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	28357^14440+14440^28357	117953	Hans Havermann	02/2021
6752	(2^391812+5)/14181	117944	Lelio R Paula	04/2014
6753	85^61124-61124^85	117934	Norman Luhn	09/2024
6754	(7*10^117930-79)/9	117930	Robert Price	01/2021
6755	27531^19168+19168^27531	117904	Hans Havermann	02/2021
6756	(46*10^117902+683)/9	117903	Robert Price	03/2019
6757	26349^26668-26668^26349	117893	Frank Doornink	03/2024
6758	27670^18189+18189^27670	117869	Hans Havermann	02/2021
6759	(7*2^391521+1)/285	117858	Lelio R Paula	04/2014
6760	(56*10^117856+583)/9	117857	Robert Price	08/2021
6761	32169^4606+4606^32169	117846	Hans Havermann	02/2021
6762	(71*10^117803-143)/9	117804	Robert Price	10/2021
6763	2^391324+90901	117801	Yves Minet	02/2011
6764	2^391301-1859923	117794	Enzo Doria	03/2016
6765	2^391261-4131	117782	Yves Minet	02/2018
6766	(2^391211+554)/2	117766	Stefano Morozzi	09/2020
6767	816^40445-40445^816	117764	Norman Luhn	09/2024
6768	38434^1157+1157^38434	117737	Hans Havermann	01/2021
6769	(2^391115-7)/11791	117734	Lelio R Paula	04/2014
6770	(85*10^117719+473)/9	117720	Robert Price	01/2020
6771	(2^391049+582)/2	117718	Stefano Morozzi	09/2020
6772	(21*23^86445-197)/22	117715	Eric Chen	08/2023
6773	31083^6122+6122^31083	117709	Hans Havermann	02/2021
6774	2^390960+1880881	117691	Enzo Doria	11/2016
6775	(71*10^117685+91)/9	117686	Robert Price	04/2022
6777	2^390897-1860553	117672	Enzo Doria	11/2015
6776	(61*10^117671+47)/9	117672	Robert Price	07/2022
6778	2^390889-115003	117670	Enzo Doria	06/2015
6779	12^109010+35	117642	Riley Fisher	08/2023
6780	2^390779-30337	117637	Paul Bourdelais	02/2012
6781	(2^390735+378)/2	117623	Stefano Morozzi	02/2021
6782	11^112916-780	117590	Enzo Doria	12/2012
6783	27641^17916+17916^27641	117564	Hans Havermann	02/2021
6784	27906^16321+16321^27906	117561	Hans Havermann	02/2021
6785	27294^20275+20275^27294	117555	Hans Havermann	02/2021
6786	(2^390473+1002)/2	117544	Stefano Morozzi	09/2020
6787	35912^1875+1875^35912	117541	Hans Havermann	02/2021
6788	(16^97613-5^97613)/11	117537	Robert Price	07/2013
6789	(2^390438+1774)/2	117534	Stefano Morozzi	01/2021
6790	(2^390418+1722)/2	117528	Stefano Morozzi	09/2020
6791	(2^390403+654)/2	117523	Stefano Morozzi	09/2020
6792	(2^390343+2246)/2	117505	Stefano Morozzi	01/2021
6793	28043^15478+15478^28043	117493	Hans Havermann	02/2021
6794	Phi(247237,3)	117487	Henri Lifchitz	12/2025
6795	(17*2^390272+1)/1983	117482	Lelio R Paula	04/2014
6796	37077^1474+1474^37077	117479	Hans Havermann	01/2021
6797	31^78759-30	117459	Theodore Burton	02/2007
6798	(2^390176+1222)/2	117455	Stefano Morozzi	09/2020
6799	(2^390133+1242)/2	117442	Stefano Morozzi	09/2020
6800	(2^390013+2634)/2	117406	Stefano Morozzi	09/2020
6801	3*10^117402+61	117403	Robert Price	09/2020
6802	2^389998+37	117402	Lelio R Paula	03/2013
6803	(2^389977+314)/2	117395	Stefano Morozzi	09/2020
6804	(2^389921+342)/2	117378	Stefano Morozzi	01/2021
6805	71830^43+43^71830	117333	Hans Havermann	01/2021
6806	(2^389768+1582)/2	117332	Stefano Morozzi	09/2020
6807	33802^2951+2951^33802	117292	Hans Havermann	02/2021
6808	(2^561185)%L(561185)	117281	Henri Lifchitz	05/2025
6809	26789^23866+23866^26789	117277	Hans Havermann	02/2021
6810	29^80192-1*80192^29	117273	Dylan Delgado	12/2019
6811	(101*10^117260+7)/9	117262	Robert Price	02/2022
6812	(13*10^117249+161)/3	117250	Robert Price	11/2018
