PRP Records

Probable Primes Top 10000

(291910 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 ?
5012^1061095-1061095319422Henri Lifchitz10/2013
5022^1060950+653119319378Enzo Doria12/2016
5032^1060363+782753319202Enzo Doria11/2016
504(71^172259-1)/70318895Paul Bourdelais08/2020
5052^1054736+483061317508Enzo Doria12/2016
5062^1053965+1879667317276Enzo Doria10/2016
507(43^194119-1)/42317086Paul Bourdelais08/2020
5082^1052186-458165316740Enzo Doria03/2015
5092^1046613-114685315062Enzo Doria04/2015
5102^1045625-459373314765Enzo Doria06/2015
511(7*10^314564-61)/9314564Erik Branger09/2016
5122^1044206+7314338Stefano Morozzi10/2022
513(7^371669-1)/6314096Paul Bourdelais02/2010
514(53^181981-1)/52313784Paul Bourdelais08/2020
5152^1041944+283051313657Enzo Doria12/2016
5162^1041153-114391313419Enzo Doria02/2015
517(2^1039700+9)/5312981Stefano Morozzi09/2022
518(74^167311+1)/75312742Paul Bourdelais12/2020
5192^1038871+1866983312732Enzo Doria04/2016
520(55^179573-1)/54312521Paul Bourdelais08/2020
5212^1037647+1881263312363Enzo Doria11/2016
5222^1037226+1879699312237Enzo Doria10/2016
5232^1036867+1865843312129Enzo Doria02/2016
524(76^165947+1)/77312114Paul Bourdelais01/2021
5252^1036020-114539311874Enzo Doria02/2015
526(90^159463-1)/89311628Paul Bourdelais08/2020
5272^1032240+1883431310736Enzo Doria01/2017
5282^1030352+1870021310167Enzo Doria06/2016
5292^1030046+1882843310075Enzo Doria11/2016
5303^648872+16309591Robert Price04/2020
5315^442281+2309142Paul Bourdelais01/2021
5322^1026190+15308914Stefano Morozzi10/2022
533A352736(16)306985Kellen Shenton05/2022
534(11^293831-1)/10305993Paul Bourdelais03/2010
535(67^167449-1)/66305773Paul Bourdelais08/2020
536(62^170539+1)/63305671Paul Bourdelais12/2020
5372^1015321-1015321305643Henri Lifchitz08/2013
5382^1014450+7305380Stefano Morozzi10/2022
5392^1014224-2791229305312Enzo Doria01/2016
540(10^304986+7)/673304984Alfred Reich11/2021
54165473^45250+45250^65473304818Hans Havermann02/2022
54266012^41423+41423^66012304794Hans Havermann03/2022
54365073^48202+48202^65073304742Hans Havermann04/2022
544238176^19+19^238176304569Hans Havermann03/2022
54573122^14615+14615^73122304539Hans Havermann05/2022
54664492^52639+52639^64492304487Hans Havermann03/2022
54765955^41288+41288^65955304437Hans Havermann04/2022
54871729^17530+17530^71729304403Hans Havermann03/2022
54970170^21733+21733^70170304336Hans Havermann03/2022
5502^1010751-107709304267Enzo Doria03/2014
55184473^3994+3994^84473304222Hans Havermann03/2022
552(2^1010623-1)/12602017578957977304212Tony Prest / Never Odd Or Even02/2014
55374442^12125+12125^74442303998Hans Havermann02/2022
55477842^8039+8039^77842303989Hans Havermann01/2022
55564209^54140+54140^64209303935Hans Havermann02/2022
5562^1009577+1869587303913Enzo Doria06/2016
55767389^32338+32338^67389303906Hans Havermann02/2022
5588^336419-7^336419303817Jean-Louis Charton01/2008
5592^1009168+15303790Stefano Morozzi10/2022
56080766^5771+5771^80766303782Hans Havermann01/2022
56166094^39385+39385^66094303724Hans Havermann01/2022
