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	31083^6122+6122^31083	117709	Hans Havermann	02/2021
6752	2^390960+1880881	117691	Enzo Doria	11/2016
6753	(71*10^117685+91)/9	117686	Robert Price	04/2022
6755	2^390897-1860553	117672	Enzo Doria	11/2015
6754	(61*10^117671+47)/9	117672	Robert Price	07/2022
6756	2^390889-115003	117670	Enzo Doria	06/2015
6757	12^109010+35	117642	Riley Fisher	08/2023
6758	2^390779-30337	117637	Paul Bourdelais	02/2012
6759	(2^390735+378)/2	117623	Stefano Morozzi	02/2021
6760	11^112916-780	117590	Enzo Doria	12/2012
6761	27641^17916+17916^27641	117564	Hans Havermann	02/2021
6762	27906^16321+16321^27906	117561	Hans Havermann	02/2021
6763	27294^20275+20275^27294	117555	Hans Havermann	02/2021
6764	(2^390473+1002)/2	117544	Stefano Morozzi	09/2020
6765	35912^1875+1875^35912	117541	Hans Havermann	02/2021
6766	(16^97613-5^97613)/11	117537	Robert Price	07/2013
6767	(2^390438+1774)/2	117534	Stefano Morozzi	01/2021
6768	(2^390418+1722)/2	117528	Stefano Morozzi	09/2020
6769	(2^390403+654)/2	117523	Stefano Morozzi	09/2020
6770	(2^390343+2246)/2	117505	Stefano Morozzi	01/2021
6771	28043^15478+15478^28043	117493	Hans Havermann	02/2021
6772	Phi(247237,3)	117487	Henri Lifchitz	12/2025
6773	(17*2^390272+1)/1983	117482	Lelio R Paula	04/2014
6774	37077^1474+1474^37077	117479	Hans Havermann	01/2021
6775	31^78759-30	117459	Theodore Burton	02/2007
6776	(2^390176+1222)/2	117455	Stefano Morozzi	09/2020
6777	(2^390133+1242)/2	117442	Stefano Morozzi	09/2020
6778	(2^390013+2634)/2	117406	Stefano Morozzi	09/2020
6779	3*10^117402+61	117403	Robert Price	09/2020
6780	2^389998+37	117402	Lelio R Paula	03/2013
6781	(2^389977+314)/2	117395	Stefano Morozzi	09/2020
6782	(2^389921+342)/2	117378	Stefano Morozzi	01/2021
6783	71830^43+43^71830	117333	Hans Havermann	01/2021
6784	(2^389768+1582)/2	117332	Stefano Morozzi	09/2020
6785	33802^2951+2951^33802	117292	Hans Havermann	02/2021
6786	(2^561185)%L(561185)	117281	Henri Lifchitz	05/2025
6787	26789^23866+23866^26789	117277	Hans Havermann	02/2021
6788	29^80192-1*80192^29	117273	Dylan Delgado	12/2019
6789	(101*10^117260+7)/9	117262	Robert Price	02/2022
6790	(13*10^117249+161)/3	117250	Robert Price	11/2018
6791	2^389478+43	117245	Lelio R Paula	03/2013
6792	(298*10^117229-7)/3	117231	Robert Price	06/2020
6793	(2^389416+342)/2	117226	Stefano Morozzi	01/2021
6794	(29*2^389351-1)/9	117207	Lelio R Paula	04/2014
6795	5*10^117205+23	117206	Robert Price	03/2019
6796	(2^389341-7)/3865	117200	Lelio R Paula	03/2014
6797	27272^19827+19827^27272	117195	Hans Havermann	01/2021
6798	(2^389276+2650)/2	117184	Stefano Morozzi	09/2020
6799	(844*10^117175-7)/9	117177	Robert Price	05/2021
6800	10^117142+209223	117143	Patrick De Geest	04/2018
6802	10^117142-1000000001	117142	Robert Price	03/2018
6801	10^117142-966057	117142	Patrick De Geest	04/2018
6803	10^117135+360577	117136	Patrick De Geest	07/2018
6804	10^117135-401	117135	Robert Price	01/2018
6805	26415^26488-26488^26415	117126	Norbert Schneider	05/2021
6806	4*10^117123+79	117124	Robert Price	08/2018
6807	2^389033-12797413	117111	Enzo Doria	04/2016
6808	(2^388987+2634)/2	117097	Stefano Morozzi	09/2020
6809	2^388960-109505	117089	Enzo Doria	04/2014
6810	7*10^117082-57	117083	Robert Price	06/2020
6811	791^40398-40398^791	117081	Norman Luhn	09/2024
6812	(2^388928-5)/569	117077	Lelio R Paula	03/2014
