PRP Records

Probable Primes Top 10000

(211563 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 (> 30000) Who ? When ?
3751(50^56099+43^56099)/9395309Serge Batalov12/2016
3752(23*2^316559+1)/392595292Lelio R Paula09/2013
3753(71*10^95277-539)/995278Robert Price11/2017
375419^74503-5695271Lelio R Paula06/2016
375511^91475-438095262Enzo Doria01/2013
3756(62*10^95251-611)/995252Robert Price05/2017
3757(2^316321-509203)/6937795218Lelio R Paula06/2013
3758(79*10^95214-43)/995215Erik Branger11/2013
3759(9*2^316233-1)/175195194Lelio R Paula02/2014
37605*2^316213+995191Lelio R Paula08/2014
37612^316205-184816395188Enzo Doria07/2015
37622^316185-278791395182Enzo Doria04/2016
3763(9787*2^316142-1)/395172Lelio R Paula04/2015
37642^316140-595168Henri Lifchitz02/2006
3765(15185*2^316117-1)/395165Lelio R Paula04/2015
3766(34*10^95153-7)/9/19/1915795149Makoto Morimoto05/2016
37672^316069+7681795147Enzo Doria05/2016
3768(199*10^95134-7)/395136Robert Price02/2017
37692^316027-9730595134Lelio R Paula03/2016
37702^316006-279805195128Enzo Doria04/2016
37712^315921-279760395102Enzo Doria04/2016
37722*10^95095+6395096Robert Price10/2017
37732^315857+129995083Lelio R Paula03/2016
377414^82955-4395078Lelio R Paula06/2016
3775(2*10^95072-17)/395072Robert Price08/2014
37762^315727+6595044Lelio R Paula11/2012
37772^315725+188575795043Enzo Doria03/2017
37781*10^94983+2194984Robert Price03/2011
377910^94983-71794983Patrick De Geest08/2013
378017^77187-8294975Lelio R Paula07/2016
37813*10^94964+3794965Robert Price10/2017
3782(2^315481-1017)/2062728594962Lelio R Paula06/2013
37832^315423-11032994952Enzo Doria05/2014
378411^91169-723094943Enzo Doria02/2013
37857*10^94938+6194939Robert Price02/2017
37862^315351+102594931Lelio R Paula03/2016
37872^315350-11225394930Enzo Doria06/2014
3790((1001327^(15817)+1)/1001328)94906Faysal YAtim10/2010
37882^315268+794906Lelio R Paula10/2012
378911^91133+6294906Lelio R Paula05/2016
379130^64244+4194897Lelio R Paula08/2012
3792(151*10^94885-7)/994887Robert Price07/2017
37934^157583+2214794875Mike Oakes01/2011
37942^315098+12394854Lelio R Paula11/2012
37953^198791-3494848Robert Price11/2013
37963*2^315067+794846Lelio R Paula08/2014
3797(9*2^315057+1)/7394841Lelio R Paula09/2013
3798(16*10^94822+53)/394823Robert Price12/2016
37998*6^121849-794818Lelio R Paula10/2014
3800(85*10^94802+473)/994803Robert Price03/2017
38012^314870-10876194786Enzo Doria03/2014
38025*2^314841-394778Lelio R Paula08/2014
38036^121772+11394758Lelio R Paula05/2016
38046^121756-1625394745Enzo Doria02/2013
38052^314718-11279394740Enzo Doria06/2014
38062^314697-184729394734Enzo Doria07/2015
38072^314548-24994689Yves Minet02/2012
38085^135469+4294689Lelio R Paula04/2016
3809gcd(V(1137755),5*F(227551)*(F(227551)-1)+1)94676Serge Batalov04/2015
3810(2*10^94604+547)/994604Robert Price10/2017
38113*2^314152+594570Lelio R Paula08/2014
38122*6^121530-594570Lelio R Paula10/2014
38137*10^94563+8794564Robert Price11/2016
38142^314114-10967794558Enzo Doria04/2014
3815(218389#+240867)/(3*11*811)94557Makoto Morimoto10/2017
38162^314059+7658394542Enzo Doria05/2016
38172^314041-403594536Lelio R Paula03/2016
3818(7*2^314003-11)/1594524Renaud Lifchitz03/2011
381911^90760-471094517Enzo Doria01/2013
3820(7*2^313926-1)/14882194497Lelio R Paula02/2014
382194*10^94493-394495Robert Price11/2016
3822(1000547^15749+1)/100054894492Faysal YAtim12/2008
3823(F(3*75345)^2+L(3*75345)^2)/494477Henri Lifchitz10/2017
38247^111792-3294476Lelio R Paula04/2016
382511^90680-585094434Enzo Doria01/2013
38262^313675-11012594426Enzo Doria04/2014
3827(2999*29^64556-2427)/494410Curtis Bright05/2015
38282^313609-11222594406Enzo Doria06/2014
38292^313584+7290194399Enzo Doria04/2016
38302^313510-11286594376Enzo Doria06/2014
38317*10^94373+8794374Robert Price11/2016
