PRP Records

Probable Primes Top 10000

(280932 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 ?
7501(22*10^87863-1)/387864Robert Price12/2014
75022^291822-279781187848Enzo Doria04/2016
7503(2^291730+1614)/287820Stefano Morozzi01/2020
75042^291716-11138987816Enzo Doria05/2014
7505(782*10^87809-71)/987811Robert Price06/2017
75063^184039+182087809Lelio R Paula12/2015
750712^81356+4187798Lelio R Paula11/2015
750821307^13188+13188^2130787789Hans Havermann08/2020
7509(2527^25801-1)/252687788Serge Batalov08/2020
7510(2^291596+1986)/287779Stefano Morozzi01/2020
75126^112792-1898387770Enzo Doria03/2013
7511(3123^25117-1)/312287770Serge Batalov08/2020
75133*6^112787-587766Lelio R Paula10/2014
75147^103848+8287762Lelio R Paula10/2015
7515(19*2^291534-1)/17869639587754Lelio R Paula02/2014
7516(2^291506+918)/287752Stefano Morozzi01/2020
751724411^3932+3932^2441187749Hans Havermann08/2020
7518(3^183915+5)/12887748Lelio R Paula01/2013
751919^68619+2487747Lelio R Paula12/2015
75212^291480+118587745Lelio R Paula10/2013
75202^291482+186736987745Enzo Doria03/2016
75222^291467-93787741Yves Minet05/2013
7523(25*10^87726+161)/387727Robert Price01/2017
752411^84239-285087726Enzo Doria12/2012
752510^87720+21554187721Patrick De Geest01/2011
752610^87720-387720Markus Tervooren07/2010
7527(2^291383+3078)/287715Stefano Morozzi01/2020
7529(5*10^87712-473)/987712Robert Price12/2017
7528(2^291373+2946)/287712Stefano Morozzi01/2020
753022591^7630+7630^2259187711Hans Havermann08/2020
753122081^9378+9378^2208187709Hans Havermann08/2020
7532(2^291357+5)/684787704Lelio R Paula01/2013
7533(2^291280+462)/287684Stefano Morozzi01/2020
753420749^16816+16816^2074987680Hans Havermann08/2020
753693^44541-287679Lelio R Paula09/2013
75352^291261-10956187679Enzo Doria04/2014
7537(4*10^87669+149)/987669Robert Price03/2017
75382^291217+425787666Lelio R Paula10/2013
753922748^7137+7137^2274887660Hans Havermann08/2020
75402*12^81214-5^8121487645Mike Oakes12/2010
7541(5005^23689-1)/500487632Serge Batalov08/2020
7542(5*10^87622-473)/987622Robert Price12/2017
754312^81188+8587617Lelio R Paula11/2015
7544(2^291030+3462)/287609Stefano Morozzi01/2020
7545(21*2^290980-1)/587595Lelio R Paula02/2014
7546(2^290980+1150)/287594Stefano Morozzi01/2020
75472^290958+12787588Lelio R Paula09/2012
754878531!4-887580Robert Price11/2019
75492^290923-6787577Lelio R Paula09/2012
75503*10^87573-9787574Robert Price08/2017
7551(13*10^87565+11)/387566Robert Price05/2015
7552(2^290881+1022)/287564Stefano Morozzi01/2020
7553(2^290857-7)/5587555Lelio R Paula01/2013
7554(2^290808+1498)/287542Stefano Morozzi01/2020
75552^290802+8287587541Lelio R Paula10/2013
7556(509203*2^290792-1)/756098787536Lelio R Paula04/2015
75573^183441+23687524Lelio R Paula12/2015
75582^290618-3387485Lelio R Paula09/2012
7559(184*10^87473-1)/387475Robert Price02/2017
75602^290534-11515187460Enzo Doria06/2015
75612^290512-10975787453Enzo Doria04/2014
7562(32*10^87448-41)/987449Robert Price05/2015
7563(2^290493+3074)/287447Stefano Morozzi01/2020
7564(2^290491+9)/317987444Lelio R Paula01/2013
7565(25*2^290489-1)/5180987443Lelio R Paula02/2014
75662^290426+8287587427Lelio R Paula11/2013
75673*2^290415-787425Lelio R Paula08/2014
757010^87408+5787409Robert Price03/2011
75692^290366+7477987409Enzo Doria04/2016
756822284^8365+8365^2228487409Hans Havermann08/2020
757110^87408-12356987408Patrick De Geest07/2013
757221517^11536+11536^2151787404Hans Havermann08/2020
75736*10^87396+7787397Robert Price06/2020
7574(2^290268+3882)/287380Stefano Morozzi01/2020
75752^290265+5890587379Lelio R Paula10/2013
75767^103391+1687376Lelio R Paula10/2015
7577(115*10^87368-7)/987370Robert Price11/2017
7578(92^44491-1)/9187369Paul Bourdelais08/2017
75798*7^103379+387367Lelio R Paula10/2014
7580(2^290226+7)/7187365Lelio R Paula01/2013
7581(3216^24907-1)/321587354Serge Batalov08/2020
7582(2^290160+2686)/287347Stefano Morozzi01/2020
758313^78407-3087341Lelio R Paula11/2015
75844*10^87337-9987338Robert Price12/2016
