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) !!!

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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 ?
6751	(2^387076+2046)/2	116522	Stefano Morozzi	09/2020
6752	(2^387073+2570)/2	116521	Stefano Morozzi	09/2020
6753	(7*10^116514-1)/3	116515	Robert Price	08/2022
6754	(26*32^77406-390071011)/31	116508	Eric Chen	11/2023
6755	28846^10931+10931^28846	116500	Hans Havermann	02/2021
6756	10^116496+3593037	116497	Paul Bourdelais	10/2021
6757	272^47851-47851^272	116497	Norman Luhn	09/2024
6758	(31*2^386968+1)/7	116490	Lelio R Paula	03/2014
6759	(944^39157+1)/945	116489	Jinyuan Wang	12/2024
6760	2^386947+1869143	116483	Enzo Doria	05/2016
6762	(30^78857-1)/29	116480	Robert Price	12/2011
6761	Phi(78857,5#)	116480	Henri Lifchitz	12/2025
6763	(2^386903-3)/5	116469	Lelio R Paula	03/2014
6764	28107^13892+13892^28107	116441	Hans Havermann	02/2021
6765	29110^9957+9957^29110	116386	Hans Havermann	02/2021
6766	26469^24838+24838^26469	116335	Hans Havermann	01/2021
6767	2^386389-1864783	116315	Enzo Doria	03/2016
6768	(8*32^77250-163)/31	116273	Eric Chen	11/2023
6769	(31*2^386231-1)/1711	116266	Lelio R Paula	03/2014
6770	297^47012+47012^297	116250	Norbert Schneider	07/2018
6771	(35*10^116223-341)/9	116224	Robert Price	08/2021
6772	(2^386087-5)/40959	116220	Lelio R Paula	03/2014
6773	(2^386054+714)/2	116214	Stefano Morozzi	09/2020
6774	(10^116201+7)/39623	116197	Alfred Reich	06/2021
6775	2^385969-823	116189	Yves Minet	05/2012
6776	57^66162+2	116173	Lelio R Paula	08/2013
6777	2^385854+75049	116154	Enzo Doria	04/2016
6778	(2^385832+2590)/2	116147	Stefano Morozzi	09/2020
6779	2^385775-109587	116130	Enzo Doria	04/2014
6780	(14*10^116112-101)/3	116113	Robert Price	02/2019
6781	Phi(236354,10)/24817171	116109	Makoto Kamada	08/2019
6782	3*10^116107+23	116108	Robert Price	03/2022
6783	28729^10990+10990^28729	116094	Hans Havermann	02/2021
6784	2^385622+71839	116084	Enzo Doria	04/2016
6786	2^385564+781	116067	Lelio R Paula	01/2012
6785	(2^385565+1562)/2	116067	Stefano Morozzi	09/2020
6787	(2^385563+378)/2	116066	Stefano Morozzi	02/2021
6788	(2^385557+2214)/2	116064	Stefano Morozzi	09/2020
6789	29431^8776+8776^29431	116056	Hans Havermann	01/2021
6790	(266*10^116024-17)/3	116026	Robert Price	07/2020
6791	30263^6820+6820^30263	116022	Hans Havermann	02/2021
6792	2^385410+71893	116020	Enzo Doria	04/2016
6793	38225^1084+1084^38225	116014	Hans Havermann	02/2021
6794	26548^23433+23433^26548	116011	Hans Havermann	02/2021
6795	Phi(183801,-9)	115960	Henri Lifchitz	12/2025
6796	12^107422-11	115928	Riley Fisher	12/2023
6797	(25*2^385091+1)/27	115924	Lelio R Paula	04/2014
6798	(11*10^115910-131)/3	115911	Robert Price	09/2018
6799	2^384953-111943	115883	Paul Bourdelais	02/2012
6800	43^70942-2	115882	Lelio R Paula	04/2014
6801	(94*10^115879-7)/3	115881	Robert Price	03/2020
6802	7*10^115863+3	115864	Robert Price	08/2015
6803	2^384834+93	115847	Donovan Johnson	07/2008
6804	2^384809+71297	115840	Enzo Doria	04/2016
6805	(55*10^115829+323)/9	115830	Robert Price	10/2021
6806	(7*2^384759-1)/5	115825	Lelio R Paula	04/2014
6807	31348^4951+4951^31348	115822	Hans Havermann	02/2021
6808	(793*10^115810+53)/9	115812	Robert Price	01/2022
6809	(71*10^115810-17)/9	115811	Ray Chandler	08/2011
6810	(97*10^115794-1)/3	115796	Serge Batalov	12/2014
6811	31115^5266+5266^31115	115794	Hans Havermann	02/2021
