Henri & Renaud Lifchitz's PRP Top records

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 ?
6751	(79^60539-1)/61747564999146	114867	Paul Vanderveen	05/2025
6752	2^381555-109051	114860	Enzo Doria	04/2014
6753	2^381551+213683	114859	Enzo Doria	09/2023
6754	2^381546-113501	114857	Enzo Doria	08/2014
6755	(7*10^114845-19)/3	114846	Robert Price	10/2020
6756	26675^20178+20178^26675	114833	Hans Havermann	02/2021
6757	(2^381436+1182)/2	114824	Stefano Morozzi	09/2020
6758	3^240644+16	114817	Robert Price	04/2020
6759	(13^114814)%(10^114814)	114814	Henri Lifchitz	05/2025
6760	2^381360-110429	114801	Enzo Doria	05/2014
6761	(17*10^114795+79)/3	114796	Robert Price	04/2019
6762	(66^63079+1)/67	114774	Paul Bourdelais	09/2017
6763	2^381252-115079	114769	Enzo Doria	06/2015
6764	(2^381251+3186)/2	114768	Stefano Morozzi	09/2020
6765	2^381209-29323	114756	Enzo Doria	07/2015
6766	2^381207-111546435	114755	Paul Bourdelais	10/2021
6767	569^41651-568^41651	114754	Jean-Louis Charton	11/2009
6768	2^381201+1873205	114753	Enzo Doria	06/2016
6770	(85*10^114737+293)/9	114738	Robert Price	12/2019
6771	(265*10^114736+17)/3	114738	Robert Price	03/2020
6769	379*10^114735+9	114738	Jason Yuen	01/2025
6772	(2^381062+2170)/2	114711	Stefano Morozzi	09/2020
6773	2^380974-112991	114685	Enzo Doria	07/2014
6774	37097^1234+1234^37097	114679	Hans Havermann	02/2021
6775	(26*10^114658-119)/3	114659	Robert Price	07/2023
6776	88^58949-87	114626	Norbert Schneider	11/2015
6777	(2^380773+662)/2	114624	Stefano Morozzi	09/2020
6778	Phi(155285,10)/242674820198201	114610	Makoto Kamada	02/2024
6779	(10^155285-1)(10^2389-1)(10^13-1)*11111/(10^31057-1)/(10^11945-1)/(10^65-1)/242674820198201	114610	Anonymous	04/2025
6780	29913^6782+6782^29913	114608	Hans Havermann	02/2021
6781	(331*10^114605-7)/9	114607	Robert Price	04/2022
6782	2^380700+91	114603	Lelio R Paula	03/2013
6783	(2^380632+2578)/2	114582	Stefano Morozzi	09/2020
6784	7*10^114577+27	114578	Robert Price	11/2020
6786	10^114575+3^114576	114576	Mike Oakes	09/2010
6785	10^114575+66561	114576	Patrick De Geest	02/2017
6787	10^114575-581081	114575	Patrick De Geest	02/2017
6788	2^380587-115315	114569	Enzo Doria	06/2015
6789	31874^3927+3927^31874	114558	Hans Havermann	02/2021
6790	2^380513-216925	114546	Enzo Doria	05/2014
6791	2^380451-1840087	114528	Enzo Doria	06/2015
6792	(2^380426+1510)/2	114520	Stefano Morozzi	09/2020
6793	(15*2^380388-1)/539	114507	Lelio R Paula	04/2014
6794	2^380279-461347	114476	Enzo Doria	07/2015
6795	(331*10^114454-7)/9	114456	Robert Price	04/2022
6796	27121^16590+16590^27121	114447	Hans Havermann	01/2021
6797	25966^25555+25555^25966	114445	Hans Havermann	01/2021
6798	(611*32^76029-53)/31	114437	Eric Chen	11/2023
6799	(11*10^114400+529)/9	114401	Robert Price	09/2021
6800	2^380021+1871147	114398	Enzo Doria	05/2016
6801	2^380005+1869707	114393	Enzo Doria	05/2016
6802	2^379958-113297	114379	Enzo Doria	07/2014
6803	(2^379897+1274)/2	114361	Stefano Morozzi	01/2021
6804	2^379881-109105	114356	Enzo Doria	04/2014
6805	(21*2^379857-1)/13	114349	Lelio R Paula	03/2014
6806	(4*10^114340+83)/3	114341	Robert Price	02/2018
6807	(26*10^114317-77)/3	114318	Robert Price	11/2019
6808	(4*10^114296+149)/9	114296	Robert Price	04/2018
6809	88^58773-87	114284	Norbert Schneider	11/2015
6810	27764^13065+13065^27764	114280	Hans Havermann	01/2021
6811	(132^53891-1)/131	114278	Anonymous	06/2024
