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	2^389478+43	117245	Lelio R Paula	03/2013
6752	(298*10^117229-7)/3	117231	Robert Price	06/2020
6753	(2^389416+342)/2	117226	Stefano Morozzi	01/2021
6754	(29*2^389351-1)/9	117207	Lelio R Paula	04/2014
6755	5*10^117205+23	117206	Robert Price	03/2019
6756	(2^389341-7)/3865	117200	Lelio R Paula	03/2014
6757	27272^19827+19827^27272	117195	Hans Havermann	01/2021
6758	(2^389276+2650)/2	117184	Stefano Morozzi	09/2020
6759	(844*10^117175-7)/9	117177	Robert Price	05/2021
6760	10^117142+209223	117143	Patrick De Geest	04/2018
6762	10^117142-1000000001	117142	Robert Price	03/2018
6761	10^117142-966057	117142	Patrick De Geest	04/2018
6763	10^117135+360577	117136	Patrick De Geest	07/2018
6764	10^117135-401	117135	Robert Price	01/2018
6765	26415^26488-26488^26415	117126	Norbert Schneider	05/2021
6766	4*10^117123+79	117124	Robert Price	08/2018
6767	2^389033-12797413	117111	Enzo Doria	04/2016
6768	(2^388987+2634)/2	117097	Stefano Morozzi	09/2020
6769	2^388960-109505	117089	Enzo Doria	04/2014
6770	7*10^117082-57	117083	Robert Price	06/2020
6771	791^40398-40398^791	117081	Norman Luhn	09/2024
6772	(2^388928-5)/569	117077	Lelio R Paula	03/2014
6773	2^388888-1529	117067	Yves Minet	01/2013
6774	10^117059+28879	117060	Patrick De Geest	05/2016
6775	(10^117059-71)/1	117059	Serge Batalov	12/2014
6776	(2^388854+3630)/2	117057	Stefano Morozzi	09/2020
6777	(2^388842+2098)/2	117053	Stefano Morozzi	09/2020
6778	(2^388789+3150)/2	117037	Stefano Morozzi	09/2020
6779	(2^388748+378)/2	117025	Stefano Morozzi	02/2021
6780	(693^41189-1)/692	117005	Michael Stocker	05/2020
6781	(26*10^116999-503)/9	117000	Robert Price	07/2018
6782	20^89917-21	116985	Anonymous	09/2024
6783	(2^388609+1554)/2	116983	Stefano Morozzi	09/2020
6784	38496^1093+1093^38496	116975	Hans Havermann	02/2021
6785	3^245154-6256	116969	Enzo Doria	05/2014
6786	5*10^116966-43	116967	Robert Price	01/2019
6787	(748^40699-1)/747	116963	Tom Wu	08/2025
6788	2^388536-113495	116961	Enzo Doria	08/2014
6789	(2^388512+382)/2	116954	Stefano Morozzi	02/2021
6790	(8*32^77701+271)/31	116952	Eric Chen	11/2023
6791	2^388469-43	116941	Lelio R Paula	03/2013
6792	27417^18416+18416^27417	116939	Hans Havermann	02/2021
6793	(2^388438+1842)/2	116932	Stefano Morozzi	02/2021
6794	(7*2^388372-1)/111	116911	Lelio R Paula	04/2014
6795	(7*2^388335-1)/25	116900	Lelio R Paula	04/2014
6796	2^388180+93	116854	Donovan Johnson	07/2008
6797	(2^388167+2510)/2	116850	Stefano Morozzi	09/2020
6798	(85*10^116842+293)/9	116843	Robert Price	12/2019
6799	35296^2043+2043^35296	116840	Hans Havermann	02/2021
6800	(2^388081+7)/1179	116821	Lelio R Paula	03/2014
6801	38633^1056+1056^38633	116814	Hans Havermann	02/2021
6802	2^387946-113261	116784	Enzo Doria	07/2014
6803	28*36^75009+305	116739	Eric Chen	12/2022
6804	28363^13056+13056^28363	116737	Hans Havermann	02/2021
6805	2^387745+75557	116723	Enzo Doria	04/2016
6806	(29*10^116719+313)/9	116720	Robert Price	04/2021
6807	29622^8699+8699^29622	116695	Hans Havermann	02/2021
6808	(206*10^116687-17)/9	116689	Robert Price	01/2020
6809	(7*10^116684+179)/3	116685	Robert Price	09/2018
6810	2^387554+71455	116666	Enzo Doria	04/2016
6811	(602*10^116647-71)/9	116649	Robert Price	12/2021
6812	3^244461-10	116638	Tyler NeSmith	09/2022
6813	(2^387447+78557)/365	116631	Lelio R Paula	12/2014