56269147^24574+24574^69147303589Hans Havermann02/2022
56378390^7459+7459^78390303580Hans Havermann01/2022
5642^1008301+1869377303529Enzo Doria06/2016
56565008^46615+46615^65008303492Hans Havermann02/2022
566(2^1007838+5)/3303389Serge Batalov08/2015
56765018^46293+46293^65018303343Hans Havermann01/2022
5686^389756+5303290Paul Bourdelais02/2021
56971016^18649+18649^71016303285Hans Havermann01/2022
57080160^6047+6047^80160303129Hans Havermann01/2022
57167434^31237+31237^67434303094Hans Havermann03/2022
57265537^42102+42102^65537303063Hans Havermann02/2022
57371790^16553+16553^71790302874Hans Havermann11/2021
57465208^44129+44129^65208302874Hans Havermann11/2021
57584181^3960+3960^84181302858Hans Havermann11/2021
57671956^16087+16087^71956302682Hans Havermann11/2021
5772^1005326+383059302634Enzo Doria12/2016
5782^1004929+1877567302514Enzo Doria08/2016
57969341^22978+22978^69341302418Hans Havermann12/2021
580111443^516+516^111443302306Hans Havermann12/2021
58167638^29387+29387^67638302218Hans Havermann11/2021
5822^1003494+1874899302082Enzo Doria06/2016
58375189^10400+10400^75189302037Hans Havermann12/2021
58467237^31042+31042^67237302026Hans Havermann12/2021
58564540^47791+47791^64540302005Hans Havermann11/2021
5862^1003046+60529301947Enzo Doria04/2016
58783278^4209+4209^83278301815Hans Havermann09/2021
58864431^48250+48250^64431301763Hans Havermann09/2021
58967237^30714+30714^67237301716Hans Havermann09/2021
59064641^46288+46288^64641301581Hans Havermann09/2021
59171513^16482+16482^71513301572Hans Havermann10/2021
59272017^15396+15396^72017301565Hans Havermann09/2021
59365534^39927+39927^65534301540Hans Havermann10/2021
594(23^221411-1)/22301501Paul Bourdelais08/2020
59563169^59152+59152^63169301441Hans Havermann09/2021
59675055^10348+10348^75055301336Hans Havermann09/2021
5972^1000647+1881353301225Enzo Doria11/2016
59883686^3961+3961^83686301086Hans Havermann10/2021
59968529^24742+24742^68529301078Hans Havermann09/2021
60065207^41416+41416^65207301072Hans Havermann10/2021
6012^1000000+821751301030Tony Prest / Never Odd Or Even10/2015
60290762^2071+2071^90762300984Hans Havermann06/2021
60363909^51142+51142^63909300934Hans Havermann08/2021
6042^999646+1874029300924Enzo Doria06/2016
60566280^34607+34607^66280300856Hans Havermann06/2021
60665534^38925+38925^65534300817Hans Havermann07/2021
60763296^56517+56517^63296300794Hans Havermann06/2021
608110610^523+523^110610300694Hans Havermann06/2021
60966428^33609+33609^66428300684Hans Havermann06/2021
61074247^11210+11210^74247300672Hans Havermann06/2021
611(59^169777-1)/58300649Paul Bourdelais08/2020
61210^300476+3300477Ed Trice10/2012
61310^300476-530913300476Patrick De Geest03/2016
61466703^31960+31960^66703300471Hans Havermann06/2021
61563722^51915+51915^63722300468Hans Havermann06/2021
6162^998053+1879667300444Enzo Doria09/2016
61777018^7959+7959^77018300437Hans Havermann07/2021
618314738^9+9^314738300337Anatoly F. Selevich02/2011
61969478^20987+20987^69478300281Hans Havermann07/2021
62064088^48393+48393^64088300239Hans Havermann07/2021
