PRP Records

Probable Primes Top 10000

(259919 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 ?
450111^92309-4296130Lelio R Paula05/2016
450214^83869-13^8386996125Jean-Louis Charton01/2009
4503(7*10^96112+143)/396113Robert Price04/2016
45042^319237+6583596100Lelio R Paula03/2016
45052^319194-184196087Yves Minet03/2013
450620^73847-3196078Lelio R Paula05/2016
450750^56543-4996065Norbert Schneider09/2018
45082^319107-10955596061Enzo Doria04/2014
4509(3*2^319114-1)/262796060Lelio R Paula02/2014
45102^319098-11215796059Enzo Doria06/2014
451115^81673+9496055Lelio R Paula07/2016
45122^319074+187174996051Enzo Doria05/2016
45132^319007-11211196031Enzo Doria06/2014
45142^318946-142196013Yves Minet01/2013
451522830^16003+16003^2283095982Hans Havermann02/2020
45162^318834-11041195979Enzo Doria05/2014
45172^318831-196595978Lelio R Paula03/2016
4518(5*10^95976+7)/395977Erik Branger03/2014
451922871^15696+15696^2287195962Hans Havermann01/2020
452023167^13860+13860^2316795953Hans Havermann01/2020
45215*3^201089-895945Lelio R Paula08/2014
45222^318711-13995942Lelio R Paula11/2012
45232^318635-116795919Lelio R Paula03/2016
452415^81555+1695917Lelio R Paula07/2016
4525(37*10^95895+377)/995896Robert Price10/2017
4526(22699*2^318527+1)/2195890Lelio R Paula07/2014
45272^318496-9730595877Lelio R Paula03/2016
45282^318466+1501595868Lelio R Paula03/2016
45296^123187-17312995859Mike Oakes04/2011
45302^318423-48795855Yves Minet03/2012
4531(10223*2^318350+1)/156395834Lelio R Paula07/2014
453245369!2+102495787Robert Price02/2015
45333^200758-8695786Lelio R Paula05/2016
4534(2^318271+1)/(3*46031404238891*654090604244843)95781Gord Palameta12/2018
45353*10^95776-5995777Robert Price10/2017
4536193^41901-295768Lelio R Paula10/2017
45374*10^95752-7195753Robert Price11/2017
453823640^11197+11197^2364095721Hans Havermann12/2019
4539((10^47850-1)*10000/9+6421)*10^47850+(10^47850-1)/995704Hans Havermann05/2019
4540(509203*2^317881-1)/5280595693Lelio R Paula04/2015
45414*10^95672+9195673Robert Price11/2017
4542(11*10^95641-113)/395642Robert Price01/2017
4543(13*10^95588+11)/395589Robert Price05/2015
4544Phi(191188,10)/19118995587Maksym Voznyy11/2015
45453^200325+7095580Lelio R Paula05/2016
4546(25*10^95574-7)/995575Robert Price12/2014
4547(2^317485-3)/2131395569Lelio R Paula06/2013
45482^317464+3195567Lelio R Paula11/2012
45497^113073+8295558Lelio R Paula04/2016
45502^317251+46595503Lelio R Paula03/2016
455119^74684+5895503Lelio R Paula06/2016
4552(2^317250-7)/33995500Lelio R Paula07/2013
45536^122718-7995494Lelio R Paula05/2016
455422168^20291+20291^2216895485Hans Havermann10/2019
45552^317141-11049195469Enzo Doria05/2014
45562^317094+7630995455Enzo Doria05/2016
45572^317085+9595453Lelio R Paula11/2012
4558(17*10^95451-377)/995452Robert Price11/2017
45592^317057-10955195444Enzo Doria04/2014
45603^200026+2895437Lelio R Paula05/2016
45612^317024+9395434Donovan Johnson06/2008
45622^316999+160595427Lelio R Paula03/2016
45632^316995-11042795426Enzo Doria05/2014
45652^316937+17795408Lelio R Paula11/2012
45644*10^95407+9195408Robert Price11/2017
45662^316908+191595399Lelio R Paula03/2016
45672^316894+9995395Lelio R Paula11/2012
45686^122547+1195361Lelio R Paula05/2016
45692^316771+8287595358Lelio R Paula03/2016
4570(23*10^95326+1)/395327Serge Batalov05/2009
45711*10^95326+5795327Robert Price03/2011
457210^95326-39368795326Patrick De Geest09/2013
4573(3^199803+4)/47953995325Lelio R Paula04/2013
45742^316654-10948195323Enzo Doria04/2014
45758*10^95316+5195317Robert Price05/2017
4576(50^56099+43^56099)/9395309Serge Batalov12/2016
4577(23*2^316559+1)/392595292Lelio R Paula09/2013
4578(71*10^95277-539)/995278Robert Price11/2017
457923422^11691+11691^2342295278Hans Havermann10/2019
458019^74503-5695271Lelio R Paula06/2016
458111^91475-438095262Enzo Doria01/2013
4582(62*10^95251-611)/995252Robert Price05/2017