6814	(2*10^116620+43)/9	116620	Serge Batalov	11/2022
6815	(19*10^116617+287)/9/12893	116614	Alfred Reich	11/2022
6816	(145*10^116610-1)/9	116612	Serge Batalov	12/2014
6817	(25*10^116601-331)/9	116602	Robert Price	08/2018
6818	25791^26428-26428^25791	116587	Frank Doornink	03/2024
6820	(17*2^387284-1)/59	116584	Lelio R Paula	04/2014
6819	(2^387284+3726)/2	116584	Stefano Morozzi	09/2020
6821	2^387211+111546435	116563	Paul Bourdelais	10/2021
6822	10^116557+987654321	116558	Robert Price	12/2019
6823	10^116557+9141	116558	Patrick De Geest	02/2020
6824	10^116557-609431	116557	Patrick De Geest	02/2020
6825	209^50234-50234^209	116551	Norman Luhn	09/2024
6826	(28*10^116546+41)/3	116547	Robert Price	07/2021
6827	(2^387123+1814)/2	116536	Stefano Morozzi	02/2021
6828	(2^387076+2046)/2	116522	Stefano Morozzi	09/2020
6829	(2^387073+2570)/2	116521	Stefano Morozzi	09/2020
6830	(7*10^116514-1)/3	116515	Robert Price	08/2022
6831	(26*32^77406-390071011)/31	116508	Eric Chen	11/2023
6832	28846^10931+10931^28846	116500	Hans Havermann	02/2021
6833	10^116496+3593037	116497	Paul Bourdelais	10/2021
6834	272^47851-47851^272	116497	Norman Luhn	09/2024
6835	(31*2^386968+1)/7	116490	Lelio R Paula	03/2014
6836	(944^39157+1)/945	116489	Jinyuan Wang	12/2024
6837	998^38840+997	116487	Alfred Reich	03/2026
6838	2^386947+1869143	116483	Enzo Doria	05/2016
6840	(30^78857-1)/29	116480	Robert Price	12/2011
6839	Phi(78857,5#)	116480	Henri Lifchitz	12/2025
6841	(2^386903-3)/5	116469	Lelio R Paula	03/2014
6842	28107^13892+13892^28107	116441	Hans Havermann	02/2021
6843	29110^9957+9957^29110	116386	Hans Havermann	02/2021
6844	26469^24838+24838^26469	116335	Hans Havermann	01/2021
6845	2^386389-1864783	116315	Enzo Doria	03/2016
6846	993^38799+992	116279	Alfred Reich	03/2026
6847	(8*32^77250-163)/31	116273	Eric Chen	11/2023
6848	(31*2^386231-1)/1711	116266	Lelio R Paula	03/2014
6849	297^47012+47012^297	116250	Norbert Schneider	07/2018
6850	(35*10^116223-341)/9	116224	Robert Price	08/2021
6851	(2^386087-5)/40959	116220	Lelio R Paula	03/2014
6852	(2^386054+714)/2	116214	Stefano Morozzi	09/2020
6853	(10^116201+7)/39623	116197	Alfred Reich	06/2021
6854	2^385969-823	116189	Yves Minet	05/2012
6855	57^66162+2	116173	Lelio R Paula	08/2013
6856	2^385854+75049	116154	Enzo Doria	04/2016
6857	(2^385832+2590)/2	116147	Stefano Morozzi	09/2020
6858	2^385775-109587	116130	Enzo Doria	04/2014
6859	(14*10^116112-101)/3	116113	Robert Price	02/2019
6860	Phi(236354,10)/24817171	116109	Makoto Kamada	08/2019
6861	3*10^116107+23	116108	Robert Price	03/2022
6862	28729^10990+10990^28729	116094	Hans Havermann	02/2021
6863	2^385622+71839	116084	Enzo Doria	04/2016
6865	2^385564+781	116067	Lelio R Paula	01/2012
6864	(2^385565+1562)/2	116067	Stefano Morozzi	09/2020
6866	(2^385563+378)/2	116066	Stefano Morozzi	02/2021
6867	(2^385557+2214)/2	116064	Stefano Morozzi	09/2020
6868	29431^8776+8776^29431	116056	Hans Havermann	01/2021
6869	(266*10^116024-17)/3	116026	Robert Price	07/2020
6870	30263^6820+6820^30263	116022	Hans Havermann	02/2021
6871	2^385410+71893	116020	Enzo Doria	04/2016
6872	38225^1084+1084^38225	116014	Hans Havermann	02/2021
6873	26548^23433+23433^26548	116011	Hans Havermann	02/2021
6874	Phi(183801,-9)	115960	Henri Lifchitz	12/2025
6875	12^107422-11	115928	Riley Fisher	12/2023
6876	(25*2^385091+1)/27	115924	Lelio R Paula	04/2014