6813	2^389478+43	117245	Lelio R Paula	03/2013
6814	(298*10^117229-7)/3	117231	Robert Price	06/2020
6815	(2^389416+342)/2	117226	Stefano Morozzi	01/2021
6816	(29*2^389351-1)/9	117207	Lelio R Paula	04/2014
6817	5*10^117205+23	117206	Robert Price	03/2019
6818	(2^389341-7)/3865	117200	Lelio R Paula	03/2014
6819	27272^19827+19827^27272	117195	Hans Havermann	01/2021
6820	(2^389276+2650)/2	117184	Stefano Morozzi	09/2020
6821	(844*10^117175-7)/9	117177	Robert Price	05/2021
6822	10^117142+209223	117143	Patrick De Geest	04/2018
6824	10^117142-1000000001	117142	Robert Price	03/2018
6823	10^117142-966057	117142	Patrick De Geest	04/2018
6825	10^117135+360577	117136	Patrick De Geest	07/2018
6826	10^117135-401	117135	Robert Price	01/2018
6827	26415^26488-26488^26415	117126	Norbert Schneider	05/2021
6828	4*10^117123+79	117124	Robert Price	08/2018
6829	2^389033-12797413	117111	Enzo Doria	04/2016
6830	(2^388987+2634)/2	117097	Stefano Morozzi	09/2020
6831	2^388960-109505	117089	Enzo Doria	04/2014
6832	7*10^117082-57	117083	Robert Price	06/2020
6833	791^40398-40398^791	117081	Norman Luhn	09/2024
6834	(2^388928-5)/569	117077	Lelio R Paula	03/2014
6835	2^388888-1529	117067	Yves Minet	01/2013
6836	10^117059+28879	117060	Patrick De Geest	05/2016
6837	(10^117059-71)/1	117059	Serge Batalov	12/2014
6838	(2^388854+3630)/2	117057	Stefano Morozzi	09/2020
6839	(2^388842+2098)/2	117053	Stefano Morozzi	09/2020
6840	(2^388789+3150)/2	117037	Stefano Morozzi	09/2020
6841	(2^388748+378)/2	117025	Stefano Morozzi	02/2021
6842	(693^41189-1)/692	117005	Michael Stocker	05/2020
6843	(26*10^116999-503)/9	117000	Robert Price	07/2018
6844	20^89917-21	116985	Anonymous	09/2024
6845	(2^388609+1554)/2	116983	Stefano Morozzi	09/2020
6846	38496^1093+1093^38496	116975	Hans Havermann	02/2021
6847	3^245154-6256	116969	Enzo Doria	05/2014
6848	5*10^116966-43	116967	Robert Price	01/2019
6849	(748^40699-1)/747	116963	Tom Wu	08/2025
6850	2^388536-113495	116961	Enzo Doria	08/2014
6851	(2^388512+382)/2	116954	Stefano Morozzi	02/2021
6852	(8*32^77701+271)/31	116952	Eric Chen	11/2023
6853	2^388469-43	116941	Lelio R Paula	03/2013
6854	27417^18416+18416^27417	116939	Hans Havermann	02/2021
6855	(2^388438+1842)/2	116932	Stefano Morozzi	02/2021
6856	(7*2^388372-1)/111	116911	Lelio R Paula	04/2014
6857	(7*2^388335-1)/25	116900	Lelio R Paula	04/2014
6858	2^388180+93	116854	Donovan Johnson	07/2008
6859	(2^388167+2510)/2	116850	Stefano Morozzi	09/2020
6860	(85*10^116842+293)/9	116843	Robert Price	12/2019
6861	35296^2043+2043^35296	116840	Hans Havermann	02/2021
6862	(2^388081+7)/1179	116821	Lelio R Paula	03/2014
6863	38633^1056+1056^38633	116814	Hans Havermann	02/2021
6864	2^387946-113261	116784	Enzo Doria	07/2014
6865	28*36^75009+305	116739	Eric Chen	12/2022
6866	28363^13056+13056^28363	116737	Hans Havermann	02/2021
6867	2^387745+75557	116723	Enzo Doria	04/2016
6868	(29*10^116719+313)/9	116720	Robert Price	04/2021
6869	29622^8699+8699^29622	116695	Hans Havermann	02/2021
6870	(206*10^116687-17)/9	116689	Robert Price	01/2020
6871	(7*10^116684+179)/3	116685	Robert Price	09/2018
6872	2^387554+71455	116666	Enzo Doria	04/2016
6873	(602*10^116647-71)/9	116649	Robert Price	12/2021
6874	3^244461-10	116638	Tyler NeSmith	09/2022
6875	(2^387447+78557)/365	116631	Lelio R Paula	12/2014
6876	(2*10^116620+43)/9	116620	Serge Batalov	11/2022