62164605^44146+44146^64605300084Hans Havermann08/2021
6227^355039-6^355039300043Jean-Louis Charton05/2011
62367594^27465+27465^67594300035Hans Havermann06/2021
62410^300000+287389300001Patrick De Geest10/2019
62510^300000-83657300000Patrick De Geest10/2019
62670599^17756+17756^70599300000Hans Havermann06/2021
627numbpart(72526161452)299999Serge Batalov04/2017
6282^996182-114431299881Enzo Doria02/2015
6292^996034-17299837Stefano Morozzi07/2022
6302^995214-2788361299590Enzo Doria12/2015
6312^994791-114319299462Enzo Doria01/2015
6322^994490-1863791299372Enzo Doria01/2016
6332^993322+1885729299020Enzo Doria03/2017
634(36395^65536+36393^65536)/2298913Kellen Shenton04/2022
6352^992711-2788807298836Enzo Doria12/2015
6362^992525-114199298780Enzo Doria12/2014
6372^992329+1884707298721Enzo Doria02/2017
6382^991968-23298613Stefano Morozzi07/2022
6392^991715-19298536Stefano Morozzi07/2022
640(10^298414+7)/191/823/56921/1334467298398Alfred Reich10/2021
6412^989562+25297888Stefano Morozzi05/2021
642(2*10^297488-23)/3297488Robert Price10/2022
643(2^986191+1)/3296873Vincent Diepeveen06/2008
6442^985217-114553296580Enzo Doria03/2015
645(76^157649-1)/75296507Paul Bourdelais07/2019
6462^984131-1828009296253Enzo Doria01/2015
6472^983620+60451296100Phil Moore03/2008
6482^982721-2683295829Yves Minet02/2016
6492^981298-2788421295401Enzo Doria12/2015
6502^981163-2790967295360Enzo Doria12/2015
6512^981016-15295316Stefano Morozzi07/2022
6522^979594+1865839294888Enzo Doria02/2016
6532^976760+1885021294035Enzo Doria02/2017
6542^974441+1878407293336Enzo Doria08/2016
6552^974180+1876831293258Enzo Doria07/2016
6562^974170+453319293255Enzo Doria01/2017
6572^972744-114419292826Enzo Doria03/2015
65811^281143+6292781Paul Bourdelais03/2021
659(4*10^292619-91)/3292620Robert Price12/2022
660CopelandErdos(292447)292447Mark Rodenkirch12/2015
6613*10^292344-97292345Robert Price01/2023
6622^970911+1873373292274Enzo Doria07/2016
6632^970670+383059292201Enzo Doria12/2016
6642^970141-100363292042Enzo Doria02/2014
6652^969945+1874717291983Enzo Doria06/2016
6662^969384+1880701291814Enzo Doria10/2016
667(3^611333-2^611333)/(99035947*87109884549431)291659Mike Oakes02/2017
6682^962194+60139289650Enzo Doria02/2016
6692^959307-1861507288781Enzo Doria11/2015
67014^251797-3288592Paul Bourdelais12/2020
671(2*10^288371-23)/3288371Robert Price10/2022
6722^957372+283531288198Enzo Doria02/2017
6732^957192-1864049288144Enzo Doria01/2016
6742^956446+1875199287919Enzo Doria06/2016
6757*10^287854+39287855Robert Price01/2023
676(17^233689+1)/18287542Paul Bourdelais09/2013
6772^955178+1883587287538Enzo Doria12/2016
6782^954127-954127^2287221Henri Lifchitz01/2021
6792^954001+1875257287183Enzo Doria07/2016
680(23891^65536+1)/2286932Serge Batalov03/2018
6812^952268+1878601286662Enzo Doria09/2016
6822^950801+81557286220Enzo Doria08/2016
68322845^65536+22844^65536285658Kellen Shenton03/2021
684(11*2^948635-13)/15285568Renaud Lifchitz11/2011
685(54^164839+1)/55285565Paul Bourdelais07/2019
6862^948510+782569285530Enzo Doria10/2016
6872^948374-114137285490Enzo Doria01/2015