6813	2^388888-1529	117067	Yves Minet	01/2013
6814	10^117059+28879	117060	Patrick De Geest	05/2016
6815	(10^117059-71)/1	117059	Serge Batalov	12/2014
6816	(2^388854+3630)/2	117057	Stefano Morozzi	09/2020
6817	(2^388842+2098)/2	117053	Stefano Morozzi	09/2020
6818	(2^388789+3150)/2	117037	Stefano Morozzi	09/2020
6819	(2^388748+378)/2	117025	Stefano Morozzi	02/2021
6820	(693^41189-1)/692	117005	Michael Stocker	05/2020
6821	(26*10^116999-503)/9	117000	Robert Price	07/2018
6822	20^89917-21	116985	Anonymous	09/2024
6823	(2^388609+1554)/2	116983	Stefano Morozzi	09/2020
6824	38496^1093+1093^38496	116975	Hans Havermann	02/2021
6825	3^245154-6256	116969	Enzo Doria	05/2014
6826	5*10^116966-43	116967	Robert Price	01/2019
6827	(748^40699-1)/747	116963	Tom Wu	08/2025
6828	2^388536-113495	116961	Enzo Doria	08/2014
6829	(2^388512+382)/2	116954	Stefano Morozzi	02/2021
6830	(8*32^77701+271)/31	116952	Eric Chen	11/2023
6831	2^388469-43	116941	Lelio R Paula	03/2013
6832	27417^18416+18416^27417	116939	Hans Havermann	02/2021
6833	(2^388438+1842)/2	116932	Stefano Morozzi	02/2021
6834	(7*2^388372-1)/111	116911	Lelio R Paula	04/2014
6835	(7*2^388335-1)/25	116900	Lelio R Paula	04/2014
6836	2^388180+93	116854	Donovan Johnson	07/2008
6837	(2^388167+2510)/2	116850	Stefano Morozzi	09/2020
6838	(85*10^116842+293)/9	116843	Robert Price	12/2019
6839	35296^2043+2043^35296	116840	Hans Havermann	02/2021
6840	(2^388081+7)/1179	116821	Lelio R Paula	03/2014
6841	38633^1056+1056^38633	116814	Hans Havermann	02/2021
6842	2^387946-113261	116784	Enzo Doria	07/2014
6843	28*36^75009+305	116739	Eric Chen	12/2022
6844	28363^13056+13056^28363	116737	Hans Havermann	02/2021
6845	2^387745+75557	116723	Enzo Doria	04/2016
6846	(29*10^116719+313)/9	116720	Robert Price	04/2021
6847	29622^8699+8699^29622	116695	Hans Havermann	02/2021
6848	(206*10^116687-17)/9	116689	Robert Price	01/2020
6849	(7*10^116684+179)/3	116685	Robert Price	09/2018
6850	2^387554+71455	116666	Enzo Doria	04/2016
6851	(602*10^116647-71)/9	116649	Robert Price	12/2021
6852	3^244461-10	116638	Tyler NeSmith	09/2022
6853	(2^387447+78557)/365	116631	Lelio R Paula	12/2014
6854	(2*10^116620+43)/9	116620	Serge Batalov	11/2022
6855	(19*10^116617+287)/9/12893	116614	Alfred Reich	11/2022
6856	(145*10^116610-1)/9	116612	Serge Batalov	12/2014
6857	(25*10^116601-331)/9	116602	Robert Price	08/2018
6858	25791^26428-26428^25791	116587	Frank Doornink	03/2024
6860	(17*2^387284-1)/59	116584	Lelio R Paula	04/2014
6859	(2^387284+3726)/2	116584	Stefano Morozzi	09/2020
6861	2^387211+111546435	116563	Paul Bourdelais	10/2021
6862	10^116557+987654321	116558	Robert Price	12/2019
6863	10^116557+9141	116558	Patrick De Geest	02/2020
6864	10^116557-609431	116557	Patrick De Geest	02/2020
6865	209^50234-50234^209	116551	Norman Luhn	09/2024
6866	(28*10^116546+41)/3	116547	Robert Price	07/2021
6867	(2^387123+1814)/2	116536	Stefano Morozzi	02/2021
6868	(2^387076+2046)/2	116522	Stefano Morozzi	09/2020
6869	(2^387073+2570)/2	116521	Stefano Morozzi	09/2020
6870	(7*10^116514-1)/3	116515	Robert Price	08/2022
6871	(26*32^77406-390071011)/31	116508	Eric Chen	11/2023
6872	28846^10931+10931^28846	116500	Hans Havermann	02/2021
6873	10^116496+3593037	116497	Paul Bourdelais	10/2021
6874	272^47851-47851^272	116497	Norman Luhn	09/2024
6875	(31*2^386968+1)/7	116490	Lelio R Paula	03/2014
6876	(944^39157+1)/945	116489	Jinyuan Wang	12/2024