6812	2^379529-2790283	114250	Enzo Doria	03/2016
6813	2^379522+1869115	114248	Enzo Doria	05/2016
6814	(145*10^114226-1)/9	114228	Serge Batalov	12/2014
6815	2^379317-115033	114186	Enzo Doria	06/2015
6816	(22*10^114178+47)/3	114179	Robert Price	06/2021
6817	(17*2^379246-1)/17407	114162	Lelio R Paula	03/2014
6818	(2^379192+226)/2	114148	Stefano Morozzi	09/2020
6819	(228^48407-1)/227	114139	Alexander Zhirkov	03/2023
6820	6*10^114091+23	114092	Robert Price	09/2020
6821	(4*10^114076+143)/3	114077	Robert Price	03/2018
6822	332*25^81584+12357	114053	Eric Chen	10/2023
6823	(2^378820+3226)/2	114036	Stefano Morozzi	01/2021
6824	(2^378754+2058)/2	114017	Stefano Morozzi	09/2020
6825	13643^27572-27572^13643	114008	Norbert Schneider	12/2022
6827	(46*10^113969+683)/9	113970	Robert Price	03/2019
6826	(83*10^113969+133)/9	113970	Robert Price	08/2021
6828	32226^3439+3439^32226	113966	Hans Havermann	02/2021
6829	(77*10^113963-149)/9	113964	Robert Price	03/2022
6830	78*10^113954-7	113956	Robert Price	10/2020
6831	2*10^113941+9	113942	Dmitry Domanov	11/2010
6832	10^113933+145897	113934	Patrick De Geest	02/2021
6835	(2^378478+1642)/2	113933	Stefano Morozzi	09/2020
6833	10^113933-8000000001	113933	Robert Price	11/2020
6834	10^113933-66167	113933	Patrick De Geest	02/2021
6836	2339662057597*10^113903+9	113916	Robert Price	03/2021
6837	4*10^113905+91	113906	Robert Price	08/2018
6838	10^113894+76609	113895	Patrick De Geest	02/2021
6840	10^113894-10000001	113894	Robert Price	09/2020
6839	10^113894-373947	113894	Patrick De Geest	02/2021
6841	33933^2270+2270^33933	113881	Hans Havermann	02/2021
6842	4*10^113874-21	113875	Robert Price	09/2018
6843	2^378272-16565	113872	Enzo Doria	04/2013
6844	2^378217-109075	113855	Enzo Doria	04/2014
6845	2^378198+67	113849	Lelio R Paula	03/2013
6846	2^378173-3249	113842	Yves Minet	12/2014
6847	(2^378155-5)/6597	113833	Lelio R Paula	03/2014
6848	2^378137+1334025	113831	Henri Lifchitz	10/2024
6849	92941#+(355049#)/(92941#)	113830	Makoto Morimoto	10/2017
6850	30030^6173+6173^30030	113829	Hans Havermann	01/2021
6851	2^378128-262977	113828	Enzo Doria	05/2014
6852	2^378123-113215	113827	Enzo Doria	07/2014
6853	6^146274-18893	113824	Enzo Doria	03/2013
6854	34596^1949+1949^34596	113815	Hans Havermann	02/2021
6855	2^378078+75	113813	Lelio R Paula	03/2013
6856	(28*10^113810+449)/9	113811	Robert Price	11/2021
6857	26273^21448+21448^26273	113799	Hans Havermann	02/2021
6858	2^377966+255255	113780	Paul Bourdelais	10/2021
6859	2^377940+63	113772	Lelio R Paula	03/2013
6860	2^377941-2785843	113772	Enzo Doria	04/2016
6861	(7*10^113757+11)/9	113757	Tyler Busby	01/2023
6862	2^377810+1875109	113733	Enzo Doria	09/2016
6863	2^377803-1838635	113731	Enzo Doria	05/2015
6864	2^377799+52223	113729	Yves Minet	08/2010
6865	(2^377791+3258)/2	113727	Stefano Morozzi	02/2021
6866	11^109190-270	113710	Enzo Doria	12/2012
6867	28206^10739+10739^28206	113698	Hans Havermann	01/2021
6868	7*10^113693+9	113694	Robert Price	09/2015
6869	13899^27442+27442^13899	113692	Norbert Schneider	12/2020
6870	(82*10^113681+161)/9	113682	Robert Price	10/2019
6871	26121^22478+22478^26121	113673	Hans Havermann	01/2021
6872	4*10^113658+49	113659	Robert Price	01/2019
6873	(10^113656+7)/40231/6439001	113645	Alfred Reich	06/2021
6874	(2*10^113631+529)/9	113631	Robert Price	01/2018
6875	2^377408-2798279	113612	Enzo Doria	04/2016