6812	2*10^115784-27	115785	Robert Price	05/2018
6813	10^115773+126739	115774	Patrick De Geest	04/2018
6815	10^115773-1000000001	115773	Robert Price	03/2018
6814	10^115773-396221	115773	Patrick De Geest	04/2018
6816	(2^384582+778)/2	115771	Stefano Morozzi	09/2020
6817	30537^6178+6178^30537	115762	Hans Havermann	01/2021
6818	2^384530+1874305	115756	Enzo Doria	06/2016
6819	(3*2^384524-1)/7631	115750	Lelio R Paula	03/2014
6820	28275^12406+12406^28275	115748	Hans Havermann	01/2021
6821	(44*10^115697-413)/9	115698	Robert Price	03/2019
6822	31408^4825+4825^31408	115692	Hans Havermann	02/2021
6823	(2^384317+1026)/2	115691	Stefano Morozzi	09/2020
6824	2^384312+81091	115690	Yves Minet	02/2010
6825	(2^384265+2150)/2	115675	Stefano Morozzi	09/2020
6826	(2^384246+2182)/2	115670	Stefano Morozzi	09/2020
6827	(4*10^115668-79)/3	115669	Robert Price	02/2018
6828	(2^384193+242)/2	115654	Stefano Morozzi	09/2020
6829	(266947#+1267)/(7^2*181)	115647	Makoto Morimoto	06/2019
6830	(266947#+273808)/(2109157)	115646	Makoto Morimoto	10/2017
6831	18^92125-92125^18	115642	Dylan Delgado	08/2019
6832	(25^82723+3^82723)/28	115641	Robert Price	09/2025
6833	3^242337-4042	115625	Enzo Doria	05/2014
6834	(17699*31^77516-29)/30	115608	Eric Chen	05/2024
6835	(2^383931+674)/2	115575	Stefano Morozzi	09/2020
6836	7*10^115561+79	115562	Robert Price	07/2019
6837	(2^383872+3046)/2	115557	Stefano Morozzi	09/2020
6838	(11*2^383859-13)/15	115553	Renaud Lifchitz	03/2011
6839	2^383780-3149	115530	Yves Minet	10/2014
6840	(41*10^115523-383)/9	115524	Robert Price	11/2018
6841	27316^16923+16923^27316	115506	Hans Havermann	02/2021
6842	(2^383618+618)/2	115481	Stefano Morozzi	09/2020
6843	2^383560-455	115464	Yves Minet	03/2012
6844	(2^383544+5)/3	115458	Lelio R Paula	03/2014
6845	(22*10^115454+119)/3	115455	Robert Price	04/2021
6846	89^59221-88^59221	115445	Robert Price	06/2015
6847	(7^136559-5^136559)/2	115406	Jon Grantham	08/2023
6848	2^383347+1869413	115399	Enzo Doria	05/2016
6849	(103*10^115366+17)/3	115368	Robert Price	08/2020
6850	(2^383232+750)/2	115365	Stefano Morozzi	09/2020
6851	(2^383130-7)/131793	115329	Lelio R Paula	03/2014
6852	(12^106859+1)/13	115320	Paul Bourdelais	02/2010
6853	29961^7060+7060^29961	115315	Hans Havermann	01/2021
6855	2^383039+1869509	115307	Enzo Doria	05/2016
6854	32918^3183+3183^32918	115307	Hans Havermann	01/2021
6856	(109^56597-1)/90183471012	115302	Paul Vanderveen	06/2025
6857	36964^1315+1315^36964	115288	Hans Havermann	02/2021
6858	(13*2^382968+1)/7	115286	Lelio R Paula	04/2014
6859	(22*10^115282+29)/3	115283	Robert Price	02/2021
6860	(2^382945+2046)/2	115278	Stefano Morozzi	09/2020
6861	(2^382789+3182)/2	115231	Stefano Morozzi	09/2020
6862	30416^6141+6141^30416	115224	Hans Havermann	02/2021
6863	6*10^115211+79	115212	Robert Price	09/2020
6864	(2^382722+3598)/2	115211	Stefano Morozzi	09/2020
6865	27987^13078+13078^27987	115210	Hans Havermann	02/2021
6866	(2^382699+2090)/2	115204	Stefano Morozzi	09/2020
6867	(22*10^115188-193)/9	115189	Robert Price	07/2022
6868	2^382633+73697	115185	Enzo Doria	04/2016
6869	2^382509-113593	115147	Enzo Doria	08/2014
6870	2^382502-2791721	115145	Enzo Doria	03/2016
6871	(2^382495+1274)/2	115143	Stefano Morozzi	01/2021
6872	2^382464+22741	115134	Enzo Doria	09/2023
6873	26752^20065+20065^26752	115099	Hans Havermann	02/2021
6874	26383^23008+23008^26383	115080	Hans Havermann	02/2021
6875	9^120590-120590	115073	Robert Price	03/2014
