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	3^244461-10	116638	Tyler NeSmith	09/2022
6752	(2^387447+78557)/365	116631	Lelio R Paula	12/2014
6753	(2*10^116620+43)/9	116620	Serge Batalov	11/2022
6754	(19*10^116617+287)/9/12893	116614	Alfred Reich	11/2022
6755	(145*10^116610-1)/9	116612	Serge Batalov	12/2014
6756	(25*10^116601-331)/9	116602	Robert Price	08/2018
6757	25791^26428-26428^25791	116587	Frank Doornink	03/2024
6759	(17*2^387284-1)/59	116584	Lelio R Paula	04/2014
6758	(2^387284+3726)/2	116584	Stefano Morozzi	09/2020
6760	2^387211+111546435	116563	Paul Bourdelais	10/2021
6761	10^116557+987654321	116558	Robert Price	12/2019
6762	10^116557+9141	116558	Patrick De Geest	02/2020
6763	10^116557-609431	116557	Patrick De Geest	02/2020
6764	209^50234-50234^209	116551	Norman Luhn	09/2024
6765	(28*10^116546+41)/3	116547	Robert Price	07/2021
6766	(2^387123+1814)/2	116536	Stefano Morozzi	02/2021
6767	(2^387076+2046)/2	116522	Stefano Morozzi	09/2020
6768	(2^387073+2570)/2	116521	Stefano Morozzi	09/2020
6769	(7*10^116514-1)/3	116515	Robert Price	08/2022
6770	(26*32^77406-390071011)/31	116508	Eric Chen	11/2023
6771	28846^10931+10931^28846	116500	Hans Havermann	02/2021
6772	10^116496+3593037	116497	Paul Bourdelais	10/2021
6773	272^47851-47851^272	116497	Norman Luhn	09/2024
6774	(31*2^386968+1)/7	116490	Lelio R Paula	03/2014
6775	(944^39157+1)/945	116489	Jinyuan Wang	12/2024
6776	2^386947+1869143	116483	Enzo Doria	05/2016
6778	(30^78857-1)/29	116480	Robert Price	12/2011
6777	Phi(78857,5#)	116480	Henri Lifchitz	12/2025
6779	(2^386903-3)/5	116469	Lelio R Paula	03/2014
6780	28107^13892+13892^28107	116441	Hans Havermann	02/2021
6781	29110^9957+9957^29110	116386	Hans Havermann	02/2021
6782	26469^24838+24838^26469	116335	Hans Havermann	01/2021
6783	2^386389-1864783	116315	Enzo Doria	03/2016
6784	(8*32^77250-163)/31	116273	Eric Chen	11/2023
6785	(31*2^386231-1)/1711	116266	Lelio R Paula	03/2014
6786	297^47012+47012^297	116250	Norbert Schneider	07/2018
6787	(35*10^116223-341)/9	116224	Robert Price	08/2021
6788	(2^386087-5)/40959	116220	Lelio R Paula	03/2014
6789	(2^386054+714)/2	116214	Stefano Morozzi	09/2020
6790	(10^116201+7)/39623	116197	Alfred Reich	06/2021
6791	2^385969-823	116189	Yves Minet	05/2012
6792	57^66162+2	116173	Lelio R Paula	08/2013
6793	2^385854+75049	116154	Enzo Doria	04/2016
6794	(2^385832+2590)/2	116147	Stefano Morozzi	09/2020
6795	2^385775-109587	116130	Enzo Doria	04/2014
6796	(14*10^116112-101)/3	116113	Robert Price	02/2019
6797	Phi(236354,10)/24817171	116109	Makoto Kamada	08/2019
6798	3*10^116107+23	116108	Robert Price	03/2022
6799	28729^10990+10990^28729	116094	Hans Havermann	02/2021
6800	2^385622+71839	116084	Enzo Doria	04/2016
6802	2^385564+781	116067	Lelio R Paula	01/2012
6801	(2^385565+1562)/2	116067	Stefano Morozzi	09/2020
6803	(2^385563+378)/2	116066	Stefano Morozzi	02/2021
6804	(2^385557+2214)/2	116064	Stefano Morozzi	09/2020
6805	29431^8776+8776^29431	116056	Hans Havermann	01/2021
6806	(266*10^116024-17)/3	116026	Robert Price	07/2020
6807	30263^6820+6820^30263	116022	Hans Havermann	02/2021
6808	2^385410+71893	116020	Enzo Doria	04/2016
6809	38225^1084+1084^38225	116014	Hans Havermann	02/2021
6810	26548^23433+23433^26548	116011	Hans Havermann	02/2021
6811	Phi(183801,-9)	115960	Henri Lifchitz	12/2025
6812	12^107422-11	115928	Riley Fisher	12/2023
6813	(25*2^385091+1)/27	115924	Lelio R Paula	04/2014
