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	2^750725+60227	225991	Enzo Doria	02/2016
752	2^750525-113743	225931	Enzo Doria	09/2014
753	(2^750151-1)/(4299340426317590093831289397764574647511836143783478715117383638888678527263)	225744	Dario Alpern	10/2014
754	2^749444-1861889	225606	Enzo Doria	12/2015
755	tau(311^16452)	225560	Nik Lygeros / Olivier Rozier / LR team	10/2013
756	2^749096+1876861	225501	Enzo Doria	07/2016
757	(519643#+43033)/(2318712706283)	225379	Makoto Morimoto	08/2019
758	2^748657+79607	225369	Enzo Doria	06/2016
759	2^746653-291583	224765	Enzo Doria	07/2015
760	2^746461-114043	224708	Enzo Doria	11/2014
761	2^745098-350471	224297	Enzo Doria	06/2015
762	(154*10^224061-1)/9	224063	Serge Batalov	12/2014
763	2^744211-1845787	224030	Enzo Doria	07/2015
764	2^743592-134579	223844	Hans Havermann	10/2018
765	2^742452+3	223501	Paul Bourdelais	06/2019
766	234178^9+9^234178	223463	Anatoly F. Selevich	07/2011
767	2^741651-461197	223260	Enzo Doria	07/2015
768	2^741362-1845251	223173	Enzo Doria	07/2015
769	2^740455-1863877	222900	Enzo Doria	12/2015
770	2^739636-2792219	222653	Enzo Doria	02/2016
771	11^213654-180	222498	Enzo Doria	01/2013
772	2^738957-1859743	222449	Enzo Doria	11/2015
773	(54^128189+1)/55	222073	Paul Bourdelais	11/2018
774	(10^221654+179)/9	221654	Serge Batalov	12/2014
775	2^736281+79817	221643	Enzo Doria	06/2016
776	10^221631+247617	221632	Patrick De Geest	10/2013
777	10^221631-9	221631	Alexander Gramolin	02/2011
778	2^735970-1839821	221550	Enzo Doria	06/2015
779	2^735367+60293	221368	Enzo Doria	03/2016
780	(29^151153+1)/30	221045	Paul Bourdelais	09/2017
781	2^733264-2784089	220735	Enzo Doria	10/2015
782	2^733114-24555	220690	Enzo Doria	09/2013
783	2^731891-636259	220322	Enzo Doria	12/2013
784	2^731124-25539	220091	Enzo Doria	09/2013
785	2^730972-462029	220045	Enzo Doria	07/2015
786	2^730833+1868627	220003	Enzo Doria	04/2016
787	2^730645-2787133	219947	Enzo Doria	11/2015
788	2^730547-25581	219917	Enzo Doria	09/2013
789	2^730460+82291	219891	Enzo Doria	09/2016
790	(2^730339+1)/(3278390620037943469324347)	219831	Gord Palameta	12/2018
791	L(1051849)	219824	Renaud Lifchitz	03/2009
792	11^210961-240	219694	Enzo Doria	01/2013
793	2^729611-113437	219635	Enzo Doria	08/2014
794	F(1049897)	219416	Henri Lifchitz	10/2008
795	2^728604+1879321	219332	Enzo Doria	10/2016
796	33^144412+2	219292	Robert Price	04/2015
797	2^728277-183313	219234	Hans Havermann	10/2018
798	2^727998-1862711	219150	Enzo Doria	12/2015
799	2^727729-114073	219069	Enzo Doria	12/2014
800	2^727496-1851809	218999	Enzo Doria	08/2015
801	2^726591+2793143	218726	Enzo Doria	02/2016
802	2^725534-2791931	218408	Enzo Doria	02/2016
803	Phi(220531,10)/2686456812680882641	217774	Makoto Kamada	10/2020
804	2^722184+1877821	217400	Enzo Doria	08/2016
805	(109*10^217360-1)/9	217362	Serge Batalov	12/2014
806	281*499979#/46410-2702372	216849	Robert Smith	08/2016
807	281*499979#/46410+2400766	216849	Robert Smith	08/2016
808	tau(311^15786)	216429	Nik Lygeros / Olivier Rozier / LR team	10/2013
809	2^718756-114107	216368	Enzo Doria	12/2014
810	2^717305+80327	215931	Enzo Doria	07/2016
811	2^717069-59773	215860	Enzo Doria	10/2015
812	30^146021-29^146021	215691	Jean-Louis Charton	09/2018
813	277^88301-276^88301	215674	Jean-Louis Charton	06/2012