6877	(19*10^116617+287)/9/12893	116614	Alfred Reich	11/2022
6878	(145*10^116610-1)/9	116612	Serge Batalov	12/2014
6879	(25*10^116601-331)/9	116602	Robert Price	08/2018
6880	25791^26428-26428^25791	116587	Frank Doornink	03/2024
6882	(17*2^387284-1)/59	116584	Lelio R Paula	04/2014
6881	(2^387284+3726)/2	116584	Stefano Morozzi	09/2020
6883	2^387211+111546435	116563	Paul Bourdelais	10/2021
6884	10^116557+987654321	116558	Robert Price	12/2019
6885	10^116557+9141	116558	Patrick De Geest	02/2020
6886	10^116557-609431	116557	Patrick De Geest	02/2020
6887	209^50234-50234^209	116551	Norman Luhn	09/2024
6888	(28*10^116546+41)/3	116547	Robert Price	07/2021
6889	(2^387123+1814)/2	116536	Stefano Morozzi	02/2021
6890	(2^387076+2046)/2	116522	Stefano Morozzi	09/2020
6891	(2^387073+2570)/2	116521	Stefano Morozzi	09/2020
6892	(7*10^116514-1)/3	116515	Robert Price	08/2022
6893	(26*32^77406-390071011)/31	116508	Eric Chen	11/2023
6894	28846^10931+10931^28846	116500	Hans Havermann	02/2021
6895	10^116496+3593037	116497	Paul Bourdelais	10/2021
6896	272^47851-47851^272	116497	Norman Luhn	09/2024
6897	(31*2^386968+1)/7	116490	Lelio R Paula	03/2014
6898	(944^39157+1)/945	116489	Jinyuan Wang	12/2024
6899	998^38840+997	116487	Alfred Reich	03/2026
6900	2^386947+1869143	116483	Enzo Doria	05/2016
6902	(30^78857-1)/29	116480	Robert Price	12/2011
6901	Phi(78857,5#)	116480	Henri Lifchitz	12/2025
6903	(2^386903-3)/5	116469	Lelio R Paula	03/2014
6904	28107^13892+13892^28107	116441	Hans Havermann	02/2021
6905	29110^9957+9957^29110	116386	Hans Havermann	02/2021
6906	26469^24838+24838^26469	116335	Hans Havermann	01/2021
6907	2^386389-1864783	116315	Enzo Doria	03/2016
6908	993^38799+992	116279	Alfred Reich	03/2026
6909	(8*32^77250-163)/31	116273	Eric Chen	11/2023
6910	(31*2^386231-1)/1711	116266	Lelio R Paula	03/2014
6911	297^47012+47012^297	116250	Norbert Schneider	07/2018
6912	(35*10^116223-341)/9	116224	Robert Price	08/2021
6913	(2^386087-5)/40959	116220	Lelio R Paula	03/2014
6914	(2^386054+714)/2	116214	Stefano Morozzi	09/2020
6915	(10^116201+7)/39623	116197	Alfred Reich	06/2021
6916	2^385969-823	116189	Yves Minet	05/2012
6917	57^66162+2	116173	Lelio R Paula	08/2013
6918	2^385854+75049	116154	Enzo Doria	04/2016
6919	(2^385832+2590)/2	116147	Stefano Morozzi	09/2020
6920	2^385775-109587	116130	Enzo Doria	04/2014
6921	(14*10^116112-101)/3	116113	Robert Price	02/2019
6922	Phi(236354,10)/24817171	116109	Makoto Kamada	08/2019
6923	3*10^116107+23	116108	Robert Price	03/2022
6924	28729^10990+10990^28729	116094	Hans Havermann	02/2021
6925	2^385622+71839	116084	Enzo Doria	04/2016
6927	2^385564+781	116067	Lelio R Paula	01/2012
6926	(2^385565+1562)/2	116067	Stefano Morozzi	09/2020
6928	(2^385563+378)/2	116066	Stefano Morozzi	02/2021
6929	(2^385557+2214)/2	116064	Stefano Morozzi	09/2020
6930	29431^8776+8776^29431	116056	Hans Havermann	01/2021
6931	(266*10^116024-17)/3	116026	Robert Price	07/2020
6932	30263^6820+6820^30263	116022	Hans Havermann	02/2021
6933	2^385410+71893	116020	Enzo Doria	04/2016
6934	38225^1084+1084^38225	116014	Hans Havermann	02/2021
6935	26548^23433+23433^26548	116011	Hans Havermann	02/2021
6936	Phi(183801,-9)	115960	Henri Lifchitz	12/2025
6937	12^107422-11	115928	Riley Fisher	12/2023
6938	(25*2^385091+1)/27	115924	Lelio R Paula	04/2014
6939	(11*10^115910-131)/3	115911	Robert Price	09/2018