6814	(11*10^115910-131)/3	115911	Robert Price	09/2018
6815	2^384953-111943	115883	Paul Bourdelais	02/2012
6816	43^70942-2	115882	Lelio R Paula	04/2014
6817	(94*10^115879-7)/3	115881	Robert Price	03/2020
6818	7*10^115863+3	115864	Robert Price	08/2015
6819	2^384834+93	115847	Donovan Johnson	07/2008
6820	2^384809+71297	115840	Enzo Doria	04/2016
6821	(55*10^115829+323)/9	115830	Robert Price	10/2021
6822	(7*2^384759-1)/5	115825	Lelio R Paula	04/2014
6823	31348^4951+4951^31348	115822	Hans Havermann	02/2021
6824	(793*10^115810+53)/9	115812	Robert Price	01/2022
6825	(71*10^115810-17)/9	115811	Ray Chandler	08/2011
6826	(97*10^115794-1)/3	115796	Serge Batalov	12/2014
6827	31115^5266+5266^31115	115794	Hans Havermann	02/2021
6828	2*10^115784-27	115785	Robert Price	05/2018
6829	10^115773+126739	115774	Patrick De Geest	04/2018
6831	10^115773-1000000001	115773	Robert Price	03/2018
6830	10^115773-396221	115773	Patrick De Geest	04/2018
6832	(2^384582+778)/2	115771	Stefano Morozzi	09/2020
6833	30537^6178+6178^30537	115762	Hans Havermann	01/2021
6834	2^384530+1874305	115756	Enzo Doria	06/2016
6835	(3*2^384524-1)/7631	115750	Lelio R Paula	03/2014
6836	28275^12406+12406^28275	115748	Hans Havermann	01/2021
6837	(44*10^115697-413)/9	115698	Robert Price	03/2019
6838	31408^4825+4825^31408	115692	Hans Havermann	02/2021
6839	(2^384317+1026)/2	115691	Stefano Morozzi	09/2020
6840	2^384312+81091	115690	Yves Minet	02/2010
6841	(2^384265+2150)/2	115675	Stefano Morozzi	09/2020
6842	(2^384246+2182)/2	115670	Stefano Morozzi	09/2020
6843	(4*10^115668-79)/3	115669	Robert Price	02/2018
6844	(2^384193+242)/2	115654	Stefano Morozzi	09/2020
6845	(266947#+1267)/(7^2*181)	115647	Makoto Morimoto	06/2019
6846	(266947#+273808)/(2109157)	115646	Makoto Morimoto	10/2017
6847	18^92125-92125^18	115642	Dylan Delgado	08/2019
6848	(25^82723+3^82723)/28	115641	Robert Price	09/2025
6849	3^242337-4042	115625	Enzo Doria	05/2014
6850	(17699*31^77516-29)/30	115608	Eric Chen	05/2024
6851	(2^383931+674)/2	115575	Stefano Morozzi	09/2020
6852	7*10^115561+79	115562	Robert Price	07/2019
6853	(2^383872+3046)/2	115557	Stefano Morozzi	09/2020
6854	(11*2^383859-13)/15	115553	Renaud Lifchitz	03/2011
6855	2^383780-3149	115530	Yves Minet	10/2014
6856	(41*10^115523-383)/9	115524	Robert Price	11/2018
6857	27316^16923+16923^27316	115506	Hans Havermann	02/2021
6858	(2^383618+618)/2	115481	Stefano Morozzi	09/2020
6859	2^383560-455	115464	Yves Minet	03/2012
6860	(2^383544+5)/3	115458	Lelio R Paula	03/2014
6861	(22*10^115454+119)/3	115455	Robert Price	04/2021
6862	89^59221-88^59221	115445	Robert Price	06/2015
6863	(7^136559-5^136559)/2	115406	Jon Grantham	08/2023
6864	2^383347+1869413	115399	Enzo Doria	05/2016
6865	(103*10^115366+17)/3	115368	Robert Price	08/2020
6866	(2^383232+750)/2	115365	Stefano Morozzi	09/2020
6867	(2^383130-7)/131793	115329	Lelio R Paula	03/2014
6868	(12^106859+1)/13	115320	Paul Bourdelais	02/2010
6869	29961^7060+7060^29961	115315	Hans Havermann	01/2021
6871	2^383039+1869509	115307	Enzo Doria	05/2016
6870	32918^3183+3183^32918	115307	Hans Havermann	01/2021
6872	(109^56597-1)/90183471012	115302	Paul Vanderveen	06/2025
6873	36964^1315+1315^36964	115288	Hans Havermann	02/2021
6874	(13*2^382968+1)/7	115286	Lelio R Paula	04/2014
6875	(22*10^115282+29)/3	115283	Robert Price	02/2021
6876	(2^382945+2046)/2	115278	Stefano Morozzi	09/2020
