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 ?
751	(20^177967+1)/21	231540	Paul Bourdelais	05/2013
752	2^767622-9221	231078	Lelio R Paula	01/2016
753	2^767344+1880311	230994	Enzo Doria	09/2016
754	(3^483611-1)/2	230741	Paul Bourdelais	02/2010
755	(10^230706+179)/9	230706	Serge Batalov	12/2014
756	2^766309+1875257	230682	Enzo Doria	06/2016
757	2^765635+1879883	230480	Enzo Doria	09/2016
758	2^764348-113697	230092	Enzo Doria	09/2014
759	2^764131+78863	230027	Enzo Doria	05/2016
760	2^763701+60197	229897	Enzo Doria	03/2016
761	2^762841-25905	229639	Enzo Doria	10/2013
762	2^761117-113569	229120	Enzo Doria	08/2014
763	(98^114859+1)/99	228709	Paul Bourdelais	12/2018
764	(2^758231+1)/(32714694297653973236839266867)	228223	Gord Palameta	12/2018
765	2^757985-2790013	228177	Enzo Doria	12/2015
766	2^757038-1862081	227892	Enzo Doria	12/2015
767	2^756839+95849	227832	Makoto Morimoto	10/2013
768	(2^756839+6989)/756091	227826	Makoto Morimoto	09/2016
769	(2^756839-50211)/(137*3203)	227826	Makoto Morimoto	08/2019
770	2^756773-112723	227812	Enzo Doria	07/2014
771	524309#+616367	227431	Makoto Morimoto	02/2016
772	2^755097-114193	227307	Enzo Doria	12/2014
773	2^754473-2791513	227120	Enzo Doria	01/2016
774	2^751426-764321	226202	Enzo Doria	12/2013
775	(18^180181-1)/17	226176	Andy Steward	04/2007
776	2^750740-3	225996	Paul Bourdelais	03/2012
777	2^750725+60227	225991	Enzo Doria	02/2016
778	2^750525-113743	225931	Enzo Doria	09/2014
779	(2^750151-1)/(4299340426317590093831289397764574647511836143783478715117383638888678527263)	225744	Dario Alpern	10/2014
780	2^749444-1861889	225606	Enzo Doria	12/2015
781	tau(311^16452)	225560	Nik Lygeros / Olivier Rozier / LR team	10/2013
782	2^749096+1876861	225501	Enzo Doria	07/2016
783	(519643#+43033)/(2318712706283)	225379	Makoto Morimoto	08/2019
784	2^748657+79607	225369	Enzo Doria	06/2016
785	2^746653-291583	224765	Enzo Doria	07/2015
786	2^746461-114043	224708	Enzo Doria	11/2014
787	2^745098-350471	224297	Enzo Doria	06/2015
788	2^745039-4897	224280	Yves Minet	03/2021
789	(154*10^224061-1)/9	224063	Serge Batalov	12/2014
790	2^744211-1845787	224030	Enzo Doria	07/2015
791	2^743592-134579	223844	Hans Havermann	10/2018
792	2^742452+3	223501	Paul Bourdelais	06/2019
793	234178^9+9^234178	223463	Anatoly F. Selevich	07/2011
794	2^741651-461197	223260	Enzo Doria	07/2015
795	2^741362-1845251	223173	Enzo Doria	07/2015
796	2^740455-1863877	222900	Enzo Doria	12/2015
797	2^739636-2792219	222653	Enzo Doria	02/2016
798	11^213654-180	222498	Enzo Doria	01/2013
799	2^738957-1859743	222449	Enzo Doria	11/2015
800	(54^128189+1)/55	222073	Paul Bourdelais	11/2018
801	(10^221654+179)/9	221654	Serge Batalov	12/2014
802	2^736281+79817	221643	Enzo Doria	06/2016
803	10^221631+247617	221632	Patrick De Geest	10/2013
804	10^221631-9	221631	Alexander Gramolin	02/2011
805	2^735970-1839821	221550	Enzo Doria	06/2015
806	2^735367+60293	221368	Enzo Doria	03/2016
807	(29^151153+1)/30	221045	Paul Bourdelais	09/2017
808	2^733264-2784089	220735	Enzo Doria	10/2015
809	2^733114-24555	220690	Enzo Doria	09/2013
810	2^731891-636259	220322	Enzo Doria	12/2013
811	2^731124-25539	220091	Enzo Doria	09/2013
812	2^730972-462029	220045	Enzo Doria	07/2015