6876	28203^12016+12016^28203	115062	Hans Havermann	02/2021
6877	2^382198+9	115054	Lelio R Paula	03/2013
6878	18268*31^77131+22839	115035	Eric Chen	05/2024
6879	30101^6630+6630^30101	115032	Hans Havermann	01/2021
6880	(89*10^115030-179)/9	115031	Robert Price	12/2019
6881	25554^26089-26089^25554	114987	Frank Doornink	02/2024
6882	25142^26129-26129^25142	114979	Frank Doornink	12/2023
6883	(2^381935+2774)/2	114974	Stefano Morozzi	02/2021
6884	27300^16271+16271^27300	114972	Hans Havermann	02/2021
6885	(23*10^114962+7)/3	114963	Robert Price	05/2023
6886	2^381883-59197	114959	Enzo Doria	10/2015
6887	27423^15542+15542^27423	114944	Hans Havermann	02/2021
6888	(2^381820+1626)/2	114939	Stefano Morozzi	09/2020
6890	2^381806-4481	114936	Yves Minet	07/2011
6889	2^381808-1851507	114936	Enzo Doria	08/2015
6891	(2^381792+2502)/2	114931	Stefano Morozzi	09/2020
6892	2^381774-112373	114926	Enzo Doria	06/2014
6893	26341^22980+22980^26341	114883	Hans Havermann	01/2021
6894	(79^60539-1)/61747564999146	114867	Paul Vanderveen	05/2025
6895	2^381555-109051	114860	Enzo Doria	04/2014
6896	2^381551+213683	114859	Enzo Doria	09/2023
6897	2^381546-113501	114857	Enzo Doria	08/2014
6898	(7*10^114845-19)/3	114846	Robert Price	10/2020
6899	26675^20178+20178^26675	114833	Hans Havermann	02/2021
6900	(2^381436+1182)/2	114824	Stefano Morozzi	09/2020
6901	3^240644+16	114817	Robert Price	04/2020
6902	(13^114814)%(10^114814)	114814	Henri Lifchitz	05/2025
6903	2^381360-110429	114801	Enzo Doria	05/2014
6904	(17*10^114795+79)/3	114796	Robert Price	04/2019
6905	(66^63079+1)/67	114774	Paul Bourdelais	09/2017
6906	2^381252-115079	114769	Enzo Doria	06/2015
6907	(2^381251+3186)/2	114768	Stefano Morozzi	09/2020
6908	2^381209-29323	114756	Enzo Doria	07/2015
6909	2^381207-111546435	114755	Paul Bourdelais	10/2021
6910	569^41651-568^41651	114754	Jean-Louis Charton	11/2009
6911	2^381201+1873205	114753	Enzo Doria	06/2016
6913	(85*10^114737+293)/9	114738	Robert Price	12/2019
6914	(265*10^114736+17)/3	114738	Robert Price	03/2020
6912	379*10^114735+9	114738	Jason Yuen	01/2025
6915	(2^381062+2170)/2	114711	Stefano Morozzi	09/2020
6916	2^380974-112991	114685	Enzo Doria	07/2014
6917	37097^1234+1234^37097	114679	Hans Havermann	02/2021
6918	(26*10^114658-119)/3	114659	Robert Price	07/2023
6919	88^58949-87	114626	Norbert Schneider	11/2015
6920	(2^380773+662)/2	114624	Stefano Morozzi	09/2020
6921	Phi(155285,10)/242674820198201	114610	Makoto Kamada	02/2024
6922	(10^155285-1)(10^2389-1)(10^13-1)*11111/(10^31057-1)/(10^11945-1)/(10^65-1)/242674820198201	114610	Anonymous	04/2025
6923	29913^6782+6782^29913	114608	Hans Havermann	02/2021
6924	(331*10^114605-7)/9	114607	Robert Price	04/2022
6925	2^380700+91	114603	Lelio R Paula	03/2013
6926	(2^380632+2578)/2	114582	Stefano Morozzi	09/2020
6927	7*10^114577+27	114578	Robert Price	11/2020
6929	10^114575+3^114576	114576	Mike Oakes	09/2010
6928	10^114575+66561	114576	Patrick De Geest	02/2017
6930	10^114575-581081	114575	Patrick De Geest	02/2017
6931	2^380587-115315	114569	Enzo Doria	06/2015
6932	31874^3927+3927^31874	114558	Hans Havermann	02/2021
6933	2^380513-216925	114546	Enzo Doria	05/2014
6934	2^380451-1840087	114528	Enzo Doria	06/2015
6935	(2^380426+1510)/2	114520	Stefano Morozzi	09/2020
6936	(15*2^380388-1)/539	114507	Lelio R Paula	04/2014
6937	2^380279-461347	114476	Enzo Doria	07/2015
6938	(331*10^114454-7)/9	114456	Robert Price	04/2022
