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) !!!


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 ?
700114^76677+6987882Lelio R Paula11/2015
7002(22*10^87863-1)/387864Robert Price12/2014
70032^291822-279781187848Enzo Doria04/2016
7004(2^291730+1614)/287820Stefano Morozzi01/2020
70052^291716-11138987816Enzo Doria05/2014
7006(782*10^87809-71)/987811Robert Price06/2017
70073^184039+182087809Lelio R Paula12/2015
700812^81356+4187798Lelio R Paula11/2015
700921307^13188+13188^2130787789Hans Havermann08/2020
7010(2527^25801-1)/252687788Serge Batalov08/2020
7011(2^291596+1986)/287779Stefano Morozzi01/2020
70136^112792-1898387770Enzo Doria03/2013
7012(3123^25117-1)/312287770Serge Batalov08/2020
70143*6^112787-587766Lelio R Paula10/2014
70157^103848+8287762Lelio R Paula10/2015
7016(19*2^291534-1)/17869639587754Lelio R Paula02/2014
7017(2^291506+918)/287752Stefano Morozzi01/2020
701824411^3932+3932^2441187749Hans Havermann08/2020
7019(3^183915+5)/12887748Lelio R Paula01/2013
702019^68619+2487747Lelio R Paula12/2015
70222^291480+118587745Lelio R Paula10/2013
70212^291482+186736987745Enzo Doria03/2016
70232^291467-93787741Yves Minet05/2013
7024(25*10^87726+161)/387727Robert Price01/2017
702511^84239-285087726Enzo Doria12/2012
702610^87720+21554187721Patrick De Geest01/2011
702710^87720-387720Markus Tervooren07/2010
7028(2^291383+3078)/287715Stefano Morozzi01/2020
7030(5*10^87712-473)/987712Robert Price12/2017
7029(2^291373+2946)/287712Stefano Morozzi01/2020
703122591^7630+7630^2259187711Hans Havermann08/2020
703222081^9378+9378^2208187709Hans Havermann08/2020
7033(2^291357+5)/684787704Lelio R Paula01/2013
7034(2^291280+462)/287684Stefano Morozzi01/2020
703520749^16816+16816^2074987680Hans Havermann08/2020
703793^44541-287679Lelio R Paula09/2013
70362^291261-10956187679Enzo Doria04/2014
7038(4*10^87669+149)/987669Robert Price03/2017
70392^291217+425787666Lelio R Paula10/2013
704022748^7137+7137^2274887660Hans Havermann08/2020
70412*12^81214-5^8121487645Mike Oakes12/2010
7042(5005^23689-1)/500487632Serge Batalov08/2020
7043(5*10^87622-473)/987622Robert Price12/2017
704412^81188+8587617Lelio R Paula11/2015
7045(2^291030+3462)/287609Stefano Morozzi01/2020
7046(21*2^290980-1)/587595Lelio R Paula02/2014
7047(2^290980+1150)/287594Stefano Morozzi01/2020
70482^290958+12787588Lelio R Paula09/2012
704978531!4-887580Robert Price11/2019
70502^290923-6787577Lelio R Paula09/2012
70513*10^87573-9787574Robert Price08/2017
7052(13*10^87565+11)/387566Robert Price05/2015
7053(2^290881+1022)/287564Stefano Morozzi01/2020
7054(2^290857-7)/5587555Lelio R Paula01/2013
7055(2^290808+1498)/287542Stefano Morozzi01/2020
70562^290802+8287587541Lelio R Paula10/2013
7057(509203*2^290792-1)/756098787536Lelio R Paula04/2015
70583^183441+23687524Lelio R Paula12/2015
70592^290618-3387485Lelio R Paula09/2012
7060(184*10^87473-1)/387475Robert Price02/2017
70612^290534-11515187460Enzo Doria06/2015
70622^290512-10975787453Enzo Doria04/2014
7063(32*10^87448-41)/987449Robert Price05/2015
7064(2^290493+3074)/287447Stefano Morozzi01/2020
7065(2^290491+9)/317987444Lelio R Paula01/2013
7066(25*2^290489-1)/5180987443Lelio R Paula02/2014
70672^290426+8287587427Lelio R Paula11/2013
70683*2^290415-787425Lelio R Paula08/2014
707110^87408+5787409Robert Price03/2011
70702^290366+7477987409Enzo Doria04/2016
706922284^8365+8365^2228487409Hans Havermann08/2020
707210^87408-12356987408Patrick De Geest07/2013
707321517^11536+11536^2151787404Hans Havermann08/2020
70746*10^87396+7787397Robert Price06/2020
7075(2^290268+3882)/287380Stefano Morozzi01/2020
70762^290265+5890587379Lelio R Paula10/2013
70777^103391+1687376Lelio R Paula10/2015
7078(115*10^87368-7)/987370Robert Price11/2017
7079(92^44491-1)/9187369Paul Bourdelais08/2017
70808*7^103379+387367Lelio R Paula10/2014
7081(2^290226+7)/7187365Lelio R Paula01/2013
7082(3216^24907-1)/321587354Serge Batalov08/2020
7083(2^290160+2686)/287347Stefano Morozzi01/2020
708413^78407-3087341Lelio R Paula11/2015