75857*10^87319+3987320Robert Price07/2016
75863*5^124921+287317Lelio R Paula10/2014
758778315!4-1687316Robert Price11/2019
75883^182984+8887306Lelio R Paula12/2015
7589(10^87323-1)/(9*33909262597306826117)87303Alfred Reich02/2019
7590(10^87323-1)/30518336337576143505387303Anonymous10/2020
7591(2^290008+958)/287301Stefano Morozzi01/2020
7592(10536^21701-1)/1053587293Serge Batalov08/2020
75934*10^87287-9987288Robert Price12/2016
759511^83813-186087283Enzo Doria12/2012
7594(3068^25033-1)/306787283Serge Batalov08/2020
7596734^30453+30453^73487270Norbert Schneider04/2017
759712^80855+2987258Lelio R Paula11/2015
759822209^8482+8482^2220987249Hans Havermann08/2020
75993*6^112119-587247Lelio R Paula10/2014
760012^80806+7987205Lelio R Paula11/2015
760191382^9+9^9138287201Andrey Kulsha11/2004
7602(21181*2^289657+1)/8187198Lelio R Paula06/2014
76036^112054-4787195Lelio R Paula12/2015
7604(55459*2^289632+1)/5587191Lelio R Paula06/2014
760515^74131-6887185Lelio R Paula11/2015
76062^289583-74187174Lelio R Paula10/2013
76077^103146+1287169Lelio R Paula10/2015
7608(2^289562+2182)/287167Stefano Morozzi01/2020
76095*2^289556-387166Lelio R Paula08/2014
76102^289543-11273587162Enzo Doria06/2014
761120204^20243-20243^2020487155Norbert Schneider04/2020
76128*3^182655-787150Lelio R Paula08/2014
76132*10^87144+8187145Robert Price01/2017
761420541^17468+17468^2054187140Hans Havermann07/2020
76167^103106+2*3^10310687135Mike Oakes08/2010
7615(65*10^87134-29)/987135Robert Price01/2021
76178*3^182614+787130Lelio R Paula08/2014
76183*10^87121-7387122Robert Price02/2021
7619(4982^23563-1)/498187119Serge Batalov08/2020
7620(2^289368-509203)/987108Lelio R Paula01/2013
76213^182566+1487107Robert Price09/2013
76221738^26881+26881^173887096Norbert Schneider04/2020
762324290^3849+3849^2429087089Hans Havermann08/2020
7624(3^182385-5)/287020Lelio R Paula01/2013
762511^83534-886992Lelio R Paula11/2015
76264^144479-1426786986Mike Oakes03/2011
7627(145*10^86982-1)/986984Serge Batalov12/2014
7629(151*10^86963-1)/386965Robert Price04/2017
7628(2^288892+826)/286965Stefano Morozzi01/2020
763015^73940-5886961Lelio R Paula11/2015
76312^288761-11314386926Enzo Doria07/2014
763224440^3603+3603^2444086925Hans Havermann08/2020
76342^288747+308386922Yves Minet03/2011
7633(2^288749+3102)/286922Stefano Morozzi01/2020
763530^58842+2986917Norbert Schneider03/2017
7636(2^288705+2186)/286909Stefano Morozzi01/2020
7637(10^86906-13)/386906Robert Price02/2017
76382^288692-11002786905Enzo Doria04/2014
7639(2^288682+7)/25989544986894Lelio R Paula01/2013
7640(26*10^86885+79)/386886Robert Price09/2020
7641(2^288636+47)/129386885Lelio R Paula01/2013
76423^182089-3486879Robert Price11/2013
7643(2^288571+1698)/286869Stefano Morozzi01/2020
76442^288543-10980186861Enzo Doria04/2014
764560^48847-5986858Norbert Schneider10/2014
7646(2^288484+3186)/286843Stefano Morozzi01/2020
76472^288470-6487586839Lelio R Paula10/2013
764810^86816+3299786817Patrick De Geest07/2013
764910^86816-9986816Robert Price05/2011
7650(89*10^86802-539)/986803Robert Price11/2017
765120272^19123+19123^2027286796Hans Havermann07/2020
7652(2^288316+1530)/286792Stefano Morozzi01/2020
7653(2^288316+2218)/286792Stefano Morozzi01/2020
765441487!2+25686786Robert Price01/2015
7655(5*2^288301-1)/99986785Lelio R Paula02/2014
7656(2^288278+1750)/286781Stefano Morozzi01/2020
76572^288243+7604386770Enzo Doria04/2016
7658(29*2^288232+1)/1586767Lelio R Paula01/2013
76599*6^111495+586761Lelio R Paula10/2014
7660(5*2^288202+1)/8186757Lelio R Paula01/2013
76619*7^102654-286754Lelio R Paula10/2014
7662(2^288155+1154)/286743Stefano Morozzi01/2020
76632^288122-11284186734Enzo Doria06/2014
76645^124062-6886716Lelio R Paula10/2015
7665(2^288007-3)/12586697Lelio R Paula01/2013
7666379*10^86691+986694Arkadiusz Wesolowski10/2011
76677^102555+4886670Lelio R Paula10/2015
76682^287902-496186668Yves Minet05/2019
766977779!4+286660Robert Price08/2017
7670(2^287842+3250)/286649Stefano Morozzi01/2020
76712^287809-11135586640Enzo Doria05/2014
