110503-1)/9-3*(10^79921-1)/9*10^15291110503Makoto Morimoto09/2020
33587*(10^110503-1)/9-3*10^60024-3*10^50478110503Makoto Morimoto09/2020
33597*(10^110503-1)/9-4*(10^103091-1)/9*10^3706110503Makoto Morimoto09/2020
33497*(10^110503-1)/9-4*10^103658-4*10^6844110503Makoto Morimoto09/2020
33487*(10^110503-1)/9-4*10^78188-4*10^32314110503Makoto Morimoto09/2020
33477*(10^110503-1)/9-5*(10^35035-1)/9*10^37734110503Makoto Morimoto09/2020
33377*(10^110503-1)/9-6*(10^67347-1)/9*10^21578110503Makoto Morimoto09/2020
33387*(10^110503-1)/9-6*10^60391-6*10^50111110503Makoto Morimoto09/2020
3339(10^110503-1)-4*(10^96247-1)/9*10^7128110503Makoto Morimoto09/2020
3340(10^110503-1)-4*10^74037-4*10^36465110503Makoto Morimoto09/2020
3341(10^110503-1)-4*10^77787-4*10^32715110503Makoto Morimoto09/2020
3342(10^110503-1)-4*10^91179-4*10^19323110503Makoto Morimoto09/2020
3333(10^110503-1)-5*(10^99143-1)/9*10^5680110503Makoto Morimoto09/2020
3343(10^110503-1)-7*(10^85075-1)/9*10^12714110503Makoto Morimoto09/2020
3344(10^110503-1)-7*10^100712-7*10^9790110503Makoto Morimoto09/2020
3345(10^110503-1)-7*10^76427-7*10^34075110503Makoto Morimoto09/2020
3346(10^110503-1)-7*10^90451-7*10^20051110503Makoto Morimoto09/2020
3360(10^110503-1)-8*10^106252-8*10^4250110503Makoto Morimoto09/2020
3361(11*10^110496+49)/3110497Robert Price07/2018
3362(31*2^366976+1)/7110472Lelio R Paula03/2014
33637*10^110468-23110469Robert Price07/2019
33642^366853+5711110434Lelio R Paula05/2017
3365(21181*2^366833+1)/3110432Lelio R Paula07/2014
33662^366816+315110423Lelio R Paula05/2017
33672^366775-2787037110411Enzo Doria03/2016
3368(112*10^110405-1)/3110407Serge Batalov12/2014
33692^366751+2797553110404Enzo Doria03/2016
33702^366748+255110403Lelio R Paula05/2017
33712^366738-2985110400Yves Minet09/2014
3372(23*2^366739+1)/74575110396Lelio R Paula03/2014
33732^366716+1871791110393Enzo Doria05/2016
33742^366649+1871687110373Enzo Doria05/2016
33752^366629-351205110367Enzo Doria06/2015
33762^366558+1874479110345Enzo Doria06/2016
3377(2^366539+770)/2110339Stefano Morozzi09/2020
3378(23*10^110290+19)/3110291Robert Price07/2019
337918^87853-4409110280Enzo Doria03/2013
33802^366218-23110243Lelio R Paula02/2013
3381(21*2^366193-1)/197110235Lelio R Paula03/2014
33822^366178-343991110231Enzo Doria07/2015
33832^365944+1871341110161Enzo Doria05/2016
33842^365838-461267110129Enzo Doria07/2015
33852^365763-6555110106Lelio R Paula04/2017
3386(2^365689+2^182845+1)/511008311/2006
33872^365666-459161110077Enzo Doria05/2015
33883*10^110076-7110077Robert Price08/2015
338913^98785-72110041Lelio R Paula03/2017
3390(25^78707+1)/26110027Robert Price06/2013
3391(16*10^110014-73)/3110015Robert Price07/2020
3392(7*10^110006-151)/9110006Robert Price02/2018
33936^141361-7110001Lelio R Paula11/2014
339420^84536+81109984Lelio R Paula03/2017
33955*2^365347-9109982Lelio R Paula09/2014
33969*6^141303+7109957Lelio R Paula11/2014
339778^58099+77109929Norbert Schneider02/2015
33982*10^109928-7109929Robert Price10/2015
3399(2^365161+1130)/2109925Stefano Morozzi09/2020
3400(27*2^365137-1)/2021109916Lelio R Paula03/2014
3401(4441*29^75152-24)/7109905Curtis Bright05/2015
3402(2^365087+7)/6015109899Lelio R Paula01/2014
3403(2^365049+722)/2109891Stefano Morozzi09/2020
340418^87533-11109878Lelio R Paula04/2017
34052^364982-5109871Henri Lifchitz04/2006
34063*10^109861+59109862Robert Price08/2018
34072^364936-1867979109857Enzo Doria04/2016
34082^364867-112087109836Enzo Doria06/2014
34094^182415-85061109825Mike Oakes06/2011
3410(2^364809+1034)/2109819Stefano Morozzi09/2020
3411(17^89227+16^89227)/33109788Robert Price08/2013
34122^364687-187109782Lelio R Paula01/2012
34132^364644+67109769Lelio R Paula01/2012
3414(9787*2^364625-1)/24947109763Lelio R Paula05/2015
3415(2^364616+5)/9109760Lelio R Paula01/2014
3416(55*10^109759+89)/9109760Robert Price03/2019
341712^101694+73109747Lelio R Paula03/2017
341813^98518-66109744Lelio R Paula03/2017
