PRP Records

Probable Primes Top 10000

(291192 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 ?
501238176^19+19^238176304569Hans Havermann03/2022
50273122^14615+14615^73122304539Hans Havermann05/2022
50364492^52639+52639^64492304487Hans Havermann03/2022
50465955^41288+41288^65955304437Hans Havermann04/2022
50571729^17530+17530^71729304403Hans Havermann03/2022
50670170^21733+21733^70170304336Hans Havermann03/2022
5072^1010751-107709304267Enzo Doria03/2014
50884473^3994+3994^84473304222Hans Havermann03/2022
509(2^1010623-1)/12602017578957977304212Tony Prest / Never Odd Or Even02/2014
51074442^12125+12125^74442303998Hans Havermann02/2022
51177842^8039+8039^77842303989Hans Havermann01/2022
51264209^54140+54140^64209303935Hans Havermann02/2022
5132^1009577+1869587303913Enzo Doria06/2016
51467389^32338+32338^67389303906Hans Havermann02/2022
5158^336419-7^336419303817Jean-Louis Charton01/2008
51680766^5771+5771^80766303782Hans Havermann01/2022
51766094^39385+39385^66094303724Hans Havermann01/2022
51869147^24574+24574^69147303589Hans Havermann02/2022
51978390^7459+7459^78390303580Hans Havermann01/2022
5202^1008301+1869377303529Enzo Doria06/2016
52165008^46615+46615^65008303492Hans Havermann02/2022
522(2^1007838+5)/3303389Serge Batalov08/2015
52365018^46293+46293^65018303343Hans Havermann01/2022
5246^389756+5303290Paul Bourdelais02/2021
52571016^18649+18649^71016303285Hans Havermann01/2022
52680160^6047+6047^80160303129Hans Havermann01/2022
52767434^31237+31237^67434303094Hans Havermann03/2022
52865537^42102+42102^65537303063Hans Havermann02/2022
52971790^16553+16553^71790302874Hans Havermann11/2021
53065208^44129+44129^65208302874Hans Havermann11/2021
53184181^3960+3960^84181302858Hans Havermann11/2021
53271956^16087+16087^71956302682Hans Havermann11/2021
5332^1005326+383059302634Enzo Doria12/2016
5342^1004929+1877567302514Enzo Doria08/2016
53569341^22978+22978^69341302418Hans Havermann12/2021
536111443^516+516^111443302306Hans Havermann12/2021
53767638^29387+29387^67638302218Hans Havermann11/2021
5382^1003494+1874899302082Enzo Doria06/2016
53975189^10400+10400^75189302037Hans Havermann12/2021
54067237^31042+31042^67237302026Hans Havermann12/2021
54164540^47791+47791^64540302005Hans Havermann11/2021
5422^1003046+60529301947Enzo Doria04/2016
54383278^4209+4209^83278301815Hans Havermann09/2021
54464431^48250+48250^64431301763Hans Havermann09/2021
54567237^30714+30714^67237301716Hans Havermann09/2021
54664641^46288+46288^64641301581Hans Havermann09/2021
54771513^16482+16482^71513301572Hans Havermann10/2021
54872017^15396+15396^72017301565Hans Havermann09/2021
54965534^39927+39927^65534301540Hans Havermann10/2021
550(23^221411-1)/22301501Paul Bourdelais08/2020
55163169^59152+59152^63169301441Hans Havermann09/2021
55275055^10348+10348^75055301336Hans Havermann09/2021
5532^1000647+1881353301225Enzo Doria11/2016
55483686^3961+3961^83686301086Hans Havermann10/2021
55568529^24742+24742^68529301078Hans Havermann09/2021
55665207^41416+41416^65207301072Hans Havermann10/2021
