PRP Records

Probable Primes Top 10000

(277054 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 ?
550126502^4297+4297^2650296287Hans Havermann07/2020
55022^319838+425796281Lelio R Paula03/2016
55032^319830-1699596279Lelio R Paula03/2016
55046^123713+14396268Lelio R Paula05/2016
5505(28*10^96265-97)/396266Robert Price07/2016
5506103^47825-10296264Norbert Schneider10/2016
5507(2^319777+2082)/296263Stefano Morozzi09/2020
5508(2^319771+3686)/296261Stefano Morozzi09/2020
55092^319713-8196244Lelio R Paula11/2012
5510(55459*2^319706+1)/2016796242Lelio R Paula07/2014
551122834^16393+16393^2283496238Hans Havermann05/2020
551212^89153-4396213Lelio R Paula06/2016
5514(2*10^96195-59)/396195Robert Price05/2017
55139*10^96194-7796195Robert Price08/2020
55152^319545+14796193Lelio R Paula11/2012
551623357^13128+13128^2335796189Hans Havermann02/2020
551725952^5073+5073^2595296160Hans Havermann12/2019
5518(50^56597+1)/5196155Robert Price03/2014
551922313^20374+20374^2231396149Hans Havermann12/2019
552022279^20668+20668^2227996141Hans Havermann11/2019
5521(41*10^96137-59)/996138Robert Price10/2017
55222^319353-11034396135Enzo Doria05/2014
552311^92309-4296130Lelio R Paula05/2016
552414^83869-13^8386996125Jean-Louis Charton01/2009
5525(7*10^96112+143)/396113Robert Price04/2016
552626731^3940+3940^2673196112Hans Havermann07/2020
552722640^17583+17583^2264096109Hans Havermann07/2020
55282^319237+6583596100Lelio R Paula03/2016
55292^319194-184196087Yves Minet03/2013
553023949^10280+10280^2394996084Hans Havermann07/2020
553120^73847-3196078Lelio R Paula05/2016
553250^56543-4996065Norbert Schneider09/2018
55332^319107-10955596061Enzo Doria04/2014
5534(3*2^319114-1)/262796060Lelio R Paula02/2014
55352^319098-11215796059Enzo Doria06/2014
553615^81673+9496055Lelio R Paula07/2016
55372^319074+187174996051Enzo Doria05/2016
553825670^5517+5517^2567096050Hans Havermann06/2020
55392^319007-11211196031Enzo Doria06/2014
55402^318946-142196013Yves Minet01/2013
554122830^16003+16003^2283095982Hans Havermann02/2020
55422^318834-11041195979Enzo Doria05/2014
55432^318831-196595978Lelio R Paula03/2016
5544(5*10^95976+7)/395977Erik Branger03/2014
554522871^15696+15696^2287195962Hans Havermann01/2020
554623167^13860+13860^2316795953Hans Havermann01/2020
55475*3^201089-895945Lelio R Paula08/2014
55482^318711-13995942Lelio R Paula11/2012
55492^318635-116795919Lelio R Paula03/2016
555015^81555+1695917Lelio R Paula07/2016
5551(37*10^95895+377)/995896Robert Price10/2017
5552(22699*2^318527+1)/2195890Lelio R Paula07/2014
55532^318496-9730595877Lelio R Paula03/2016
555422129^21496+21496^2212995871Hans Havermann07/2020
55562^318466+1501595868Lelio R Paula03/2016
555524847^7216+7216^2484795868Hans Havermann07/2020
555723706^11065+11065^2370695866Hans Havermann07/2020
55586^123187-17312995859Mike Oakes04/2011
55592^318423-48795855Yves Minet03/2012
5560(2^318359+678)/295836Stefano Morozzi09/2020
5561(10223*2^318350+1)/156395834Lelio R Paula07/2014