34192^364478-113261109719Enzo Doria07/2014
3420(2^364513+1)/(3*44290516579)109719Gord Palameta08/2018
3421(24737*2^364454+1)/3109716Lelio R Paula07/2014
3422(62*10^109673+1)/9109674Serge Batalov11/2010
34233^229824+340109654Lelio R Paula03/2017
3424(2*10^109645-71)/3109645Robert Price12/2017
34252^364169-112813109626Enzo Doria06/2014
342610^109615+21109616Lelio R Paula03/2017
342710^109615-456267109615Patrick De Geest03/2017
34282^364094-113109604Lelio R Paula01/2012
3429(4^182026+11)/3109591Robert Price02/2017
34302^364041-6883109588Lelio R Paula09/2011
343112^101545+11109586Lelio R Paula03/2017
34322^363842-2787101109528Enzo Doria03/2016
3433(2^363812+3570)/2109519Stefano Morozzi09/2020
3434(22699*2^363782+1)/763109511Lelio R Paula07/2014
34352^363769+5711109506Lelio R Paula04/2017
3436(31*2^363748+1)/49109499Lelio R Paula03/2014
3437p(22245)#/2-8109462Robert Price01/2017
34382^363556+55109442Lelio R Paula01/2012
3439(2^363437+1682)/2109406Stefano Morozzi09/2020
3440(55459*2^363411+1)/81109401Lelio R Paula07/2014
34412^363406+1871569109397Enzo Doria05/2016
3442(2^363349+7)/9109378Lelio R Paula01/2014
34433^229236+100109374Lelio R Paula03/2017
34442^363268-58695109355Lelio R Paula04/2017
34452^363191-112321109332Enzo Doria06/2014
34464*10^109316-63109317Robert Price10/2018
34472^363120+3109311Donovan Johnson04/2006
3448(10^109297-1)/9109297Paul Bourdelais, Harvey Dubner04/2007
34492^363042-114641109287Enzo Doria04/2015
34502^363020-112793109280Enzo Doria06/2014
3451(85*10^109253+203)/9109254Robert Price09/2020
3452(2^362746+3738)/2109198Stefano Morozzi09/2020
3453(67607*2^362695+1)/70499109183Lelio R Paula07/2014
3454(9*2^362644+1)/5109167Lelio R Paula03/2014
34555^156181+38109166Lelio R Paula02/2017
3456(2^362623+3618)/2109161Stefano Morozzi09/2020
34574*10^109142+91109143Robert Price08/2018
34583^228750+68109142Lelio R Paula03/2017
3459(2^362561+786)/2109142Stefano Morozzi09/2020
34602*10^109100-49109101Robert Price09/2020
3461(10223*2^362376+1)/9109090Lelio R Paula07/2014
346265^60167-64^60167109078Robert Price08/2013
34637*3^228589-2109066Lelio R Paula09/2014
3464(78557*2^362188+1)/189109033Lelio R Paula07/2014
34652*7^129008+9109025Lelio R Paula11/2014
346688*10^109022+7109024Robert Price03/2020
3467(5*10^108960+91)/3108961Robert Price04/2018
34682^361957+76367108960Enzo Doria05/2016
34692^361873-1411108935Yves Minet01/2013
3470(24737*2^361857+1)/35108933Lelio R Paula07/2014
3471115^52842-114108892Norbert Schneider07/2018
347213^97745-24108883Lelio R Paula03/2017
3473(2^361696+2562)/2108882Stefano Morozzi09/2020
347417^88475+8108864Lelio R Paula04/2017
34752^361567+51108843Lelio R Paula01/2012
34762^361563-109501108842Enzo Doria04/2014
347712^100852+83108838Lelio R Paula03/2017
34782^361497+767108822Lelio R Paula01/2012
34792^361280-112349108757Enzo Doria06/2014
34802^361271-5955108754Lelio R Paula04/2017
348112^100757+19108736Lelio R Paula03/2017
3482(2^361195+3618)/2108731Stefano Morozzi09/2020
348314^94849-61108710Lelio R Paula05/2017
3484(19^85009-5^85009)/14108705Robert Price07/2013
3485(11*2^361027+1)/40463108677Lelio R Paula03/2014
34862^360973+1299108664Lelio R Paula04/2017
34872^360959-109101108660Enzo Doria04/2014
34886*5^155454+7108659Lelio R Paula11/2014
348910^108656+79108657Lelio R Paula02/2017
349010^108656-50001108656Patrick De Geest03/2017
34912^360918-35108648Lelio R Paula01/2012
3492(11*2^360886-1)/7108638Lelio R Paula03/2014
34933*10^108624-49108625Robert Price07/2018
3494(2^360831+666)/2108621Stefano Morozzi09/2020
3495(134*10^108610+7)/3108612Robert Price02/2020
3496(2^360742+3222)/2108594Stefano Morozzi09/2020
34972^360706-458903108584Enzo Doria04/2015
34982^360641-113185108564Enzo Doria07/2014
34992^360618+75019108557Enzo Doria04/2016
3500(14*10^108545-221)/9108546Robert Price04/2018


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 30 2020 10:03 (Time in France)

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