6882^947739+1872923285298Enzo Doria06/2016
6892^944561-21284342Stefano Morozzi07/2022
690(4*10^284330-31)/9284330Serge Batalov11/2022
691(32*10^283826-23)/9283827Serge Batalov01/2023
6922^942533+82067283731Enzo Doria09/2016
6932^940950+1874989283255Enzo Doria06/2016
6942^940426-2786141283097Enzo Doria11/2015
695(2*10^282948-11)/9282948Serge Batalov11/2022
6962^939881-114115282933Enzo Doria12/2014
69710^282493+632551282494Patrick De Geest02/2017
69910^282493-9^282493282493Jean-Louis Charton03/2007
69810^282493-132327282493Patrick De Geest02/2017
7003^591827-2^591827282374Mike Oakes08/2009
701Tau(509^18946)282048Nik Lygeros / Olivier Rozier05/2015
7022^936716-1835519281980Enzo Doria04/2015
7032^936588+79411281942Enzo Doria06/2016
7042^936047+1877423281779Enzo Doria08/2016
7052^935713+1869377281678Enzo Doria05/2016
7062^933082+1877059280886Enzo Doria08/2016
707(5*10^280710+1)/3280711Serge Batalov10/2014
7082^931976+25280553Stefano Morozzi05/2021
709(42^172663+1)/43280274Paul Bourdelais07/2019
710(10^279978+11)/3279978Serge Batalov07/2015
7112^929524-1864829279815Enzo Doria01/2016
7122^929152+60181279703Enzo Doria02/2016
7132^928621-2787883279543Enzo Doria11/2015
714(2^927763+lucasV(-1,2,927763)+1)/2279285Mike Oakes04/2017
7152^927429+1882277279184Enzo Doria12/2016
7162^926766-11278985Stefano Morozzi07/2022
717(71^150697-1)/70278978Paul Bourdelais07/2019
718(33^183661-1)/32278891Paul Bourdelais12/2018
719(2^925391+lucasV(-1,2,925391)+1)/2278571Mike Oakes03/2017
7202^925330-1301278553Yves Minet06/2015
721(299*10^278546+1)/3278548Robert Price01/2023
722(21^210599+1)/22278457Paul Bourdelais08/2013
723(266*10^278325+1)/3278327Robert Price01/2023
7242^923261-69175277930Enzo Doria11/2015
725757^96487-756^96487277796Jean-Louis Charton12/2012
7262^922301+57277641Stefano Morozzi05/2021
727((((((((((((((291487327^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2277369Serge Batalov07/2016
728(5^396413-1)/4277081Paul Bourdelais06/2010
7292^920318+2792299277044Enzo Doria02/2016
7302^918596-2786939276525Enzo Doria11/2015
7312^916639+60563275936Enzo Doria04/2016
732(2*10^275922+1)/3275922Serge Batalov11/2022
7332^916385-2786383275860Enzo Doria11/2015
7342^915928+82081275722Enzo Doria09/2016
7352^915576-114137275616Enzo Doria01/2015
7362^914828+1876741275391Enzo Doria07/2016
7372^914757-2203275370Yves Minet12/2015
7387*10^275157-27275158Robert Price11/2022
7392^911900+1871245274510Enzo Doria05/2016
740(16*10^274251-91)/3274252Robert Price11/2022
7412^910999+9274239Stefano Morozzi05/2021
742(2^910869-7)/5274199Stefano Morozzi08/2022
7432^910490+283429274085Enzo Doria01/2017
7447*10^273983+39273984Robert Price01/2023
7452^909988-1862249273934Enzo Doria12/2015
7462^909297+1879157273726Enzo Doria08/2016
7472^909257-1864423273714Enzo Doria01/2016
7482^908739-7273558Stefano Morozzi07/2022
7492^908579-1861747273510Enzo Doria12/2015
7502^907635-2791597273226Enzo Doria01/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 02 2023 13:22 (Time in France)

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