6940	2^384953-111943	115883	Paul Bourdelais	02/2012
6941	43^70942-2	115882	Lelio R Paula	04/2014
6942	(94*10^115879-7)/3	115881	Robert Price	03/2020
6943	7*10^115863+3	115864	Robert Price	08/2015
6944	2^384834+93	115847	Donovan Johnson	07/2008
6945	2^384809+71297	115840	Enzo Doria	04/2016
6946	(55*10^115829+323)/9	115830	Robert Price	10/2021
6947	(7*2^384759-1)/5	115825	Lelio R Paula	04/2014
6948	31348^4951+4951^31348	115822	Hans Havermann	02/2021
6949	(793*10^115810+53)/9	115812	Robert Price	01/2022
6950	(71*10^115810-17)/9	115811	Ray Chandler	08/2011
6951	(97*10^115794-1)/3	115796	Serge Batalov	12/2014
6952	31115^5266+5266^31115	115794	Hans Havermann	02/2021
6953	2*10^115784-27	115785	Robert Price	05/2018
6954	10^115773+126739	115774	Patrick De Geest	04/2018
6956	10^115773-1000000001	115773	Robert Price	03/2018
6955	10^115773-396221	115773	Patrick De Geest	04/2018
6957	(2^384582+778)/2	115771	Stefano Morozzi	09/2020
6958	30537^6178+6178^30537	115762	Hans Havermann	01/2021
6959	2^384530+1874305	115756	Enzo Doria	06/2016
6960	(3*2^384524-1)/7631	115750	Lelio R Paula	03/2014
6961	28275^12406+12406^28275	115748	Hans Havermann	01/2021
6962	(44*10^115697-413)/9	115698	Robert Price	03/2019
6963	31408^4825+4825^31408	115692	Hans Havermann	02/2021
6964	(2^384317+1026)/2	115691	Stefano Morozzi	09/2020
6965	2^384312+81091	115690	Yves Minet	02/2010
6966	(2^384265+2150)/2	115675	Stefano Morozzi	09/2020
6967	(2^384246+2182)/2	115670	Stefano Morozzi	09/2020
6968	(4*10^115668-79)/3	115669	Robert Price	02/2018
6969	(2^384193+242)/2	115654	Stefano Morozzi	09/2020
6970	994^38584+993	115652	Alfred Reich	03/2026
6971	(266947#+1267)/(7^2*181)	115647	Makoto Morimoto	06/2019
6972	(266947#+273808)/(2109157)	115646	Makoto Morimoto	10/2017
6973	18^92125-92125^18	115642	Dylan Delgado	08/2019
6974	(25^82723+3^82723)/28	115641	Robert Price	09/2025
6975	3^242337-4042	115625	Enzo Doria	05/2014
6976	(17699*31^77516-29)/30	115608	Eric Chen	05/2024
6977	(2^383931+674)/2	115575	Stefano Morozzi	09/2020
6978	7*10^115561+79	115562	Robert Price	07/2019
6979	(2^383872+3046)/2	115557	Stefano Morozzi	09/2020
6980	(11*2^383859-13)/15	115553	Renaud Lifchitz	03/2011
6981	2^383780-3149	115530	Yves Minet	10/2014
6982	(41*10^115523-383)/9	115524	Robert Price	11/2018
6983	27316^16923+16923^27316	115506	Hans Havermann	02/2021
6984	(2^383618+618)/2	115481	Stefano Morozzi	09/2020
6985	2^383560-455	115464	Yves Minet	03/2012
6986	(2^383544+5)/3	115458	Lelio R Paula	03/2014
6987	(22*10^115454+119)/3	115455	Robert Price	04/2021
6988	89^59221-88^59221	115445	Robert Price	06/2015
6989	(7^136559-5^136559)/2	115406	Jon Grantham	08/2023
6990	2^383347+1869413	115399	Enzo Doria	05/2016
6991	(103*10^115366+17)/3	115368	Robert Price	08/2020
6992	(2^383232+750)/2	115365	Stefano Morozzi	09/2020
6993	(2^383130-7)/131793	115329	Lelio R Paula	03/2014
6994	(12^106859+1)/13	115320	Paul Bourdelais	02/2010
6995	29961^7060+7060^29961	115315	Hans Havermann	01/2021
6997	2^383039+1869509	115307	Enzo Doria	05/2016
6996	32918^3183+3183^32918	115307	Hans Havermann	01/2021
6998	(109^56597-1)/90183471012	115302	Paul Vanderveen	06/2025
6999	36964^1315+1315^36964	115288	Hans Havermann	02/2021
7000	(13*2^382968+1)/7	115286	Lelio R Paula	04/2014

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Probable Primes Top 10000

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