6876	(292^46336+1)/(292^256+1)	113605	Martin Hopf	12/2023
6877	13706^27459+27459^13706	113596	Norbert Schneider	12/2020
6878	5*10^113586+57	113587	Robert Price	12/2018
6879	(2^377242+2794)/2	113561	Stefano Morozzi	02/2021
6880	2^377222+93679	113556	Yves Minet	02/2011
6882	262147#+316847	113552	Makoto Morimoto	02/2016
6881	27172^15101+15101^27172	113552	Hans Havermann	01/2021
6883	(2^377131+2018)/2	113528	Stefano Morozzi	09/2020
6884	2^377026-458903	113497	Enzo Doria	04/2015
6885	(2^377014+2202)/2	113493	Stefano Morozzi	09/2020
6886	34791^1828+1828^34791	113488	Hans Havermann	02/2021
6887	(2^376967+258)/2	113479	Stefano Morozzi	09/2020
6888	(29*10^113468-17)/3	113469	Robert Price	09/2019
6889	35^73477-34^73477	113454	Robert Price	05/2012
6890	(14*10^113451-89)/3	113452	Robert Price	05/2020
6891	2^376790+27	113426	Lelio R Paula	03/2013
6892	2^376786-112701	113424	Enzo Doria	06/2014
6893	2^376731+21	113408	Lelio R Paula	03/2013
6894	9*10^113394-73	113395	Robert Price	01/2021
6895	29660^6651+6651^29660	113387	Hans Havermann	01/2021
6897	2^376634+1871245	113379	Enzo Doria	05/2016
6896	(4^188318+17)/3	113379	Robert Price	02/2017
6898	E(29532)/492842728006750534663978950979381235	113367	Thomas Ritschel	01/2021
6899	2^376576-344369	113361	Enzo Doria	07/2015
6900	2^376549-4543	113353	Yves Minet	03/2019
6901	(17*2^376526-1)/223	113345	Lelio R Paula	03/2014
6902	(27*2^376441-1)/811	113319	Lelio R Paula	03/2014
6903	(2^376350+3538)/2	113293	Stefano Morozzi	09/2020
6904	27265^14272+14272^27265	113273	Hans Havermann	02/2021
6905	32174^3315+3315^32174	113269	Hans Havermann	02/2021
6906	(2*10^113248+73)/3	113248	Robert Price	09/2020
6907	2^376128-21237	113226	Enzo Doria	06/2013
6908	5*10^113224-81	113225	Robert Price	01/2019
6909	10^113220+51409	113221	Patrick De Geest	02/2021
6911	10^113220-1000001	113220	Robert Price	08/2020
6910	10^113220-61779	113220	Patrick De Geest	02/2021
6912	(2^376102+1578)/2	113218	Stefano Morozzi	09/2020
6913	(2^375996+3102)/2	113186	Stefano Morozzi	09/2020
6914	37258^1091+1091^37258	113184	Hans Havermann	02/2021
6915	(94*10^113176+11)/3	113178	Robert Price	04/2020
6916	(46*10^113162+521)/9	113163	Robert Price	02/2019
6917	14*29^77375+17875	113155	Eric Chen	06/2025
6918	(2^375885+3614)/2	113153	Stefano Morozzi	09/2020
6919	(2^375873+2006)/2	113149	Stefano Morozzi	09/2020
6920	3*10^113137+23	113138	Robert Price	03/2022
6921	(8*10^113135-269)/9	113135	Robert Price	09/2021
6922	(2^375726+694)/2	113105	Stefano Morozzi	09/2020
6923	26050^21959+21959^26050	113100	Hans Havermann	02/2021
6924	2^375638-1787171	113079	Enzo Doria	03/2016
6925	(2^375563+2178)/2	113056	Stefano Morozzi	09/2020
6926	2^375537+4847	113048	Yves Minet	02/2011
6927	(17^91837+16^91837)/33	113000	Robert Price	08/2013
6928	5F(270343)(F(270343)+1)+1	112997	Serge Batalov	04/2015
6929	2^375350-3221	112992	Yves Minet	07/2011
6930	(13*2^375306+1)/7	112979	Lelio R Paula	03/2014
6931	2^375305+76757	112979	Enzo Doria	05/2016
6932	2^375258+1874989	112964	Enzo Doria	07/2016
6933	(29^77237-1)/28	112950	Robert Price	04/2012
6934	26620^17483+17483^26620	112939	Hans Havermann	01/2021
6935	2^375154+74959	112933	Enzo Doria	04/2016
6936	(266*10^112930-17)/3	112932	Robert Price	07/2020
6937	(2^375134+778)/2	112927	Stefano Morozzi	09/2020
6938	(85*10^112919+293)/9	112920	Robert Price	12/2019