70854*10^87337-9987338Robert Price12/2016
70867*10^87319+3987320Robert Price07/2016
70873*5^124921+287317Lelio R Paula10/2014
708878315!4-1687316Robert Price11/2019
70893^182984+8887306Lelio R Paula12/2015
7090(10^87323-1)/(9*33909262597306826117)87303Alfred Reich02/2019
7091(10^87323-1)/30518336337576143505387303Anonymous10/2020
7092(2^290008+958)/287301Stefano Morozzi01/2020
7093(10536^21701-1)/1053587293Serge Batalov08/2020
70944*10^87287-9987288Robert Price12/2016
709611^83813-186087283Enzo Doria12/2012
7095(3068^25033-1)/306787283Serge Batalov08/2020
7097734^30453+30453^73487270Norbert Schneider04/2017
709812^80855+2987258Lelio R Paula11/2015
709922209^8482+8482^2220987249Hans Havermann08/2020
71003*6^112119-587247Lelio R Paula10/2014
710112^80806+7987205Lelio R Paula11/2015
710291382^9+9^9138287201Andrey Kulsha11/2004
7103(21181*2^289657+1)/8187198Lelio R Paula06/2014
71046^112054-4787195Lelio R Paula12/2015
7105(55459*2^289632+1)/5587191Lelio R Paula06/2014
710615^74131-6887185Lelio R Paula11/2015
71072^289583-74187174Lelio R Paula10/2013
71087^103146+1287169Lelio R Paula10/2015
7109(2^289562+2182)/287167Stefano Morozzi01/2020
71105*2^289556-387166Lelio R Paula08/2014
71112^289543-11273587162Enzo Doria06/2014
711220204^20243-20243^2020487155Norbert Schneider04/2020
71138*3^182655-787150Lelio R Paula08/2014
71142*10^87144+8187145Robert Price01/2017
711520541^17468+17468^2054187140Hans Havermann07/2020
71177^103106+2*3^10310687135Mike Oakes08/2010
7116(65*10^87134-29)/987135Robert Price01/2021
71188*3^182614+787130Lelio R Paula08/2014
7119(4982^23563-1)/498187119Serge Batalov08/2020
7120(2^289368-509203)/987108Lelio R Paula01/2013
71213^182566+1487107Robert Price09/2013
71221738^26881+26881^173887096Norbert Schneider04/2020
712324290^3849+3849^2429087089Hans Havermann08/2020
7124(3^182385-5)/287020Lelio R Paula01/2013
712511^83534-886992Lelio R Paula11/2015
71264^144479-1426786986Mike Oakes03/2011
7127(145*10^86982-1)/986984Serge Batalov12/2014
7129(151*10^86963-1)/386965Robert Price04/2017
7128(2^288892+826)/286965Stefano Morozzi01/2020
713015^73940-5886961Lelio R Paula11/2015
71312^288761-11314386926Enzo Doria07/2014
713224440^3603+3603^2444086925Hans Havermann08/2020
71342^288747+308386922Yves Minet03/2011
7133(2^288749+3102)/286922Stefano Morozzi01/2020
713530^58842+2986917Norbert Schneider03/2017
7136(2^288705+2186)/286909Stefano Morozzi01/2020
7137(10^86906-13)/386906Robert Price02/2017
71382^288692-11002786905Enzo Doria04/2014
7139(2^288682+7)/25989544986894Lelio R Paula01/2013
7140(26*10^86885+79)/386886Robert Price09/2020
7141(2^288636+47)/129386885Lelio R Paula01/2013
71423^182089-3486879Robert Price11/2013
7143(2^288571+1698)/286869Stefano Morozzi01/2020
71442^288543-10980186861Enzo Doria04/2014
714560^48847-5986858Norbert Schneider10/2014
7146(2^288484+3186)/286843Stefano Morozzi01/2020
71472^288470-6487586839Lelio R Paula10/2013
714810^86816+3299786817Patrick De Geest07/2013
714910^86816-9986816Robert Price05/2011
7150(89*10^86802-539)/986803Robert Price11/2017
715120272^19123+19123^2027286796Hans Havermann07/2020
7152(2^288316+1530)/286792Stefano Morozzi01/2020
7153(2^288316+2218)/286792Stefano Morozzi01/2020
715441487!2+25686786Robert Price01/2015
7155(5*2^288301-1)/99986785Lelio R Paula02/2014
7156(2^288278+1750)/286781Stefano Morozzi01/2020
71572^288243+7604386770Enzo Doria04/2016
7158(29*2^288232+1)/1586767Lelio R Paula01/2013
71599*6^111495+586761Lelio R Paula10/2014
7160(5*2^288202+1)/8186757Lelio R Paula01/2013
71619*7^102654-286754Lelio R Paula10/2014
7162(2^288155+1154)/286743Stefano Morozzi01/2020
71632^288122-11284186734Enzo Doria06/2014
71645^124062-6886716Lelio R Paula10/2015
7165(2^288007-3)/12586697Lelio R Paula01/2013
7166379*10^86691+986694Arkadiusz Wesolowski10/2011
71677^102555+4886670Lelio R Paula10/2015
71682^287902-496186668Yves Minet05/2019
716977779!4+286660Robert Price08/2017
7170(2^287842+3250)/286649Stefano Morozzi01/2020