6877	(2^382789+3182)/2	115231	Stefano Morozzi	09/2020
6878	30416^6141+6141^30416	115224	Hans Havermann	02/2021
6879	6*10^115211+79	115212	Robert Price	09/2020
6880	(2^382722+3598)/2	115211	Stefano Morozzi	09/2020
6881	27987^13078+13078^27987	115210	Hans Havermann	02/2021
6882	(2^382699+2090)/2	115204	Stefano Morozzi	09/2020
6883	(22*10^115188-193)/9	115189	Robert Price	07/2022
6884	2^382633+73697	115185	Enzo Doria	04/2016
6885	2^382509-113593	115147	Enzo Doria	08/2014
6886	2^382502-2791721	115145	Enzo Doria	03/2016
6887	(2^382495+1274)/2	115143	Stefano Morozzi	01/2021
6888	2^382464+22741	115134	Enzo Doria	09/2023
6889	26752^20065+20065^26752	115099	Hans Havermann	02/2021
6890	26383^23008+23008^26383	115080	Hans Havermann	02/2021
6891	9^120590-120590	115073	Robert Price	03/2014
6892	28203^12016+12016^28203	115062	Hans Havermann	02/2021
6893	2^382198+9	115054	Lelio R Paula	03/2013
6894	18268*31^77131+22839	115035	Eric Chen	05/2024
6895	30101^6630+6630^30101	115032	Hans Havermann	01/2021
6896	(89*10^115030-179)/9	115031	Robert Price	12/2019
6897	25554^26089-26089^25554	114987	Frank Doornink	02/2024
6898	25142^26129-26129^25142	114979	Frank Doornink	12/2023
6899	(2^381935+2774)/2	114974	Stefano Morozzi	02/2021
6900	27300^16271+16271^27300	114972	Hans Havermann	02/2021
6901	(23*10^114962+7)/3	114963	Robert Price	05/2023
6902	2^381883-59197	114959	Enzo Doria	10/2015
6903	27423^15542+15542^27423	114944	Hans Havermann	02/2021
6904	(2^381820+1626)/2	114939	Stefano Morozzi	09/2020
6906	2^381806-4481	114936	Yves Minet	07/2011
6905	2^381808-1851507	114936	Enzo Doria	08/2015
6907	(2^381792+2502)/2	114931	Stefano Morozzi	09/2020
6908	2^381774-112373	114926	Enzo Doria	06/2014
6909	26341^22980+22980^26341	114883	Hans Havermann	01/2021
6910	(79^60539-1)/61747564999146	114867	Paul Vanderveen	05/2025
6911	2^381555-109051	114860	Enzo Doria	04/2014
6912	2^381551+213683	114859	Enzo Doria	09/2023
6913	2^381546-113501	114857	Enzo Doria	08/2014
6914	(7*10^114845-19)/3	114846	Robert Price	10/2020
6915	26675^20178+20178^26675	114833	Hans Havermann	02/2021
6916	(2^381436+1182)/2	114824	Stefano Morozzi	09/2020
6917	3^240644+16	114817	Robert Price	04/2020
6918	(13^114814)%(10^114814)	114814	Henri Lifchitz	05/2025
6919	2^381360-110429	114801	Enzo Doria	05/2014
6920	(17*10^114795+79)/3	114796	Robert Price	04/2019
6921	(66^63079+1)/67	114774	Paul Bourdelais	09/2017
6922	2^381252-115079	114769	Enzo Doria	06/2015
6923	(2^381251+3186)/2	114768	Stefano Morozzi	09/2020
6924	2^381209-29323	114756	Enzo Doria	07/2015
6925	2^381207-111546435	114755	Paul Bourdelais	10/2021
6926	569^41651-568^41651	114754	Jean-Louis Charton	11/2009
6927	2^381201+1873205	114753	Enzo Doria	06/2016
6929	(85*10^114737+293)/9	114738	Robert Price	12/2019
6930	(265*10^114736+17)/3	114738	Robert Price	03/2020
6928	379*10^114735+9	114738	Jason Yuen	01/2025
6931	(2^381062+2170)/2	114711	Stefano Morozzi	09/2020
6932	2^380974-112991	114685	Enzo Doria	07/2014
6933	37097^1234+1234^37097	114679	Hans Havermann	02/2021
6934	(26*10^114658-119)/3	114659	Robert Price	07/2023
6935	88^58949-87	114626	Norbert Schneider	11/2015
6936	(2^380773+662)/2	114624	Stefano Morozzi	09/2020
6937	Phi(155285,10)/242674820198201	114610	Makoto Kamada	02/2024
6938	(10^155285-1)(10^2389-1)(10^13-1)*11111/(10^31057-1)/(10^11945-1)/(10^65-1)/242674820198201	114610	Anonymous	04/2025