3832(9^98897+8^98897)/1794371Robert Price12/2012
38332^313453-11470394359Enzo Doria04/2015
38348*10^94357-5194358Robert Price10/2017
3835(379*10^94337-1)/994339Robert Price08/2017
38362^313344-313344+194326Robert Price10/2014
383720^72481-4994300Lelio R Paula05/2016
383844725!2+12894289Robert Price03/2015
38394*10^94286+994287Robert Price05/2015
384017^76621+2494279Lelio R Paula07/2016
38412^313156-11285994270Enzo Doria06/2014
38426^121130-5994258Lelio R Paula05/2016
38433^197542+2894252Robert Price11/2013
3844(3^197521+2)/5165594237Lelio R Paula04/2013
38452^313045-595594236Lelio R Paula03/2016
3846(67*10^94212+23)/994213Ray Chandler02/2011
38472^312909-186520394195Enzo Doria03/2016
38482^312848-14994177Lelio R Paula11/2012
38494^156403-7759794164Mike Oakes04/2011
385018^75004-8594151Lelio R Paula06/2016
385119^73622-4894145Lelio R Paula06/2016
3852(11^90397-3^90397)/894138Robert Price04/2011
3853(3^197287+5)/1694129Lelio R Paula04/2013
385412^87212-3794118Lelio R Paula06/2016
385511^90376+7694117Lelio R Paula05/2016
3856(6^120946-11)/594114Paul Bourdelais11/2011
3857(10^94096+191)/394096Robert Price11/2017
38582^312562-11268594091Enzo Doria06/2014
3859137^44026-294072Lelio R Paula10/2017
38602^312404-86968810594043Lelio R Paula09/2016
38612^312387+279353394038Enzo Doria03/2016
386310^94016+9194017Robert Price04/2011
3862(15*2^312325-1)/720194017Lelio R Paula02/2014
386510^94016-18896394016Patrick De Geest08/2013
3864(17*2^312315-1)/4594016Lelio R Paula02/2014
38666^120802+766194003Mike Oakes04/2011
3867(67607*2^312254+1)/17794001Lelio R Paula06/2014
3868(11*2^312207+1)/1993984Lelio R Paula09/2013
38692^312201+5193982Lelio R Paula11/2012
3870(4*6^120749+1)/593961Serge Batalov10/2014
38713^196892+5893942Lelio R Paula05/2016
38722^312060+1891593940Lelio R Paula03/2016
38732^311992-1620993919Enzo Doria04/2013
3874(85^48677+1)/8693917Paul Bourdelais08/2017
38752^311965-3993911Lelio R Paula11/2012
38762^311920-11168993898Enzo Doria05/2014
38777*10^93887-4793888Robert Price02/2017
387812^86965-1393851Lelio R Paula06/2016
38792^311705+1609593833Lelio R Paula03/2016
38802^311665-8193821Lelio R Paula11/2012
3881730^32761+32761^73093806Norbert Schneider09/2017
388211^90073+9293802Lelio R Paula05/2016
38836*10^93792+4193793Robert Price01/2017
3884(2^311580+7)/59132993790Lelio R Paula06/2013
388512^86900-7793781Lelio R Paula06/2016
38862^311508-10976993774Enzo Doria04/2014
38872^311486-185962193767Enzo Doria03/2016
3888Phi(93811,10)/968129521/2109997013/3280113810431/63963778254583193765Kurt Beschorner04/2015
38892^311471+31146993763Renaud Lifchitz01/2003
3890(88*10^93760-1)/393762Robert Price10/2017
38912^311426+7945993749Enzo Doria06/2016
38922^311294+577593709Lelio R Paula03/2016
38932^311252-101793697Lelio R Paula03/2016
38942^311247-11204193695Enzo Doria06/2014
38957*10^93692-8393693Robert Price09/2017
38962^311205-10964593683Enzo Doria04/2014
38975^134027-8493681Lelio R Paula04/2016
3898(2^311148-1017)/55793663Lelio R Paula06/2013
3899(2^311027-2^155514+1)/59362811/2006
39003^196192-2893608Robert Price12/2013
3901216091#+26143393606Makoto Morimoto12/2015
39025^133917+6893604Lelio R Paula04/2016
39032^310924-170993598Yves Minet03/2013
3904(266*10^93577-11)/393579Robert Price09/2016
3905(16*10^93577+161)/393578Robert Price05/2016
39063^196113-5693570Lelio R Paula04/2016
39072^310806-11034593562Enzo Doria05/2014
39083^196093+8693561Lelio R Paula04/2016
39092^310780-232793555Yves Minet10/2013
391030^63332+4193550Lelio R Paula08/2012
3911(21181*2^310707+1)/2193536Lelio R Paula06/2014
39128*5^133807+793528Lelio R Paula10/2014
39132^310686+819393526Lelio R Paula03/2016
39142^310646+6393514Lelio R Paula11/2012
3915(77*10^93508+31)/993509Robert Price10/2015
3916(1000907^15583+1)/100090893499Faysal YAtim04/2009
3917(2*10^93497+7)/993497Erik Branger03/2011