6877	998^38840+997	116487	Alfred Reich	03/2026
6878	2^386947+1869143	116483	Enzo Doria	05/2016
6880	(30^78857-1)/29	116480	Robert Price	12/2011
6879	Phi(78857,5#)	116480	Henri Lifchitz	12/2025
6881	(2^386903-3)/5	116469	Lelio R Paula	03/2014
6882	28107^13892+13892^28107	116441	Hans Havermann	02/2021
6883	29110^9957+9957^29110	116386	Hans Havermann	02/2021
6884	26469^24838+24838^26469	116335	Hans Havermann	01/2021
6885	2^386389-1864783	116315	Enzo Doria	03/2016
6886	993^38799+992	116279	Alfred Reich	03/2026
6887	(8*32^77250-163)/31	116273	Eric Chen	11/2023
6888	(31*2^386231-1)/1711	116266	Lelio R Paula	03/2014
6889	297^47012+47012^297	116250	Norbert Schneider	07/2018
6890	(35*10^116223-341)/9	116224	Robert Price	08/2021
6891	(2^386087-5)/40959	116220	Lelio R Paula	03/2014
6892	(2^386054+714)/2	116214	Stefano Morozzi	09/2020
6893	(10^116201+7)/39623	116197	Alfred Reich	06/2021
6894	2^385969-823	116189	Yves Minet	05/2012
6895	57^66162+2	116173	Lelio R Paula	08/2013
6896	2^385854+75049	116154	Enzo Doria	04/2016
6897	(2^385832+2590)/2	116147	Stefano Morozzi	09/2020
6898	2^385775-109587	116130	Enzo Doria	04/2014
6899	(14*10^116112-101)/3	116113	Robert Price	02/2019
6900	Phi(236354,10)/24817171	116109	Makoto Kamada	08/2019
6901	3*10^116107+23	116108	Robert Price	03/2022
6902	28729^10990+10990^28729	116094	Hans Havermann	02/2021
6903	2^385622+71839	116084	Enzo Doria	04/2016
6905	2^385564+781	116067	Lelio R Paula	01/2012
6904	(2^385565+1562)/2	116067	Stefano Morozzi	09/2020
6906	(2^385563+378)/2	116066	Stefano Morozzi	02/2021
6907	(2^385557+2214)/2	116064	Stefano Morozzi	09/2020
6908	29431^8776+8776^29431	116056	Hans Havermann	01/2021
6909	(266*10^116024-17)/3	116026	Robert Price	07/2020
6910	30263^6820+6820^30263	116022	Hans Havermann	02/2021
6911	2^385410+71893	116020	Enzo Doria	04/2016
6912	38225^1084+1084^38225	116014	Hans Havermann	02/2021
6913	26548^23433+23433^26548	116011	Hans Havermann	02/2021
6914	Phi(183801,-9)	115960	Henri Lifchitz	12/2025
6915	12^107422-11	115928	Riley Fisher	12/2023
6916	(25*2^385091+1)/27	115924	Lelio R Paula	04/2014
6917	(11*10^115910-131)/3	115911	Robert Price	09/2018
6918	2^384953-111943	115883	Paul Bourdelais	02/2012
6919	43^70942-2	115882	Lelio R Paula	04/2014
6920	(94*10^115879-7)/3	115881	Robert Price	03/2020
6921	7*10^115863+3	115864	Robert Price	08/2015
6922	2^384834+93	115847	Donovan Johnson	07/2008
6923	2^384809+71297	115840	Enzo Doria	04/2016
6924	(55*10^115829+323)/9	115830	Robert Price	10/2021
6925	(7*2^384759-1)/5	115825	Lelio R Paula	04/2014
6926	31348^4951+4951^31348	115822	Hans Havermann	02/2021
6927	(793*10^115810+53)/9	115812	Robert Price	01/2022
6928	(71*10^115810-17)/9	115811	Ray Chandler	08/2011
6929	(97*10^115794-1)/3	115796	Serge Batalov	12/2014
6930	31115^5266+5266^31115	115794	Hans Havermann	02/2021
6931	2*10^115784-27	115785	Robert Price	05/2018
6932	10^115773+126739	115774	Patrick De Geest	04/2018
6934	10^115773-1000000001	115773	Robert Price	03/2018
6933	10^115773-396221	115773	Patrick De Geest	04/2018
6935	(2^384582+778)/2	115771	Stefano Morozzi	09/2020
6936	30537^6178+6178^30537	115762	Hans Havermann	01/2021
6937	2^384530+1874305	115756	Enzo Doria	06/2016
6938	(3*2^384524-1)/7631	115750	Lelio R Paula	03/2014
6939	28275^12406+12406^28275	115748	Hans Havermann	01/2021
6940	(44*10^115697-413)/9	115698	Robert Price	03/2019