7672(47*2^287795+1)/786636Lelio R Paula04/2015
76739*7^102504+886627Lelio R Paula10/2014
76743^181551+3286622Robert Price11/2013
76752^287735-52134786617Paul Bourdelais05/2013
767621912^8953+8953^2191286596Hans Havermann08/2020
7677(1017*2^287600-1)/9186578Lelio R Paula04/2015
7678(2^287552+1302)/286562Stefano Morozzi01/2020
76792^287540-11296786559Enzo Doria06/2014
76803^181407+2086554Robert Price10/2013
7681(28*10^86550+101)/386551Robert Price09/2020
7683(13*10^86546+83)/386547Robert Price09/2016
7682(2^287502+2238)/286547Stefano Morozzi01/2020
76842^287482-471586541Yves Minet05/2019
76853^181378-2^(181378-1)86540Robert Price01/2016
768624588^3305+3305^2458886530Hans Havermann08/2020
768783^45080-286513Lelio R Paula08/2013
7688(2^287367+2570)/286506Stefano Morozzi01/2020
7690(78557*2^287351+1)/61186504Lelio R Paula06/2014
7689(2^287360+1006)/286504Stefano Morozzi01/2020
769125*29^59147+2093686498Curtis Bright05/2015
76922^287298+187135986486Enzo Doria05/2016
7693118^41740-11786481Norbert Schneider08/2018
76943*10^86478+8986479Robert Price03/2017
76952^287272-7904986478Paul Bourdelais02/2012
7696(2^287259+2846)/286474Stefano Morozzi01/2020
7697906705*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
7698811824*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
7699779064*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
7700768385*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
7701700891*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
7702652320*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
7703377920*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
7704255060*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
7705187111*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
7706(10^86453-1)/986453Lew Baxter10/2000
7707(2^287172+658)/286448Stefano Morozzi01/2020
7708(2^287146+2542)/286440Stefano Morozzi01/2020
7709(2^287136+1726)/286437Stefano Morozzi01/2020
7710(2^287128+958)/286434Stefano Morozzi01/2020
771187^44563-86^4456386431Robert Price05/2015
77126^111057+6186420Lelio R Paula12/2015
77132^287057-10990986413Enzo Doria04/2014
77145^123608+2286399Lelio R Paula10/2015
7715(2^286970+618)/286387Stefano Morozzi01/2020
7716(2^286916+2646)/286371Stefano Morozzi01/2020
7717(2^286907+3690)/286368Stefano Morozzi01/2020
7718(31*10^86364-121)/986365Robert Price06/2016
7719(2^286868+2686)/286356Stefano Morozzi01/2020
77202^286859+7166386354Enzo Doria04/2016
7721(2^286845+1866)/286349Stefano Morozzi01/2020
77222^286740+2983586318Lelio R Paula10/2013
77232*10^86310+9^8631086311Mike Oakes05/2011
772411^82878-186086309Enzo Doria12/2012
77252223^25780+25780^222386285Norbert Schneider12/2019
77262^286547+1609586260Lelio R Paula10/2013
7727(58*10^86242+329)/986243Robert Price11/2017
77282^286455-11042786232Enzo Doria05/2014
7729(37*10^86230+53)/986231Robert Price05/2015
77308*3^180700+586217Lelio R Paula08/2014
77313^180697-4086215Lelio R Paula12/2015
7732(2^286383+3386)/286210Stefano Morozzi01/2020
7733(13*2^286318-1)/1325786188Lelio R Paula02/2014
7734(2^286295+1934)/286184Stefano Morozzi01/2020
7735(2^286251+3974)/286170Stefano Morozzi01/2020
77362^286165+7786145Lelio R Paula08/2012
77379*2^286140+786138Lelio R Paula08/2014
7738(2^286128+1762)/286133Stefano Morozzi01/2020
7739(29*2^286108-1)/200236786123Lelio R Paula02/2014
7740(2^286077+1122)/286118Stefano Morozzi01/2020
774110^86110+16111386111Patrick De Geest07/2013
774210^86110-6986110Robert Price05/2011
77432^286036-86968810586106Lelio R Paula07/2016
7744(2^285946+2358)/286079Stefano Morozzi01/2020
7746(77*10^86072+31)/986073Robert Price10/2015
7745(2^285926+3382)/286073Stefano Morozzi01/2020
77472^285923+34586072Lelio R Paula09/2013
774813^77266-9086070Lelio R Paula11/2015
77492^285910-45890386068Enzo Doria04/2015
77502^285904-12586066Lelio R Paula08/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 13 2021 12:02 (Time in France)

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