39183^195958-11285293496Enzo Doria07/2014
39192^310583+1638593495Lelio R Paula03/2016
3920(9913*2^310557-1)/3593490Lelio R Paula04/2015
39219*7^110614+293481Lelio R Paula11/2014
39222^310469-829593461Lelio R Paula03/2016
39232^310459-115993458Yves Minet11/2012
39246^120075-9593437Lelio R Paula05/2016
39252^310289+9832793407Yves Minet11/2010
39262^310217-11314393385Enzo Doria07/2014
39277^110494-6893379Lelio R Paula04/2016
39282^310184-11309393375Enzo Doria07/2014
39292^310180-11041793374Enzo Doria05/2014
3930gcd(V(1124905),5*F(224981)*(F(224981)-1)+1)93372Serge Batalov04/2015
39313^195669+6893358Lelio R Paula04/2016
393210^93356+9193357Robert Price04/2011
393310^93356-2831393356Patrick De Geest08/2013
3934(85*10^93346+23)/993347Robert Price11/2015
3935(3^195648-5)/315827693342Lelio R Paula04/2013
39363^195556+868093304Lelio R Paula04/2016
39372^309942-10999193302Enzo Doria04/2014
39382^309926-186730193298Enzo Doria03/2016
39392^309924+8595193297Yves Minet03/2011
3940(86*10^93263-77)/993264Robert Price05/2016
39416^119836-12593251Lelio R Paula05/2016
3942(77*10^93249-257)/993250Robert Price10/2017
39433^195430-293244Theodore Burton02/2007
3944(13*10^93236+47)/393237Robert Price01/2017
3945(67*10^93226-7)/393228Robert Price10/2017
3946(86*10^93217-221)/993218Robert Price06/2017
39472^309637-1632993211Enzo Doria04/2013
3948(41*10^93207+49)/993208Robert Price04/2016
394914^81312-5793194Lelio R Paula06/2016
395041^57783-4093192Theodore Burton02/2007
39513*10^93179-9793180Robert Price08/2017
39525*7^110252-493175Lelio R Paula11/2014
39532^309380-2793133Lelio R Paula11/2012
395423*10^93116-793118Robert Price03/2016
3955(29*10^93082+1)/393083Robert Price11/2015
3956(58*10^93062-13)/993063Robert Price09/2015
39572^309131+186938393058Enzo Doria05/2016
39582^309066-9393039Lelio R Paula11/2012
39592^309063-11326993038Enzo Doria07/2014
39603^194965+1693022Robert Price10/2013
39612^308979+186914393012Enzo Doria05/2016
39625^133064+5493008Lelio R Paula04/2016
3963(2^308905-509203)/11992988Lelio R Paula06/2013
3964(94*10^92981-49)/9992981Ray Chandler07/2011
3965(2*10^92976-17)/392976Robert Price08/2014
39662^308809+3796792961Phil Moore03/2008
3967(3^194825+5)/1165692952Lelio R Paula04/2013
3968(2^308679+5)/157392919Lelio R Paula06/2013
39692^308650+51392913Lelio R Paula02/2016
39705*7^109936+692908Lelio R Paula10/2014
39712*10^92897+8992898Robert Price07/2016
397212^86073-2992889Lelio R Paula06/2016
39732^308566-11792888Lelio R Paula11/2012
3974(17*10^92869-11)/392870Robert Price07/2015
39752^308459+7543192856Enzo Doria04/2016
39762^308426-186637792846Enzo Doria03/2016
3977(96^46831-1)/9592830Paul Bourdelais09/2017
39782^308349-11211192823Enzo Doria06/2014
39799*10^92821+1992822Robert Price05/2016
39802^308337-7592819Lelio R Paula11/2012
39814*3^194508+792805Lelio R Paula08/2014
398222*25^66379-11392796Curtis Bright05/2015
398311^89101-108092790Enzo Doria12/2012
39842^308236-186785992789Enzo Doria04/2016
398512^85963+2592770Lelio R Paula06/2016
39867^109750-6692750Lelio R Paula04/2016
39879*10^92742+1192743Robert Kinser01/2017
3988(21*2^308046-1)/885792729Lelio R Paula02/2014
39892^307997-11065592717Enzo Doria05/2014
3990L(443609)92709Renaud Lifchitz11/2003
399110^92691+992692Robert Price03/2011
399210^92691-25229192691Patrick De Geest08/2013
39932^307879-252192681Yves Minet07/2014
3994(2^307780-7)/1995966992644Lelio R Paula06/2013
399514^80831+4792643Lelio R Paula06/2016
399615^78744+9292611Lelio R Paula07/2016
399765^51083-6492610Norbert Schneider11/2014
39986^118996-1694392597Enzo Doria02/2013
3999(16*10^92591+41)/392592Robert Price10/2017
4000(3^194014-7)/292568Lelio R Paula04/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 18 2018 23:06 (Time in France)

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