813	2^730833+1868627	220003	Enzo Doria	04/2016
814	2^730645-2787133	219947	Enzo Doria	11/2015
815	2^730547-25581	219917	Enzo Doria	09/2013
816	2^730460+82291	219891	Enzo Doria	09/2016
817	(2^730339+1)/(3278390620037943469324347)	219831	Gord Palameta	12/2018
818	L(1051849)	219824	Renaud Lifchitz	03/2009
819	11^210961-240	219694	Enzo Doria	01/2013
820	2^729611-113437	219635	Enzo Doria	08/2014
821	7^259710-2	219481	Paul Bourdelais	01/2021
822	F(1049897)	219416	Henri Lifchitz	10/2008
823	2^728604+1879321	219332	Enzo Doria	10/2016
824	33^144412+2	219292	Robert Price	04/2015
825	2^728277-183313	219234	Hans Havermann	10/2018
826	2^727998-1862711	219150	Enzo Doria	12/2015
827	2^727729-114073	219069	Enzo Doria	12/2014
828	2^727496-1851809	218999	Enzo Doria	08/2015
829	2^726591+2793143	218726	Enzo Doria	02/2016
830	2^725534-2791931	218408	Enzo Doria	02/2016
831	Phi(220531,10)/2686456812680882641	217774	Makoto Kamada	10/2020
832	2^722184+1877821	217400	Enzo Doria	08/2016
833	(109*10^217360-1)/9	217362	Serge Batalov	12/2014
834	2^721721-4453	217260	Yves Minet	03/2021
835	281*499979#/46410-2702372	216849	Robert Smith	08/2016
836	281*499979#/46410+2400766	216849	Robert Smith	08/2016
837	tau(311^15786)	216429	Nik Lygeros / Olivier Rozier / LR team	10/2013
838	2^718756-114107	216368	Enzo Doria	12/2014
839	2^717305+80327	215931	Enzo Doria	07/2016
840	2^717069-59773	215860	Enzo Doria	10/2015
841	30^146021-29^146021	215691	Jean-Louis Charton	09/2018
842	277^88301-276^88301	215674	Jean-Louis Charton	06/2012
843	227^91413-40	215372	Enzo Doria	04/2015
844	2^714717+782897	215152	Enzo Doria	11/2016
845	tau(373^15186)	214796	Nik Lygeros / Olivier Rozier / LR team	10/2013
846	2^713241+1879157	214707	Enzo Doria	08/2016
847	11^206081-10^206081	214612	Jean-Louis Charton	10/2011
848	2^712801-69553	214575	Enzo Doria	01/2016
849	2^712603-25357	214515	Enzo Doria	09/2013
850	2^711721-1846723	214250	Enzo Doria	07/2015
851	2^710730-396765	213952	Enzo Doria	09/2013
852	2^708468-114329	213271	Enzo Doria	02/2015
853	(163*10^212779-1)/9	212781	Serge Batalov	12/2014
854	2^706838-69041	212780	Enzo Doria	11/2015
855	2^704577-113871	212099	Enzo Doria	10/2014
856	2^704110-2792441	211959	Enzo Doria	02/2016
857	2^703943-1862947	211908	Enzo Doria	12/2015
858	(60^119083+1)/61	211746	Paul Bourdelais	10/2018
859	(10^211610-91)/9	211610	Serge Batalov	12/2014
860	227^89797+2	211565	Lelio R Paula	08/2012
861	2^702194-3	211382	Paul Bourdelais	03/2012
862	2^702064+1874911	211343	Enzo Doria	07/2016
863	2^701968-113873	211314	Enzo Doria	10/2014
864	2^701713-113779	211237	Enzo Doria	09/2014
865	2^701449-25201	211158	Enzo Doria	09/2013
866	2^701403-2786977	211144	Enzo Doria	11/2015
867	2^701189-25423	211079	Enzo Doria	09/2013
868	2^701162-459161	211071	Enzo Doria	05/2015
869	(24^152783-1)/23	210872	Paul Bourdelais	04/2018
870	2^700400+9385	210842	Lelio R Paula	01/2014
871	2^700131+1874693	210761	Enzo Doria	06/2016
872	(2^700095+225414)/2	210750	Stefano Morozzi	04/2020
873	(2^700090+278254)/2	210748	Stefano Morozzi	04/2020
874	(2^700075+303666)/2	210744	Stefano Morozzi	04/2020
875	(2^700073+75882)/2	210743	Stefano Morozzi	04/2020
876	(2^700074+328890)/2	210743	Stefano Morozzi	04/2020