6941	31408^4825+4825^31408	115692	Hans Havermann	02/2021
6942	(2^384317+1026)/2	115691	Stefano Morozzi	09/2020
6943	2^384312+81091	115690	Yves Minet	02/2010
6944	(2^384265+2150)/2	115675	Stefano Morozzi	09/2020
6945	(2^384246+2182)/2	115670	Stefano Morozzi	09/2020
6946	(4*10^115668-79)/3	115669	Robert Price	02/2018
6947	(2^384193+242)/2	115654	Stefano Morozzi	09/2020
6948	994^38584+993	115652	Alfred Reich	03/2026
6949	(266947#+1267)/(7^2*181)	115647	Makoto Morimoto	06/2019
6950	(266947#+273808)/(2109157)	115646	Makoto Morimoto	10/2017
6951	18^92125-92125^18	115642	Dylan Delgado	08/2019
6952	(25^82723+3^82723)/28	115641	Robert Price	09/2025
6953	3^242337-4042	115625	Enzo Doria	05/2014
6954	(17699*31^77516-29)/30	115608	Eric Chen	05/2024
6955	(2^383931+674)/2	115575	Stefano Morozzi	09/2020
6956	7*10^115561+79	115562	Robert Price	07/2019
6957	(2^383872+3046)/2	115557	Stefano Morozzi	09/2020
6958	(11*2^383859-13)/15	115553	Renaud Lifchitz	03/2011
6959	2^383780-3149	115530	Yves Minet	10/2014
6960	(41*10^115523-383)/9	115524	Robert Price	11/2018
6961	27316^16923+16923^27316	115506	Hans Havermann	02/2021
6962	(2^383618+618)/2	115481	Stefano Morozzi	09/2020
6963	2^383560-455	115464	Yves Minet	03/2012
6964	(2^383544+5)/3	115458	Lelio R Paula	03/2014
6965	(22*10^115454+119)/3	115455	Robert Price	04/2021
6966	89^59221-88^59221	115445	Robert Price	06/2015
6967	(7^136559-5^136559)/2	115406	Jon Grantham	08/2023
6968	2^383347+1869413	115399	Enzo Doria	05/2016
6969	(103*10^115366+17)/3	115368	Robert Price	08/2020
6970	(2^383232+750)/2	115365	Stefano Morozzi	09/2020
6971	(2^383130-7)/131793	115329	Lelio R Paula	03/2014
6972	(12^106859+1)/13	115320	Paul Bourdelais	02/2010
6973	29961^7060+7060^29961	115315	Hans Havermann	01/2021
6975	2^383039+1869509	115307	Enzo Doria	05/2016
6974	32918^3183+3183^32918	115307	Hans Havermann	01/2021
6976	(109^56597-1)/90183471012	115302	Paul Vanderveen	06/2025
6977	36964^1315+1315^36964	115288	Hans Havermann	02/2021
6978	(13*2^382968+1)/7	115286	Lelio R Paula	04/2014
6979	(22*10^115282+29)/3	115283	Robert Price	02/2021
6980	(2^382945+2046)/2	115278	Stefano Morozzi	09/2020
6981	(2^382789+3182)/2	115231	Stefano Morozzi	09/2020
6982	30416^6141+6141^30416	115224	Hans Havermann	02/2021
6983	6*10^115211+79	115212	Robert Price	09/2020
6984	(2^382722+3598)/2	115211	Stefano Morozzi	09/2020
6985	27987^13078+13078^27987	115210	Hans Havermann	02/2021
6986	(2^382699+2090)/2	115204	Stefano Morozzi	09/2020
6987	(22*10^115188-193)/9	115189	Robert Price	07/2022
6988	2^382633+73697	115185	Enzo Doria	04/2016
6989	2^382509-113593	115147	Enzo Doria	08/2014
6990	2^382502-2791721	115145	Enzo Doria	03/2016
6991	(2^382495+1274)/2	115143	Stefano Morozzi	01/2021
6992	2^382464+22741	115134	Enzo Doria	09/2023
6993	26752^20065+20065^26752	115099	Hans Havermann	02/2021
6994	26383^23008+23008^26383	115080	Hans Havermann	02/2021
6995	9^120590-120590	115073	Robert Price	03/2014
6996	28203^12016+12016^28203	115062	Hans Havermann	02/2021
6997	2^382198+9	115054	Lelio R Paula	03/2013
6998	18268*31^77131+22839	115035	Eric Chen	05/2024
6999	30101^6630+6630^30101	115032	Hans Havermann	01/2021
7000	(89*10^115030-179)/9	115031	Robert Price	12/2019

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Probable Primes Top 10000

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