6877	(11*10^115910-131)/3	115911	Robert Price	09/2018
6878	2^384953-111943	115883	Paul Bourdelais	02/2012
6879	43^70942-2	115882	Lelio R Paula	04/2014
6880	(94*10^115879-7)/3	115881	Robert Price	03/2020
6881	7*10^115863+3	115864	Robert Price	08/2015
6882	2^384834+93	115847	Donovan Johnson	07/2008
6883	2^384809+71297	115840	Enzo Doria	04/2016
6884	(55*10^115829+323)/9	115830	Robert Price	10/2021
6885	(7*2^384759-1)/5	115825	Lelio R Paula	04/2014
6886	31348^4951+4951^31348	115822	Hans Havermann	02/2021
6887	(793*10^115810+53)/9	115812	Robert Price	01/2022
6888	(71*10^115810-17)/9	115811	Ray Chandler	08/2011
6889	(97*10^115794-1)/3	115796	Serge Batalov	12/2014
6890	31115^5266+5266^31115	115794	Hans Havermann	02/2021
6891	2*10^115784-27	115785	Robert Price	05/2018
6892	10^115773+126739	115774	Patrick De Geest	04/2018
6894	10^115773-1000000001	115773	Robert Price	03/2018
6893	10^115773-396221	115773	Patrick De Geest	04/2018
6895	(2^384582+778)/2	115771	Stefano Morozzi	09/2020
6896	30537^6178+6178^30537	115762	Hans Havermann	01/2021
6897	2^384530+1874305	115756	Enzo Doria	06/2016
6898	(3*2^384524-1)/7631	115750	Lelio R Paula	03/2014
6899	28275^12406+12406^28275	115748	Hans Havermann	01/2021
6900	(44*10^115697-413)/9	115698	Robert Price	03/2019
6901	31408^4825+4825^31408	115692	Hans Havermann	02/2021
6902	(2^384317+1026)/2	115691	Stefano Morozzi	09/2020
6903	2^384312+81091	115690	Yves Minet	02/2010
6904	(2^384265+2150)/2	115675	Stefano Morozzi	09/2020
6905	(2^384246+2182)/2	115670	Stefano Morozzi	09/2020
6906	(4*10^115668-79)/3	115669	Robert Price	02/2018
6907	(2^384193+242)/2	115654	Stefano Morozzi	09/2020
6908	994^38584+993	115652	Alfred Reich	03/2026
6909	(266947#+1267)/(7^2*181)	115647	Makoto Morimoto	06/2019
6910	(266947#+273808)/(2109157)	115646	Makoto Morimoto	10/2017
6911	18^92125-92125^18	115642	Dylan Delgado	08/2019
6912	(25^82723+3^82723)/28	115641	Robert Price	09/2025
6913	3^242337-4042	115625	Enzo Doria	05/2014
6914	(17699*31^77516-29)/30	115608	Eric Chen	05/2024
6915	(2^383931+674)/2	115575	Stefano Morozzi	09/2020
6916	7*10^115561+79	115562	Robert Price	07/2019
6917	(2^383872+3046)/2	115557	Stefano Morozzi	09/2020
6918	(11*2^383859-13)/15	115553	Renaud Lifchitz	03/2011
6919	2^383780-3149	115530	Yves Minet	10/2014
6920	(41*10^115523-383)/9	115524	Robert Price	11/2018
6921	27316^16923+16923^27316	115506	Hans Havermann	02/2021
6922	(2^383618+618)/2	115481	Stefano Morozzi	09/2020
6923	2^383560-455	115464	Yves Minet	03/2012
6924	(2^383544+5)/3	115458	Lelio R Paula	03/2014
6925	(22*10^115454+119)/3	115455	Robert Price	04/2021
6926	89^59221-88^59221	115445	Robert Price	06/2015
6927	(7^136559-5^136559)/2	115406	Jon Grantham	08/2023
6928	2^383347+1869413	115399	Enzo Doria	05/2016
6929	(103*10^115366+17)/3	115368	Robert Price	08/2020
6930	(2^383232+750)/2	115365	Stefano Morozzi	09/2020
6931	(2^383130-7)/131793	115329	Lelio R Paula	03/2014
6932	(12^106859+1)/13	115320	Paul Bourdelais	02/2010
6933	29961^7060+7060^29961	115315	Hans Havermann	01/2021
6935	2^383039+1869509	115307	Enzo Doria	05/2016
6934	32918^3183+3183^32918	115307	Hans Havermann	01/2021
6936	(109^56597-1)/90183471012	115302	Paul Vanderveen	06/2025
6937	36964^1315+1315^36964	115288	Hans Havermann	02/2021
6938	(13*2^382968+1)/7	115286	Lelio R Paula	04/2014