5562(2^318267+2550)/295808Stefano Morozzi09/2020
556345369!2+102495787Robert Price02/2015
55643^200758-8695786Lelio R Paula05/2016
5565(2^318271+1)/(3*46031404238891*654090604244843)95781Gord Palameta12/2018
5566(2^318171+2030)/295779Stefano Morozzi09/2020
55673*10^95776-5995777Robert Price10/2017
5568193^41901-295768Lelio R Paula10/2017
5569(2^318124+2502)/295765Stefano Morozzi09/2020
55704*10^95752-7195753Robert Price11/2017
557123640^11197+11197^2364095721Hans Havermann12/2019
5572((10^47850-1)*10000/9+6421)*10^47850+(10^47850-1)/995704Hans Havermann05/2019
5573(509203*2^317881-1)/5280595693Lelio R Paula04/2015
5574(2^317853+1086)/295683Stefano Morozzi09/2020
55754*10^95672+9195673Robert Price11/2017
55766*10^95665+4395666Robert Price07/2020
5577(11*10^95641-113)/395642Robert Price01/2017
5578(13*10^95588+11)/395589Robert Price05/2015
5579Phi(191188,10)/19118995587Maksym Voznyy11/2015
55803^200325+7095580Lelio R Paula05/2016
5581(25*10^95574-7)/995575Robert Price12/2014
5582(2^317485-3)/2131395569Lelio R Paula06/2013
55832^317464+3195567Lelio R Paula11/2012
5584(2^317451+2114)/295562Stefano Morozzi09/2020
55857^113073+8295558Lelio R Paula04/2016
55862^317251+46595503Lelio R Paula03/2016
558719^74684+5895503Lelio R Paula06/2016
5588(2^317250-7)/33995500Lelio R Paula07/2013
55896^122718-7995494Lelio R Paula05/2016
559022168^20291+20291^2216895485Hans Havermann10/2019
55912^317141-11049195469Enzo Doria05/2014
5592(2^317097+3014)/295456Stefano Morozzi09/2020
55932^317094+7630995455Enzo Doria05/2016
55942^317085+9595453Lelio R Paula11/2012
5595(17*10^95451-377)/995452Robert Price11/2017
55962^317057-10955195444Enzo Doria04/2014
55973^200026+2895437Lelio R Paula05/2016
55982^317024+9395434Donovan Johnson06/2008
56002^316999+160595427Lelio R Paula03/2016
5599(2^317000+3210)/295427Stefano Morozzi09/2020
56012^316995-11042795426Enzo Doria05/2014
560222300^18987+18987^2230095410Hans Havermann06/2020
56042^316937+17795408Lelio R Paula11/2012
56034*10^95407+9195408Robert Price11/2017
56052^316908+191595399Lelio R Paula03/2016
56062^316894+9995395Lelio R Paula11/2012
5607(2^316887+2546)/295393Stefano Morozzi09/2020
56082*10^95374-2195375Robert Price09/2020
56096^122547+1195361Lelio R Paula05/2016
56102^316771+8287595358Lelio R Paula03/2016
5611(2^316765+3102)/295356Stefano Morozzi09/2020
5612(23*10^95326+1)/395327Serge Batalov05/2009
56131*10^95326+5795327Robert Price03/2011
561410^95326-39368795326Patrick De Geest09/2013
5615(3^199803+4)/47953995325Lelio R Paula04/2013
56162^316654-10948195323Enzo Doria04/2014
56178*10^95316+5195317Robert Price05/2017
5618(50^56099+43^56099)/9395309Serge Batalov12/2016
5619(23*2^316559+1)/392595292Lelio R Paula09/2013
5621(71*10^95277-539)/995278Robert Price11/2017
562023422^11691+11691^2342295278Hans Havermann10/2019
562219^74503-5695271Lelio R Paula06/2016
562311^91475-438095262Enzo Doria01/2013
5624(62*10^95251-611)/995252Robert Price05/2017
5625(2^316321-509203)/6937795218Lelio R Paula06/2013