6939	29412^6899+6899^29412	112907	Hans Havermann	02/2021
6940	(191*10^112903-17)/3	112905	Robert Price	11/2021
6941	(2^375022+1210)/2	112893	Stefano Morozzi	09/2020
6942	25992^22039+22039^25992	112889	Hans Havermann	02/2021
6943	2^374993-2787163	112885	Enzo Doria	11/2015
6944	(697*10^112869+23)/9	112871	Robert Price	04/2021
6945	(19*10^112851+377)/9	112852	Alfred Reich	11/2022
6946	30420^5111+5111^30420	112813	Hans Havermann	02/2021
6947	13699^27268+27268^13699	112800	Norbert Schneider	12/2020
6948	123^53970+2	112793	Lelio R Paula	06/2013
6949	12308*27^78796+23	112790	Eric Chen	07/2023
6950	28942^7887+7887^28942	112785	Hans Havermann	01/2021
6951	2^374640-4685	112778	Yves Minet	05/2019
6952	12^104501-11	112776	Riley Fisher	12/2023
6953	57290^93+93^57290	112775	Hans Havermann	01/2021
6954	115^54726-54726^115	112774	Norman Luhn	09/2024
6955	13608^27277-27277^13608	112758	Norbert Schneider	12/2022
6956	(2^374556+682)/2	112753	Stefano Morozzi	09/2020
6957	p(22852)#/2+512	112745	Robert Price	05/2017
6958	(11*10^112742-131)/3	112743	Robert Price	09/2018
6959	2^374441-21049	112718	Enzo Doria	06/2013
6960	(15056!^2+1)/(30113*454287444157)	112711	Michael Porter	09/2025
6961	4*10^112706-93	112707	Robert Price	07/2020
6962	(2^374321+1)/3	112682	H.&R. Lifchitz	12/2000
6963	(2^374213+1766)/2	112650	Stefano Morozzi	09/2020
6964	(2^374094+2674)/2	112614	Stefano Morozzi	09/2020
6965	(13^101089-1)/12	112607	Paul Bourdelais	03/2010
6966	3^236011-8828	112606	Enzo Doria	05/2014
6967	31854^3427+3427^31854	112602	Hans Havermann	02/2021
6968	(85*10^112530-373)/9	112531	Robert Price	05/2021
6969	(2^373748+1090)/2	112510	Stefano Morozzi	09/2020
6970	(2^373727+1806)/2	112503	Stefano Morozzi	01/2021
6971	27618^11821+11821^27618	112479	Hans Havermann	01/2021
6972	U(602921)/4823369	112479	Serge Batalov	07/2024
6973	26343^18580+18580^26343	112460	Hans Havermann	01/2021
6974	39^70666+2	112435	Lelio R Paula	11/2013
6975	(134*10^112400+7)/3	112402	Robert Price	02/2020
6976	(2^373365+326)/2	112394	Stefano Morozzi	09/2020
6977	(2^373350-7)/3	112390	Lelio R Paula	03/2014
6978	3^235532-235532	112378	Anonymous	09/2025
6979	2^373306-1840931	112377	Enzo Doria	06/2015
6980	8*10^112371-37	112372	Robert Price	03/2022
6981	(2^373262+270)/2	112363	Stefano Morozzi	09/2020
6982	6*10^112359-79	112360	Robert Price	03/2022
6983	34409^1842+1842^34409	112356	Hans Havermann	02/2021
6984	(142*10^112352-7)/9	112354	Robert Price	12/2019
6985	25580^24633+24633^25580	112336	Hans Havermann	01/2021
6986	2^373117+1872107	112320	Enzo Doria	05/2016
6987	(2^373083+2226)/2	112309	Stefano Morozzi	01/2021
6988	(35*10^112308+37)/9	112309	Robert Price	05/2022
6989	27963^10376+10376^27963	112301	Hans Havermann	01/2021
6990	2^373040+2792761	112297	Enzo Doria	03/2016
6991	(156^51203-1)/155	112293	Anonymous	06/2024
6992	EPrime(112280)	112280	Eric W. Weisstein	10/2010
6993	2^372950+7	112270	Lelio R Paula	03/2013
6994	2^372945+1872167	112268	Enzo Doria	05/2016
6995	36274^1243+1243^36274	112249	Hans Havermann	02/2021
6996	(55*10^112246+629)/9	112247	Robert Price	01/2022
6997	(2^372872+3798)/2	112246	Stefano Morozzi	02/2021
6998	25513^25060+25060^25513	112232	Hans Havermann	02/2021
6999	(53*10^112229-611)/9	112230	Robert Price	02/2022
7000	(2^372754+3094)/2	112210	Stefano Morozzi	09/2020

Find by discoverer :

PRP Records

Probable Primes Top 10000

(301969 PRPs in the top)