5572^1000000+821751301030Tony Prest / Never Odd Or Even10/2015
55890762^2071+2071^90762300984Hans Havermann06/2021
55963909^51142+51142^63909300934Hans Havermann08/2021
5602^999646+1874029300924Enzo Doria06/2016
56166280^34607+34607^66280300856Hans Havermann06/2021
56265534^38925+38925^65534300817Hans Havermann07/2021
56363296^56517+56517^63296300794Hans Havermann06/2021
564110610^523+523^110610300694Hans Havermann06/2021
56566428^33609+33609^66428300684Hans Havermann06/2021
56674247^11210+11210^74247300672Hans Havermann06/2021
567(59^169777-1)/58300649Paul Bourdelais08/2020
56810^300476+3300477Ed Trice10/2012
56910^300476-530913300476Patrick De Geest03/2016
57066703^31960+31960^66703300471Hans Havermann06/2021
57163722^51915+51915^63722300468Hans Havermann06/2021
5722^998053+1879667300444Enzo Doria09/2016
57377018^7959+7959^77018300437Hans Havermann07/2021
574314738^9+9^314738300337Anatoly F. Selevich02/2011
57569478^20987+20987^69478300281Hans Havermann07/2021
57664088^48393+48393^64088300239Hans Havermann07/2021
57764605^44146+44146^64605300084Hans Havermann08/2021
5787^355039-6^355039300043Jean-Louis Charton05/2011
57967594^27465+27465^67594300035Hans Havermann06/2021
58010^300000+287389300001Patrick De Geest10/2019
58110^300000-83657300000Patrick De Geest10/2019
58270599^17756+17756^70599300000Hans Havermann06/2021
583numbpart(72526161452)299999Serge Batalov04/2017
5842^996182-114431299881Enzo Doria02/2015
5852^996034-17299837Stefano Morozzi07/2022
5862^995214-2788361299590Enzo Doria12/2015
5872^994791-114319299462Enzo Doria01/2015
5882^994490-1863791299372Enzo Doria01/2016
5892^993322+1885729299020Enzo Doria03/2017
590(36395^65536+36393^65536)/2298913Kellen Shenton04/2022
5912^992711-2788807298836Enzo Doria12/2015
5922^992525-114199298780Enzo Doria12/2014
5932^992329+1884707298721Enzo Doria02/2017
5942^991968-23298613Stefano Morozzi07/2022
5952^991715-19298536Stefano Morozzi07/2022
596(10^298414+7)/191/823/56921/1334467298398Alfred Reich10/2021
5972^989562+25297888Stefano Morozzi05/2021
598(2^986191+1)/3296873Vincent Diepeveen06/2008
5992^985217-114553296580Enzo Doria03/2015
600(76^157649-1)/75296507Paul Bourdelais07/2019
6012^984131-1828009296253Enzo Doria01/2015
6022^983620+60451296100Phil Moore03/2008
6032^982721-2683295829Yves Minet02/2016
6042^981298-2788421295401Enzo Doria12/2015
6052^981163-2790967295360Enzo Doria12/2015
6062^981016-15295316Stefano Morozzi07/2022
6072^979594+1865839294888Enzo Doria02/2016
6082^976760+1885021294035Enzo Doria02/2017
6092^974441+1878407293336Enzo Doria08/2016
6102^974180+1876831293258Enzo Doria07/2016
6112^974170+453319293255Enzo Doria01/2017
6122^972744-114419292826Enzo Doria03/2015
61311^281143+6292781Paul Bourdelais03/2021
614CopelandErdos(292447)292447Mark Rodenkirch12/2015
6152^970911+1873373292274Enzo Doria07/2016
6162^970670+383059292201Enzo Doria12/2016
6172^970141-100363292042Enzo Doria02/2014
6182^969945+1874717291983Enzo Doria06/2016
6192^969384+1880701291814Enzo Doria10/2016