562626541^3868+3868^2654195216Hans Havermann07/2020
5627(79*10^95214-43)/995215Erik Branger11/2013
5628(7176^24691-1)/717595202Anonymous11/2020
5629(9*2^316233-1)/175195194Lelio R Paula02/2014
56305*2^316213+995191Lelio R Paula08/2014
56312*10^95188-9195189Robert Price04/2020
56322^316205-184816395188Enzo Doria07/2015
56332^316185-278791395182Enzo Doria04/2016
5634(2^316174+3538)/295178Stefano Morozzi09/2020
5635(9787*2^316142-1)/395172Lelio R Paula04/2015
56362^316140-595168Henri Lifchitz02/2006
5637(15185*2^316117-1)/395165Lelio R Paula04/2015
5638(34*10^95153-7)/9/19/1915795149Makoto Morimoto05/2016
56392^316069+7681795147Enzo Doria05/2016
5640(199*10^95134-7)/395136Robert Price02/2017
56412^316027-9730595134Lelio R Paula03/2016
56422^316006-279805195128Enzo Doria04/2016
564324994^6397+6397^2499495127Hans Havermann02/2020
56442^315921-279760395102Enzo Doria04/2016
56452*10^95095+6395096Robert Price10/2017
56462^315857+129995083Lelio R Paula03/2016
5647(2^315858+2598)/295083Stefano Morozzi09/2020
564814^82955-4395078Lelio R Paula06/2016
5649(2*10^95072-17)/395072Robert Price08/2014
5650(286*10^95059-1)/395061Robert Price11/2020
5651(2^315779+1610)/295059Stefano Morozzi09/2020
565221938^21513+21513^2193895051Hans Havermann09/2020
56532^315727+6595044Lelio R Paula11/2012
56542^315725+188575795043Enzo Doria03/2017
565523277^12058+12058^2327795000Hans Havermann09/2020
56561*10^94983+2194984Robert Price03/2011
565710^94983-71794983Patrick De Geest08/2013
565817^77187-8294975Lelio R Paula07/2016
56593*10^94964+3794965Robert Price10/2017
5660(2^315481-1017)/2062728594962Lelio R Paula06/2013
56612^315423-11032994952Enzo Doria05/2014
566211^91169-723094943Enzo Doria02/2013
56637*10^94938+6194939Robert Price02/2017
56642^315351+102594931Lelio R Paula03/2016
56652^315350-11225394930Enzo Doria06/2014
5666(2^315343+1766)/294928Stefano Morozzi09/2020
5667(2^315343+3066)/294928Stefano Morozzi09/2020
5670((1001327^(15817)+1)/1001328)94906Faysal YAtim10/2010
56692^315268+794906Lelio R Paula10/2012
566811^91133+6294906Lelio R Paula05/2016
5671(2^315264+1558)/294904Stefano Morozzi09/2020
567230^64244+4194897Lelio R Paula08/2012
5673(151*10^94885-7)/994887Robert Price07/2017
56744^157583+2214794875Mike Oakes01/2011
56752^315098+12394854Lelio R Paula11/2012
56763^198791-3494848Robert Price11/2013
56773*2^315067+794846Lelio R Paula08/2014
5678(9*2^315057+1)/7394841Lelio R Paula09/2013
567922576^15875+15875^2257694836Hans Havermann09/2020
5680(16*10^94822+53)/394823Robert Price12/2016
56818*6^121849-794818Lelio R Paula10/2014
5682(85*10^94802+473)/994803Robert Price03/2017
568321767^21852-21852^2176794790Norbert Schneider06/2020
56842^314870-10876194786Enzo Doria03/2014
56855*2^314841-394778Lelio R Paula08/2014
5686(2^314842+550)/294777Stefano Morozzi09/2020
5687(2^314787+2630)/294761Stefano Morozzi09/2020
56886^121772+11394758Lelio R Paula05/2016
5689(2^314740+3642)/294746Stefano Morozzi09/2020