4583(2^316321-509203)/6937795218Lelio R Paula06/2013
4584(79*10^95214-43)/995215Erik Branger11/2013
4585(9*2^316233-1)/175195194Lelio R Paula02/2014
45865*2^316213+995191Lelio R Paula08/2014
45872^316205-184816395188Enzo Doria07/2015
45882^316185-278791395182Enzo Doria04/2016
4589(9787*2^316142-1)/395172Lelio R Paula04/2015
45902^316140-595168Henri Lifchitz02/2006
4591(15185*2^316117-1)/395165Lelio R Paula04/2015
4592(34*10^95153-7)/9/19/1915795149Makoto Morimoto05/2016
45932^316069+7681795147Enzo Doria05/2016
4594(199*10^95134-7)/395136Robert Price02/2017
45952^316027-9730595134Lelio R Paula03/2016
45962^316006-279805195128Enzo Doria04/2016
459724994^6397+6397^2499495127Hans Havermann02/2020
45982^315921-279760395102Enzo Doria04/2016
45992*10^95095+6395096Robert Price10/2017
46002^315857+129995083Lelio R Paula03/2016
460114^82955-4395078Lelio R Paula06/2016
4602(2*10^95072-17)/395072Robert Price08/2014
46032^315727+6595044Lelio R Paula11/2012
46042^315725+188575795043Enzo Doria03/2017
46051*10^94983+2194984Robert Price03/2011
460610^94983-71794983Patrick De Geest08/2013
460717^77187-8294975Lelio R Paula07/2016
46083*10^94964+3794965Robert Price10/2017
4609(2^315481-1017)/2062728594962Lelio R Paula06/2013
46102^315423-11032994952Enzo Doria05/2014
461111^91169-723094943Enzo Doria02/2013
46127*10^94938+6194939Robert Price02/2017
46132^315351+102594931Lelio R Paula03/2016
46142^315350-11225394930Enzo Doria06/2014
4617((1001327^(15817)+1)/1001328)94906Faysal YAtim10/2010
46162^315268+794906Lelio R Paula10/2012
461511^91133+6294906Lelio R Paula05/2016
461830^64244+4194897Lelio R Paula08/2012
4619(151*10^94885-7)/994887Robert Price07/2017
46204^157583+2214794875Mike Oakes01/2011
46212^315098+12394854Lelio R Paula11/2012
46223^198791-3494848Robert Price11/2013
46233*2^315067+794846Lelio R Paula08/2014
4624(9*2^315057+1)/7394841Lelio R Paula09/2013
4625(16*10^94822+53)/394823Robert Price12/2016
46268*6^121849-794818Lelio R Paula10/2014
4627(85*10^94802+473)/994803Robert Price03/2017
46282^314870-10876194786Enzo Doria03/2014
46295*2^314841-394778Lelio R Paula08/2014
46306^121772+11394758Lelio R Paula05/2016
46316^121756-1625394745Enzo Doria02/2013
46322^314718-11279394740Enzo Doria06/2014
46332^314697-184729394734Enzo Doria07/2015
46352^314548-24994689Yves Minet02/2012
46345^135469+4294689Lelio R Paula04/2016
4636gcd(V(1137755),5*F(227551)*(F(227551)-1)+1)94676Serge Batalov04/2015
4637(2*10^94604+547)/994604Robert Price10/2017
46383*2^314152+594570Lelio R Paula08/2014
46392*6^121530-594570Lelio R Paula10/2014
46407*10^94563+8794564Robert Price11/2016
46412^314114-10967794558Enzo Doria04/2014
4642(218389#+240867)/(3*11*811)94557Makoto Morimoto10/2017
46432^314059+7658394542Enzo Doria05/2016
46442^314041-403594536Lelio R Paula03/2016
4645(7*2^314003-11)/1594524Renaud Lifchitz03/2011
464611^90760-471094517Enzo Doria01/2013
4647(7*2^313926-1)/14882194497Lelio R Paula02/2014
464894*10^94493-394495Robert Price11/2016
4649(1000547^15749+1)/100054894492Faysal YAtim12/2008
4650(F(3*75345)^2+L(3*75345)^2)/494477Henri Lifchitz10/2017
46517^111792-3294476Lelio R Paula04/2016
465211^90680-585094434Enzo Doria01/2013
46532^313675-11012594426Enzo Doria04/2014
4654(2999*29^64556-2427)/494410Curtis Bright05/2015
46552^313609-11222594406Enzo Doria06/2014
46562^313584+7290194399Enzo Doria04/2016
46572^313510-11286594376Enzo Doria06/2014
46587*10^94373+8794374Robert Price11/2016
4659(9^98897+8^98897)/1794371Robert Price12/2012
46602^313453-11470394359Enzo Doria04/2015
46618*10^94357-5194358Robert Price10/2017
4662(379*10^94337-1)/994339Robert Price08/2017
46632^313344-313344+194326Robert Price10/2014
466420^72481-4994300Lelio R Paula05/2016
466544725!2+12894289Robert Price03/2015
46664*10^94286+994287Robert Price05/2015
466717^76621+2494279Lelio R Paula07/2016
46682^313156-11285994270Enzo Doria06/2014