6939	29913^6782+6782^29913	114608	Hans Havermann	02/2021
6940	(331*10^114605-7)/9	114607	Robert Price	04/2022
6941	2^380700+91	114603	Lelio R Paula	03/2013
6942	(2^380632+2578)/2	114582	Stefano Morozzi	09/2020
6943	7*10^114577+27	114578	Robert Price	11/2020
6945	10^114575+3^114576	114576	Mike Oakes	09/2010
6944	10^114575+66561	114576	Patrick De Geest	02/2017
6946	10^114575-581081	114575	Patrick De Geest	02/2017
6947	2^380587-115315	114569	Enzo Doria	06/2015
6948	31874^3927+3927^31874	114558	Hans Havermann	02/2021
6949	2^380513-216925	114546	Enzo Doria	05/2014
6950	2^380451-1840087	114528	Enzo Doria	06/2015
6951	(2^380426+1510)/2	114520	Stefano Morozzi	09/2020
6952	(15*2^380388-1)/539	114507	Lelio R Paula	04/2014
6953	2^380279-461347	114476	Enzo Doria	07/2015
6954	(331*10^114454-7)/9	114456	Robert Price	04/2022
6955	27121^16590+16590^27121	114447	Hans Havermann	01/2021
6956	25966^25555+25555^25966	114445	Hans Havermann	01/2021
6957	(611*32^76029-53)/31	114437	Eric Chen	11/2023
6958	(11*10^114400+529)/9	114401	Robert Price	09/2021
6959	2^380021+1871147	114398	Enzo Doria	05/2016
6960	2^380005+1869707	114393	Enzo Doria	05/2016
6961	2^379958-113297	114379	Enzo Doria	07/2014
6962	(2^379897+1274)/2	114361	Stefano Morozzi	01/2021
6963	2^379881-109105	114356	Enzo Doria	04/2014
6964	(21*2^379857-1)/13	114349	Lelio R Paula	03/2014
6965	(4*10^114340+83)/3	114341	Robert Price	02/2018
6966	(26*10^114317-77)/3	114318	Robert Price	11/2019
6967	(4*10^114296+149)/9	114296	Robert Price	04/2018
6968	88^58773-87	114284	Norbert Schneider	11/2015
6969	27764^13065+13065^27764	114280	Hans Havermann	01/2021
6970	(132^53891-1)/131	114278	Anonymous	06/2024
6971	2^379529-2790283	114250	Enzo Doria	03/2016
6972	2^379522+1869115	114248	Enzo Doria	05/2016
6973	(145*10^114226-1)/9	114228	Serge Batalov	12/2014
6974	2^379317-115033	114186	Enzo Doria	06/2015
6975	(22*10^114178+47)/3	114179	Robert Price	06/2021
6976	(17*2^379246-1)/17407	114162	Lelio R Paula	03/2014
6977	(2^379192+226)/2	114148	Stefano Morozzi	09/2020
6978	(228^48407-1)/227	114139	Alexander Zhirkov	03/2023
6979	6*10^114091+23	114092	Robert Price	09/2020
6980	(4*10^114076+143)/3	114077	Robert Price	03/2018
6981	332*25^81584+12357	114053	Eric Chen	10/2023
6982	(2^378820+3226)/2	114036	Stefano Morozzi	01/2021
6983	(2^378754+2058)/2	114017	Stefano Morozzi	09/2020
6984	13643^27572-27572^13643	114008	Norbert Schneider	12/2022
6986	(46*10^113969+683)/9	113970	Robert Price	03/2019
6985	(83*10^113969+133)/9	113970	Robert Price	08/2021
6987	32226^3439+3439^32226	113966	Hans Havermann	02/2021
6988	(77*10^113963-149)/9	113964	Robert Price	03/2022
6989	78*10^113954-7	113956	Robert Price	10/2020
6990	2*10^113941+9	113942	Dmitry Domanov	11/2010
6991	10^113933+145897	113934	Patrick De Geest	02/2021
6994	(2^378478+1642)/2	113933	Stefano Morozzi	09/2020
6992	10^113933-8000000001	113933	Robert Price	11/2020
6993	10^113933-66167	113933	Patrick De Geest	02/2021
6995	2339662057597*10^113903+9	113916	Robert Price	03/2021
6997	4*10^113905+91	113906	Robert Price	08/2018
6996	Phi(256695,7)	113906	Henri Lifchitz	02/2026
6998	10^113894+76609	113895	Patrick De Geest	02/2021
7000	10^113894-10000001	113894	Robert Price	09/2020
6999	10^113894-373947	113894	Patrick De Geest	02/2021

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Probable Primes Top 10000

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