6939	(22*10^115282+29)/3	115283	Robert Price	02/2021
6940	(2^382945+2046)/2	115278	Stefano Morozzi	09/2020
6941	(2^382789+3182)/2	115231	Stefano Morozzi	09/2020
6942	30416^6141+6141^30416	115224	Hans Havermann	02/2021
6943	6*10^115211+79	115212	Robert Price	09/2020
6944	(2^382722+3598)/2	115211	Stefano Morozzi	09/2020
6945	27987^13078+13078^27987	115210	Hans Havermann	02/2021
6946	(2^382699+2090)/2	115204	Stefano Morozzi	09/2020
6947	(22*10^115188-193)/9	115189	Robert Price	07/2022
6948	2^382633+73697	115185	Enzo Doria	04/2016
6949	2^382509-113593	115147	Enzo Doria	08/2014
6950	2^382502-2791721	115145	Enzo Doria	03/2016
6951	(2^382495+1274)/2	115143	Stefano Morozzi	01/2021
6952	2^382464+22741	115134	Enzo Doria	09/2023
6953	26752^20065+20065^26752	115099	Hans Havermann	02/2021
6954	26383^23008+23008^26383	115080	Hans Havermann	02/2021
6955	9^120590-120590	115073	Robert Price	03/2014
6956	28203^12016+12016^28203	115062	Hans Havermann	02/2021
6957	2^382198+9	115054	Lelio R Paula	03/2013
6958	18268*31^77131+22839	115035	Eric Chen	05/2024
6959	30101^6630+6630^30101	115032	Hans Havermann	01/2021
6960	(89*10^115030-179)/9	115031	Robert Price	12/2019
6961	25554^26089-26089^25554	114987	Frank Doornink	02/2024
6962	25142^26129-26129^25142	114979	Frank Doornink	12/2023
6963	(2^381935+2774)/2	114974	Stefano Morozzi	02/2021
6964	27300^16271+16271^27300	114972	Hans Havermann	02/2021
6965	(23*10^114962+7)/3	114963	Robert Price	05/2023
6966	2^381883-59197	114959	Enzo Doria	10/2015
6967	27423^15542+15542^27423	114944	Hans Havermann	02/2021
6968	(2^381820+1626)/2	114939	Stefano Morozzi	09/2020
6970	2^381806-4481	114936	Yves Minet	07/2011
6969	2^381808-1851507	114936	Enzo Doria	08/2015
6971	(2^381792+2502)/2	114931	Stefano Morozzi	09/2020
6972	2^381774-112373	114926	Enzo Doria	06/2014
6973	26341^22980+22980^26341	114883	Hans Havermann	01/2021
6974	(79^60539-1)/61747564999146	114867	Paul Vanderveen	05/2025
6975	2^381555-109051	114860	Enzo Doria	04/2014
6976	2^381551+213683	114859	Enzo Doria	09/2023
6977	2^381546-113501	114857	Enzo Doria	08/2014
6978	(7*10^114845-19)/3	114846	Robert Price	10/2020
6979	26675^20178+20178^26675	114833	Hans Havermann	02/2021
6980	(2^381436+1182)/2	114824	Stefano Morozzi	09/2020
6981	3^240644+16	114817	Robert Price	04/2020
6982	(13^114814)%(10^114814)	114814	Henri Lifchitz	05/2025
6983	2^381360-110429	114801	Enzo Doria	05/2014
6984	(17*10^114795+79)/3	114796	Robert Price	04/2019
6985	(66^63079+1)/67	114774	Paul Bourdelais	09/2017
6986	2^381252-115079	114769	Enzo Doria	06/2015
6987	(2^381251+3186)/2	114768	Stefano Morozzi	09/2020
6988	2^381209-29323	114756	Enzo Doria	07/2015
6989	2^381207-111546435	114755	Paul Bourdelais	10/2021
6990	569^41651-568^41651	114754	Jean-Louis Charton	11/2009
6991	2^381201+1873205	114753	Enzo Doria	06/2016
6993	(85*10^114737+293)/9	114738	Robert Price	12/2019
6994	(265*10^114736+17)/3	114738	Robert Price	03/2020
6992	379*10^114735+9	114738	Jason Yuen	01/2025
6995	(2^381062+2170)/2	114711	Stefano Morozzi	09/2020
6996	2^380974-112991	114685	Enzo Doria	07/2014
6997	37097^1234+1234^37097	114679	Hans Havermann	02/2021
6998	(26*10^114658-119)/3	114659	Robert Price	07/2023
6999	88^58949-87	114626	Norbert Schneider	11/2015
7000	(2^380773+662)/2	114624	Stefano Morozzi	09/2020

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