877	(2^700052+79162)/2	210737	Stefano Morozzi	04/2020
878	(2^700052+304458)/2	210737	Stefano Morozzi	04/2020
879	(2^700048+376578)/2	210736	Stefano Morozzi	04/2020
880	11^202357-1140	210734	Enzo Doria	12/2012
881	(2^700021+25874)/2	210728	Stefano Morozzi	04/2020
882	(2^700018+377518)/2	210727	Stefano Morozzi	04/2020
883	2^698929-2788423	210399	Enzo Doria	11/2015
884	(5^300893+4^300893)/9	210315	Jean-Louis Charton	11/2011
885	2^698316+1878601	210215	Enzo Doria	08/2016
886	2^697036+1878751	209829	Enzo Doria	08/2016
887	6^269407+5	209640	Paul Bourdelais	02/2021
888	(2^696343-1)/11141489/36009913139329	209600	Tony Prest / Never Odd Or Even	02/2014
889	2^696254-115151	209594	Enzo Doria	06/2015
890	(35^135623+1)/36	209410	Paul Bourdelais	07/2018
891	2^694633+1887257	209106	Enzo Doria	05/2017
892	2^693959+180923	208903	Enzo Doria	07/2016
893	2^693462-1847561	208753	Enzo Doria	07/2015
894	2^690890-59981	207979	Enzo Doria	11/2015
895	(38^131591+1)/39	207884	Paul Bourdelais	07/2018
896	2^690163+1877063	207760	Enzo Doria	07/2016
897	7^245608-2	207563	Paul Bourdelais	01/2021
898	2^689286-29381	207496	Enzo Doria	08/2015
899	2^689122-114521	207447	Enzo Doria	04/2015
900	2^688373+6077	207221	Enzo Doria	02/2016
901	2^688201+1875527	207170	Enzo Doria	07/2016
902	(42^127609+1)/43	207140	Paul Bourdelais	07/2018
903	2^687619+81563	206994	Enzo Doria	08/2016
904	2^686572-1845299	206679	Enzo Doria	07/2015
905	(21^156217-1)/20	206552	Paul Bourdelais	04/2010
906	(2^685739+1)/(3*87774593)	206420	Gord Palameta	08/2018
907	2^685578+3	206380	Paul Bourdelais	04/2012
908	2^684836-49349	206157	Enzo Doria	10/2015
909	(73^110603-1)/72	206088	Paul Bourdelais	06/2018
910	2^684163-2790967	205954	Enzo Doria	12/2015
911	326^81943-325^81943	205941	Jean-Louis Charton	07/2012
912	(2^684127-1)/23765203727	205933	Jens K. Andersen	04/2009
913	4^341233-3^341233	205443	Jean-Louis Charton	01/2006
914	2^681545+467	205166	Lelio R Paula	11/2013
915	2^681306+81049	205094	Enzo Doria	07/2016
916	2^680697+1877057	204911	Enzo Doria	07/2016
917	2^680415+71783	204826	Enzo Doria	04/2016
918	2^679860-459995	204659	Enzo Doria	06/2015
919	2^679593+1879547	204578	Enzo Doria	09/2016
920	2^678651+1875023	204295	Enzo Doria	07/2016
921	2^678561+678561	204268	Henri Lifchitz	05/2006
922	2^678101-114043	204129	Enzo Doria	11/2014
923	2^678028+1875631	204107	Enzo Doria	06/2016
924	2^676992-59783	203795	Enzo Doria	10/2015
925	2^676972+1866871	203789	Enzo Doria	03/2016
926	2^676761-9	203726	Robert Price	01/2017
927	2^676563-2792407	203666	Enzo Doria	02/2016
928	2^676306-114713	203589	Enzo Doria	04/2015
929	(2^675977-1)/(1686378749257*7171117283326998925471)	203456	Dario Alpern	07/2015
930	2^674627-25161	203083	Enzo Doria	09/2013
931	2^674603-69337	203076	Enzo Doria	12/2015
932	2^674459+74213	203033	Enzo Doria	04/2016
933	2^674116-458879	202930	Enzo Doria	04/2015
934	2^674076-114755	202918	Enzo Doria	04/2015
935	5^289937-4^289937	202658	Jean-Louis Charton	03/2013
936	(467617#+14534)/(2^21343)	202603	Makoto Morimoto	06/2019
937	2^672556-1835519	202460	Enzo Doria	04/2015
938	2^671446-351401	202126	Enzo Doria	07/2015
939	2^671373+77747	202104	Enzo Doria	05/2016
940	2^670726-114845	201909	Enzo Doria	05/2015