71712^287809-11135586640Enzo Doria05/2014
7172(47*2^287795+1)/786636Lelio R Paula04/2015
71739*7^102504+886627Lelio R Paula10/2014
71743^181551+3286622Robert Price11/2013
71752^287735-52134786617Paul Bourdelais05/2013
717621912^8953+8953^2191286596Hans Havermann08/2020
7177(1017*2^287600-1)/9186578Lelio R Paula04/2015
7178(2^287552+1302)/286562Stefano Morozzi01/2020
71792^287540-11296786559Enzo Doria06/2014
71803^181407+2086554Robert Price10/2013
7181(28*10^86550+101)/386551Robert Price09/2020
7183(13*10^86546+83)/386547Robert Price09/2016
7182(2^287502+2238)/286547Stefano Morozzi01/2020
71842^287482-471586541Yves Minet05/2019
71853^181378-2^(181378-1)86540Robert Price01/2016
718624588^3305+3305^2458886530Hans Havermann08/2020
718783^45080-286513Lelio R Paula08/2013
7188(2^287367+2570)/286506Stefano Morozzi01/2020
7190(78557*2^287351+1)/61186504Lelio R Paula06/2014
7189(2^287360+1006)/286504Stefano Morozzi01/2020
719125*29^59147+2093686498Curtis Bright05/2015
71922^287298+187135986486Enzo Doria05/2016
7193118^41740-11786481Norbert Schneider08/2018
71943*10^86478+8986479Robert Price03/2017
71952^287272-7904986478Paul Bourdelais02/2012
7196(2^287259+2846)/286474Stefano Morozzi01/2020
7197906705*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
7198811824*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
7199779064*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
7200768385*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
7201700891*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
7202652320*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
7203377920*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
7204255060*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
7205187111*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
7206(10^86453-1)/986453Lew Baxter10/2000
7207(2^287172+658)/286448Stefano Morozzi01/2020
7208(2^287146+2542)/286440Stefano Morozzi01/2020
7209(2^287136+1726)/286437Stefano Morozzi01/2020
7210(2^287128+958)/286434Stefano Morozzi01/2020
721187^44563-86^4456386431Robert Price05/2015
72126^111057+6186420Lelio R Paula12/2015
72132^287057-10990986413Enzo Doria04/2014
72145^123608+2286399Lelio R Paula10/2015
7215(2^286970+618)/286387Stefano Morozzi01/2020
7216(2^286916+2646)/286371Stefano Morozzi01/2020
7217(2^286907+3690)/286368Stefano Morozzi01/2020
7218(31*10^86364-121)/986365Robert Price06/2016
7219(2^286868+2686)/286356Stefano Morozzi01/2020
72202^286859+7166386354Enzo Doria04/2016
7221(2^286845+1866)/286349Stefano Morozzi01/2020
72222^286740+2983586318Lelio R Paula10/2013
72232*10^86310+9^8631086311Mike Oakes05/2011
722411^82878-186086309Enzo Doria12/2012
72252223^25780+25780^222386285Norbert Schneider12/2019
72262^286547+1609586260Lelio R Paula10/2013
7227(58*10^86242+329)/986243Robert Price11/2017
72282^286455-11042786232Enzo Doria05/2014
7229(37*10^86230+53)/986231Robert Price05/2015
72308*3^180700+586217Lelio R Paula08/2014
72313^180697-4086215Lelio R Paula12/2015
7232(2^286383+3386)/286210Stefano Morozzi01/2020
7233(13*2^286318-1)/1325786188Lelio R Paula02/2014
7234(2^286295+1934)/286184Stefano Morozzi01/2020
7235(2^286251+3974)/286170Stefano Morozzi01/2020
72362^286165+7786145Lelio R Paula08/2012
72379*2^286140+786138Lelio R Paula08/2014
7238(2^286128+1762)/286133Stefano Morozzi01/2020
7239(29*2^286108-1)/200236786123Lelio R Paula02/2014
7240(2^286077+1122)/286118Stefano Morozzi01/2020
724110^86110+16111386111Patrick De Geest07/2013
724210^86110-6986110Robert Price05/2011
72432^286036-86968810586106Lelio R Paula07/2016
7244(2^285946+2358)/286079Stefano Morozzi01/2020
7246(77*10^86072+31)/986073Robert Price10/2015
7245(2^285926+3382)/286073Stefano Morozzi01/2020
72472^285923+34586072Lelio R Paula09/2013
724813^77266-9086070Lelio R Paula11/2015
72492^285910-45890386068Enzo Doria04/2015
72502^285904-12586066Lelio R Paula08/2012


Find by discoverer :


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

Go back
Valid XHTML 1.0!    Valid CSS!