620(3^611333-2^611333)/(99035947*87109884549431)291659Mike Oakes02/2017
6212^962194+60139289650Enzo Doria02/2016
6222^959307-1861507288781Enzo Doria11/2015
62314^251797-3288592Paul Bourdelais12/2020
6242^957372+283531288198Enzo Doria02/2017
6252^957192-1864049288144Enzo Doria01/2016
6262^956446+1875199287919Enzo Doria06/2016
627(17^233689+1)/18287542Paul Bourdelais09/2013
6282^955178+1883587287538Enzo Doria12/2016
6292^954127-954127^2287221Henri Lifchitz01/2021
6302^954001+1875257287183Enzo Doria07/2016
631(23891^65536+1)/2286932Serge Batalov03/2018
6322^952268+1878601286662Enzo Doria09/2016
6332^950801+81557286220Enzo Doria08/2016
63422845^65536+22844^65536285658Kellen Shenton03/2021
635(11*2^948635-13)/15285568Renaud Lifchitz11/2011
636(54^164839+1)/55285565Paul Bourdelais07/2019
6372^948510+782569285530Enzo Doria10/2016
6382^948374-114137285490Enzo Doria01/2015
6392^947739+1872923285298Enzo Doria06/2016
6402^944561-21284342Stefano Morozzi07/2022
6412^942533+82067283731Enzo Doria09/2016
6422^940950+1874989283255Enzo Doria06/2016
6432^940426-2786141283097Enzo Doria11/2015
6442^939881-114115282933Enzo Doria12/2014
64510^282493+632551282494Patrick De Geest02/2017
64710^282493-9^282493282493Jean-Louis Charton03/2007
64610^282493-132327282493Patrick De Geest02/2017
6483^591827-2^591827282374Mike Oakes08/2009
649Tau(509^18946)282048Nik Lygeros / Olivier Rozier05/2015
6502^936716-1835519281980Enzo Doria04/2015
6512^936588+79411281942Enzo Doria06/2016
6522^936047+1877423281779Enzo Doria08/2016
6532^935713+1869377281678Enzo Doria05/2016
6542^933082+1877059280886Enzo Doria08/2016
655(5*10^280710+1)/3280711Serge Batalov10/2014
6562^931976+25280553Stefano Morozzi05/2021
657(42^172663+1)/43280274Paul Bourdelais07/2019
658(10^279978+11)/3279978Serge Batalov07/2015
6592^929524-1864829279815Enzo Doria01/2016
6602^929152+60181279703Enzo Doria02/2016
6612^928621-2787883279543Enzo Doria11/2015
662(2^927763+lucasV(-1,2,927763)+1)/2279285Mike Oakes04/2017
6632^927429+1882277279184Enzo Doria12/2016
6642^926766-11278985Stefano Morozzi07/2022
665(71^150697-1)/70278978Paul Bourdelais07/2019
666(33^183661-1)/32278891Paul Bourdelais12/2018
667(2^925391+lucasV(-1,2,925391)+1)/2278571Mike Oakes03/2017
6682^925330-1301278553Yves Minet06/2015
669(21^210599+1)/22278457Paul Bourdelais08/2013
6702^923261-69175277930Enzo Doria11/2015
671757^96487-756^96487277796Jean-Louis Charton12/2012
6722^922301+57277641Stefano Morozzi05/2021
673((((((((((((((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
674(5^396413-1)/4277081Paul Bourdelais06/2010
6752^920318+2792299277044Enzo Doria02/2016
6762^918596-2786939276525Enzo Doria11/2015
6772^916639+60563275936Enzo Doria04/2016
6782^916385-2786383275860Enzo Doria11/2015
6792^915928+82081275722Enzo Doria09/2016
6802^915576-114137275616Enzo Doria01/2015
6812^914828+1876741275391Enzo Doria07/2016
6822^914757-2203275370Yves Minet12/2015
6832^911900+1871245274510Enzo Doria05/2016
6842^910999+9274239Stefano Morozzi05/2021