6939	27121^16590+16590^27121	114447	Hans Havermann	01/2021
6940	25966^25555+25555^25966	114445	Hans Havermann	01/2021
6941	(611*32^76029-53)/31	114437	Eric Chen	11/2023
6942	(11*10^114400+529)/9	114401	Robert Price	09/2021
6943	2^380021+1871147	114398	Enzo Doria	05/2016
6944	2^380005+1869707	114393	Enzo Doria	05/2016
6945	2^379958-113297	114379	Enzo Doria	07/2014
6946	(2^379897+1274)/2	114361	Stefano Morozzi	01/2021
6947	2^379881-109105	114356	Enzo Doria	04/2014
6948	(21*2^379857-1)/13	114349	Lelio R Paula	03/2014
6949	(4*10^114340+83)/3	114341	Robert Price	02/2018
6950	(26*10^114317-77)/3	114318	Robert Price	11/2019
6951	(4*10^114296+149)/9	114296	Robert Price	04/2018
6952	88^58773-87	114284	Norbert Schneider	11/2015
6953	27764^13065+13065^27764	114280	Hans Havermann	01/2021
6954	(132^53891-1)/131	114278	Anonymous	06/2024
6955	2^379529-2790283	114250	Enzo Doria	03/2016
6956	2^379522+1869115	114248	Enzo Doria	05/2016
6957	(145*10^114226-1)/9	114228	Serge Batalov	12/2014
6958	2^379317-115033	114186	Enzo Doria	06/2015
6959	(22*10^114178+47)/3	114179	Robert Price	06/2021
6960	(17*2^379246-1)/17407	114162	Lelio R Paula	03/2014
6961	(2^379192+226)/2	114148	Stefano Morozzi	09/2020
6962	(228^48407-1)/227	114139	Alexander Zhirkov	03/2023
6963	6*10^114091+23	114092	Robert Price	09/2020
6964	(4*10^114076+143)/3	114077	Robert Price	03/2018
6965	332*25^81584+12357	114053	Eric Chen	10/2023
6966	(2^378820+3226)/2	114036	Stefano Morozzi	01/2021
6967	(2^378754+2058)/2	114017	Stefano Morozzi	09/2020
6968	13643^27572-27572^13643	114008	Norbert Schneider	12/2022
6970	(46*10^113969+683)/9	113970	Robert Price	03/2019
6969	(83*10^113969+133)/9	113970	Robert Price	08/2021
6971	32226^3439+3439^32226	113966	Hans Havermann	02/2021
6972	(77*10^113963-149)/9	113964	Robert Price	03/2022
6973	78*10^113954-7	113956	Robert Price	10/2020
6974	2*10^113941+9	113942	Dmitry Domanov	11/2010
6975	10^113933+145897	113934	Patrick De Geest	02/2021
6978	(2^378478+1642)/2	113933	Stefano Morozzi	09/2020
6976	10^113933-8000000001	113933	Robert Price	11/2020
6977	10^113933-66167	113933	Patrick De Geest	02/2021
6979	2339662057597*10^113903+9	113916	Robert Price	03/2021
6980	4*10^113905+91	113906	Robert Price	08/2018
6981	10^113894+76609	113895	Patrick De Geest	02/2021
6983	10^113894-10000001	113894	Robert Price	09/2020
6982	10^113894-373947	113894	Patrick De Geest	02/2021
6984	33933^2270+2270^33933	113881	Hans Havermann	02/2021
6985	4*10^113874-21	113875	Robert Price	09/2018
6986	2^378272-16565	113872	Enzo Doria	04/2013
6987	2^378217-109075	113855	Enzo Doria	04/2014
6988	2^378198+67	113849	Lelio R Paula	03/2013
6989	2^378173-3249	113842	Yves Minet	12/2014
6990	(2^378155-5)/6597	113833	Lelio R Paula	03/2014
6991	2^378137+1334025	113831	Henri Lifchitz	10/2024
6992	92941#+(355049#)/(92941#)	113830	Makoto Morimoto	10/2017
6993	30030^6173+6173^30030	113829	Hans Havermann	01/2021
6994	2^378128-262977	113828	Enzo Doria	05/2014
6995	2^378123-113215	113827	Enzo Doria	07/2014
6996	6^146274-18893	113824	Enzo Doria	03/2013
6997	34596^1949+1949^34596	113815	Hans Havermann	02/2021
6998	2^378078+75	113813	Lelio R Paula	03/2013
6999	(28*10^113810+449)/9	113811	Robert Price	11/2021
7000	26273^21448+21448^26273	113799	Hans Havermann	02/2021

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Probable Primes Top 10000

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