941	2^670539-25045	201853	Enzo Doria	09/2013
942	43284^43519-43519^43284	201769	Norbert Schneider	08/2018
943	2^670213+282317	201755	Enzo Doria	09/2016
944	2^669854-113501	201647	Enzo Doria	08/2014
945	2^669718+81619	201606	Enzo Doria	08/2016
946	(145*10^201504-1)/9	201506	Serge Batalov	12/2014
947	2^668938-1839821	201371	Enzo Doria	06/2015
948	2^668492+1879303	201237	Enzo Doria	08/2016
949	6^258413-5^258413	201085	Jean-Louis Charton	03/2013
950	10194^50161-50161^10194	201063	Norbert Schneider	09/2020
951	2^667894+1875589	201057	Enzo Doria	06/2016
952	2^667569-1836559	200959	Enzo Doria	05/2015
953	(172*10^200746-1)/9	200748	Serge Batalov	12/2014
954	2^666430+782569	200616	Enzo Doria	10/2016
955	(86^103471+1)/87	200163	Paul Bourdelais	05/2018
957	103(10^100000+20110)^2-4707(10^100000+20110)+50383	200003	Robert Price	05/2017
956	103(10^100000+33798)^2-4707(10^100000+33798)+50383	200003	Robert Price	01/2018
958	numbpart(32235776596)	200002	Serge Batalov	04/2017
959	(10^200001+149)/3	200001	Serge Batalov	12/2014
960	10^200000+571791	200001	Patrick De Geest	08/2019
961	(3^419180-621444)/3	200000	Stefano Morozzi	06/2019
962	(3^419180-1941384)/3	200000	Stefano Morozzi	08/2019
963	10^200000-45557	200000	Patrick De Geest	08/2019
964	(10^200000-1)/9-10^58838	200000	Akihiko Yoshida	04/2020
965	(299*10^199801-17)/3	199803	Robert Price	04/2020
966	6*10^199788+77	199789	Robert Price	06/2020
967	(14*10^199447+73)/3	199448	Robert Price	12/2018
968	2^662103-29287	199313	Enzo Doria	08/2015
969	(2*10^199283+457)/9	199283	Robert Price	01/2018
970	(10^199248-19)/9	199248	Robert Price	01/2018
971	(194*10^199146-17)/3	199148	Robert Price	09/2020
972	(151*10^199003-1)/3	199005	Robert Price	03/2020
973	9*10^198946-73	198947	Robert Price	01/2021
974	45*10^198931-7	198933	Robert Price	07/2020
975	2^660482-2891	198825	Yves Minet	05/2016
976	2^659583+1879223	198555	Enzo Doria	08/2016
977	(53*10^198529+1)/9	198530	Serge Batalov	07/2010
978	(49*10^198403+311)/9	198404	Robert Price	06/2019
979	96*10^198376-7	198378	Robert Price	03/2021
980	2^658828-29819	198327	Enzo Doria	08/2015
981	2^658776-2791229	198312	Enzo Doria	01/2016
982	(35*10^198294-377)/9	198295	Robert Price	07/2018
983	(4*10^198268+137)/3	198269	Robert Price	03/2018
984	2^658544-1854029	198242	Enzo Doria	09/2015
985	(157^90239-1)/156	198154	Alexander Zhirkov	06/2016
986	(232*10^197897+17)/3	197899	Robert Price	04/2021
987	(4*10^197778+173)/3	197779	Robert Price	02/2018
988	78*10^197702-7	197704	Robert Price	10/2020
989	(17*10^197640-23)/3	197641	Robert Price	03/2021
990	(29*10^197629-77)/3	197630	Robert Price	02/2020
991	2^656462+1874419	197615	Enzo Doria	06/2016
992	(89^101363+1)/90	197595	Paul Bourdelais	11/2017
993	2^655893-344563	197444	Enzo Doria	07/2015
994	2^655875+71333	197439	Enzo Doria	04/2016
995	2^655845-9	197430	Robert Price	01/2017
996	(299*10^197426+1)/3	197428	Robert Price	04/2020
997	2^655682-1849121	197380	Enzo Doria	08/2015
998	4*10^197268-89	197269	Robert Price	11/2018
999	2^655045-49603	197189	Enzo Doria	10/2015
1000	2^655000-2784089	197175	Enzo Doria	10/2015

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Probable Primes Top 10000

(280932 PRPs in the top)