56906^121756-1625394745Enzo Doria02/2013
56912^314718-11279394740Enzo Doria06/2014
56922^314697-184729394734Enzo Doria07/2015
569322836^14065+14065^2283694727Hans Havermann09/2020
56952^314548-24994689Yves Minet02/2012
56945^135469+4294689Lelio R Paula04/2016
5696gcd(V(1137755),5*F(227551)*(F(227551)-1)+1)94676Serge Batalov04/2015
569725773^4712+4712^2577394670Hans Havermann08/2020
5698(2^314485+3614)/294670Stefano Morozzi09/2020
5699(2*10^94604+547)/994604Robert Price10/2017
5700(2^314164+2562)/294573Stefano Morozzi09/2020
57013*2^314152+594570Lelio R Paula08/2014
57022*6^121530-594570Lelio R Paula10/2014
57037*10^94563+8794564Robert Price11/2016
57042^314114-10967794558Enzo Doria04/2014
5705(218389#+240867)/(3*11*811)94557Makoto Morimoto10/2017
57062^314059+7658394542Enzo Doria05/2016
57072^314041-403594536Lelio R Paula03/2016
5708(2^314028+3102)/294532Stefano Morozzi09/2020
5709(2^314012+618)/294527Stefano Morozzi09/2020
5710(7*2^314003-11)/1594524Renaud Lifchitz03/2011
571111^90760-471094517Enzo Doria01/2013
571221675^21796+21796^2167594507Norbert Schneider04/2020
5713(7*2^313926-1)/14882194497Lelio R Paula02/2014
571494*10^94493-394495Robert Price11/2016
5715(1000547^15749+1)/100054894492Faysal YAtim12/2008
5716(2^313859+2706)/294481Stefano Morozzi09/2020
5717(F(3*75345)^2+L(3*75345)^2)/494477Henri Lifchitz10/2017
57187^111792-3294476Lelio R Paula04/2016
5719(2^313800+822)/294463Stefano Morozzi01/2021
5720(202*10^94441-1)/394443Robert Price05/2020
572111^90680-585094434Enzo Doria01/2013
5722(752^32833-1)/75194432Michael Stocker05/2020
57232^313675-11012594426Enzo Doria04/2014
5724(2999*29^64556-2427)/494410Curtis Bright05/2015
57252^313609-11222594406Enzo Doria06/2014
57262^313584+7290194399Enzo Doria04/2016
5727(2^313562+730)/294392Stefano Morozzi09/2020
57282^313510-11286594376Enzo Doria06/2014
57297*10^94373+8794374Robert Price11/2016
5730(9^98897+8^98897)/1794371Robert Price12/2012
57312^313453-11470394359Enzo Doria04/2015
57328*10^94357-5194358Robert Price10/2017
573325903^4392+4392^2590394356Hans Havermann09/2020
573431706^945+945^3170694340Hans Havermann09/2020
5735(379*10^94337-1)/994339Robert Price08/2017
57362^313344-313344+194326Robert Price10/2014
5737(2^313313+3662)/294317Stefano Morozzi09/2020
573820^72481-4994300Lelio R Paula05/2016
573944725!2+12894289Robert Price03/2015
57404*10^94286+994287Robert Price05/2015
574117^76621+2494279Lelio R Paula07/2016
574226274^3875+3875^2627494279Hans Havermann09/2020
57432^313156-11285994270Enzo Doria06/2014
57446^121130-5994258Lelio R Paula05/2016
57453^197542+2894252Robert Price11/2013
5746(2^313076+3550)/294245Stefano Morozzi09/2020
5747(3^197521+2)/5165594237Lelio R Paula04/2013
57482^313045-595594236Lelio R Paula03/2016
574922099^18358+18358^2209994227Hans Havermann08/2020
5750(67*10^94212+23)/994213Ray Chandler02/2011


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 25 2021 11:23 (Time in France)

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