685(2^910869-7)/5274199Stefano Morozzi08/2022
6862^910490+283429274085Enzo Doria01/2017
6872^909988-1862249273934Enzo Doria12/2015
6882^909297+1879157273726Enzo Doria08/2016
6892^909257-1864423273714Enzo Doria01/2016
6902^908739-7273558Stefano Morozzi07/2022
6912^908579-1861747273510Enzo Doria12/2015
6922^907635-2791597273226Enzo Doria01/2016
693(53^158341+1)/54273022Paul Bourdelais07/2019
6942^906594-113201272912Enzo Doria08/2014
6952^904773+1872167272364Enzo Doria06/2016
6966^349903+5272278Paul Bourdelais02/2021
6972^904149-1862473272176Enzo Doria12/2015
698(7*10^271757-61)/9271757Erik Branger03/2012
6992^902497+1880117271679Enzo Doria09/2016
7002^901858+77689271487Enzo Doria06/2016
7012^901372+1875301271341Enzo Doria06/2016
7022^899121-115033270663Enzo Doria07/2015
7032^898900+883021270596Enzo Doria12/2016
7042^898762-251511270555Enzo Doria12/2013
7052^898589+47270503Lelio R Paula03/2016
706187322*10^270343-187321270349Danilo Nitsche09/2013
70748358*10^270343-48357270348Danilo Nitsche09/2013
708(10^270343-1)/9270343Maksym Voznyy07/2007
7092^897867-3217270285Yves Minet12/2016
7102^897849-115273270280Enzo Doria07/2015
7112^896616-114179269909Enzo Doria12/2014
7122^894928+583561269401Enzo Doria04/2017
7132^894673-39343269324Enzo Doria08/2015
714F(1285607)268676Henri Lifchitz11/2008
7152^892112+187663268553Enzo Doria08/2016
716(10^268207+1)/11268206Paul Bourdelais02/2010
7172^890957-69583268205Enzo Doria12/2015
71832841!^2+32840!^2+...+2!^2+1!^2268128Serge Batalov07/2017
7192^890122-351401267954Enzo Doria07/2015
720(19^209359-1)/18267718Paul Bourdelais08/2010
721(85^138647+1)/86267507Paul Bourdelais07/2019
722(485^99523-1)/484267291Michael Stocker05/2020
7232^886324+77791266811Enzo Doria06/2016
7242^884714+1880527266326Enzo Doria10/2016
72511^255426+255426^11265999Serge Batalov05/2014
7262^883462-343421265949Enzo Doria07/2015
7272^883442+1875019265943Enzo Doria06/2016
7282^883333-291583265910Enzo Doria07/2015
7292^880411+1882673265031Enzo Doria12/2016
730(14*10^264791-11)/3264792Robert Price08/2022
7312^879530-2788031264765Enzo Doria12/2015
7322^878118+2793079264340Enzo Doria02/2016
733(2^878073-7)/5264326Stefano Morozzi08/2022
734(37^168527-1)/36264283Paul Bourdelais08/2019
7352^876202-17263764Stefano Morozzi07/2022
736(14*10^263720-11)/3263721Robert Price08/2022
7372^875748-461129263627Enzo Doria07/2015
7382^875518-15263558Stefano Morozzi07/2022
7392^875181-2789923263456Enzo Doria12/2015
7402^875101-350083263432Enzo Doria08/2015
7412^874684+1883587263307Enzo Doria01/2017
7422^874616+1872211263286Enzo Doria05/2016
7433^551491+16263129Robert Price04/2020
7442^874073+2792957263123Enzo Doria02/2016
7452^873628+1878751262989Enzo Doria08/2016
7462^873288-269262886Yves Minet01/2015
7472^871991-4207262496Yves Minet03/2021
7482^871146-3173262242Yves Minet07/2016
7492^869601-163261776Yves Minet01/2015
7502^869326+282859261694Enzo Doria11/2016


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 22 2022 18:03 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!