46696^121130-5994258Lelio R Paula05/2016
46703^197542+2894252Robert Price11/2013
4671(3^197521+2)/5165594237Lelio R Paula04/2013
46722^313045-595594236Lelio R Paula03/2016
4673(67*10^94212+23)/994213Ray Chandler02/2011
46742^312909-186520394195Enzo Doria03/2016
46752^312848-14994177Lelio R Paula11/2012
46764^156403-7759794164Mike Oakes04/2011
467718^75004-8594151Lelio R Paula06/2016
467819^73622-4894145Lelio R Paula06/2016
4679(11^90397-3^90397)/894138Robert Price04/2011
4680(3^197287+5)/1694129Lelio R Paula04/2013
468112^87212-3794118Lelio R Paula06/2016
468211^90376+7694117Lelio R Paula05/2016
4683(6^120946-11)/594114Paul Bourdelais11/2011
4684(10^94096+191)/394096Robert Price11/2017
46852^312562-11268594091Enzo Doria06/2014
4686137^44026-294072Lelio R Paula10/2017
46872^312404-86968810594043Lelio R Paula09/2016
46882^312387+279353394038Enzo Doria03/2016
469010^94016+9194017Robert Price04/2011
4689(15*2^312325-1)/720194017Lelio R Paula02/2014
469110^94016-18896394016Patrick De Geest08/2013
4692(17*2^312315-1)/4594016Lelio R Paula02/2014
46936^120802+766194003Mike Oakes04/2011
4694(67607*2^312254+1)/17794001Lelio R Paula06/2014
4695(11*2^312207+1)/1993984Lelio R Paula09/2013
46962^312201+5193982Lelio R Paula11/2012
4697(4*6^120749+1)/593961Serge Batalov10/2014
46983^196892+5893942Lelio R Paula05/2016
46992^312060+1891593940Lelio R Paula03/2016
470042^57867-4193933Norbert Schneider08/2018
47012^311992-1620993919Enzo Doria04/2013
4702(85^48677+1)/8693917Paul Bourdelais08/2017
47032^311965-3993911Lelio R Paula11/2012
47042^311920-11168993898Enzo Doria05/2014
4705130^44414+12993889Norbert Schneider01/2019
47067*10^93887-4793888Robert Price02/2017
470712^86965-1393851Lelio R Paula06/2016
47082^311705+1609593833Lelio R Paula03/2016
47092^311665-8193821Lelio R Paula11/2012
4710730^32761+32761^73093806Norbert Schneider09/2017
471111^90073+9293802Lelio R Paula05/2016
47126*10^93792+4193793Robert Price01/2017
4714(2^311580+7)/59132993790Lelio R Paula06/2013
471310^93790-12345678993790Robert Price02/2020
471512^86900-7793781Lelio R Paula06/2016
47162^311508-10976993774Enzo Doria04/2014
47172^311486-185962193767Enzo Doria03/2016
4718Phi(93811,10)/968129521/2109997013/3280113810431/63963778254583193765Kurt Beschorner04/2015
4719(10^93811-1)/(9*968129521*2109997013*3280113810431*639637782545831)93765Gord Palameta10/2018
47202^311471+31146993763Renaud Lifchitz01/2003
4721(88*10^93760-1)/393762Robert Price10/2017
47222^311426+7945993749Enzo Doria06/2016
47232^311294+577593709Lelio R Paula03/2016
47242^311252-101793697Lelio R Paula03/2016
47252^311247-11204193695Enzo Doria06/2014
47267*10^93692-8393693Robert Price09/2017
47272^311205-10964593683Enzo Doria04/2014
47285^134027-8493681Lelio R Paula04/2016
4729(2^311148-1017)/55793663Lelio R Paula06/2013
4730(2^311027-2^155514+1)/59362811/2006
47313^196192-2893608Robert Price12/2013
4732216091#+26143393606Makoto Morimoto12/2015
47335^133917+6893604Lelio R Paula04/2016
47342^310924-170993598Yves Minet03/2013
4735(266*10^93577-11)/393579Robert Price09/2016
4736(16*10^93577+161)/393578Robert Price05/2016
47373^196113-5693570Lelio R Paula04/2016
47382^310806-11034593562Enzo Doria05/2014
47393^196093+8693561Lelio R Paula04/2016
47402^310780-232793555Yves Minet10/2013
474130^63332+4193550Lelio R Paula08/2012
4742(21181*2^310707+1)/2193536Lelio R Paula06/2014
47438*5^133807+793528Lelio R Paula10/2014
47442^310686+819393526Lelio R Paula03/2016
47452^310646+6393514Lelio R Paula11/2012
4746(77*10^93508+31)/993509Robert Price10/2015
4747(1000907^15583+1)/100090893499Faysal YAtim04/2009
4748(2*10^93497+7)/993497Erik Branger03/2011
47493^195958-11285293496Enzo Doria07/2014
47502^310583+1638593495Lelio R Paula03/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 29 2020 17:41 (Time in France)

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