814	227^91413-40	215372	Enzo Doria	04/2015
815	2^714717+782897	215152	Enzo Doria	11/2016
816	tau(373^15186)	214796	Nik Lygeros / Olivier Rozier / LR team	10/2013
817	2^713241+1879157	214707	Enzo Doria	08/2016
818	11^206081-10^206081	214612	Jean-Louis Charton	10/2011
819	2^712801-69553	214575	Enzo Doria	01/2016
820	2^712603-25357	214515	Enzo Doria	09/2013
821	2^711721-1846723	214250	Enzo Doria	07/2015
822	2^710730-396765	213952	Enzo Doria	09/2013
823	2^708468-114329	213271	Enzo Doria	02/2015
824	(163*10^212779-1)/9	212781	Serge Batalov	12/2014
825	2^706838-69041	212780	Enzo Doria	11/2015
826	2^704577-113871	212099	Enzo Doria	10/2014
827	2^704110-2792441	211959	Enzo Doria	02/2016
828	2^703943-1862947	211908	Enzo Doria	12/2015
829	(60^119083+1)/61	211746	Paul Bourdelais	10/2018
830	(10^211610-91)/9	211610	Serge Batalov	12/2014
831	227^89797+2	211565	Lelio R Paula	08/2012
832	2^702194-3	211382	Paul Bourdelais	03/2012
833	2^702064+1874911	211343	Enzo Doria	07/2016
834	2^701968-113873	211314	Enzo Doria	10/2014
835	2^701713-113779	211237	Enzo Doria	09/2014
836	2^701449-25201	211158	Enzo Doria	09/2013
837	2^701403-2786977	211144	Enzo Doria	11/2015
838	2^701189-25423	211079	Enzo Doria	09/2013
839	2^701162-459161	211071	Enzo Doria	05/2015
840	(24^152783-1)/23	210872	Paul Bourdelais	04/2018
841	2^700400+9385	210842	Lelio R Paula	01/2014
842	2^700131+1874693	210761	Enzo Doria	06/2016
843	(2^700095+225414)/2	210750	Stefano Morozzi	04/2020
844	(2^700090+278254)/2	210748	Stefano Morozzi	04/2020
845	(2^700075+303666)/2	210744	Stefano Morozzi	04/2020
846	(2^700073+75882)/2	210743	Stefano Morozzi	04/2020
847	(2^700074+328890)/2	210743	Stefano Morozzi	04/2020
848	(2^700052+79162)/2	210737	Stefano Morozzi	04/2020
849	(2^700052+304458)/2	210737	Stefano Morozzi	04/2020
850	(2^700048+376578)/2	210736	Stefano Morozzi	04/2020
851	11^202357-1140	210734	Enzo Doria	12/2012
852	(2^700021+25874)/2	210728	Stefano Morozzi	04/2020
853	(2^700018+377518)/2	210727	Stefano Morozzi	04/2020
854	2^698929-2788423	210399	Enzo Doria	11/2015
855	(5^300893+4^300893)/9	210315	Jean-Louis Charton	11/2011
856	2^698316+1878601	210215	Enzo Doria	08/2016
857	2^697036+1878751	209829	Enzo Doria	08/2016
858	(2^696343-1)/11141489/36009913139329	209600	Tony Prest / Never Odd Or Even	02/2014
859	2^696254-115151	209594	Enzo Doria	06/2015
860	(35^135623+1)/36	209410	Paul Bourdelais	07/2018
861	2^694633+1887257	209106	Enzo Doria	05/2017
862	2^693959+180923	208903	Enzo Doria	07/2016
863	2^693462-1847561	208753	Enzo Doria	07/2015
864	2^690890-59981	207979	Enzo Doria	11/2015
865	(38^131591+1)/39	207884	Paul Bourdelais	07/2018
866	2^690163+1877063	207760	Enzo Doria	07/2016
867	2^689286-29381	207496	Enzo Doria	08/2015
868	2^689122-114521	207447	Enzo Doria	04/2015
869	2^688373+6077	207221	Enzo Doria	02/2016
870	2^688201+1875527	207170	Enzo Doria	07/2016
871	(42^127609+1)/43	207140	Paul Bourdelais	07/2018
872	2^687619+81563	206994	Enzo Doria	08/2016
873	2^686572-1845299	206679	Enzo Doria	07/2015
874	(21^156217-1)/20	206552	Paul Bourdelais	04/2010
875	(2^685739+1)/(3*87774593)	206420	Gord Palameta	08/2018
876	2^685578+3	206380	Paul Bourdelais	04/2012
877	2^684836-49349	206157	Enzo Doria	10/2015
878	(73^110603-1)/72	206088	Paul Bourdelais	06/2018
879	2^684163-2790967	205954	Enzo Doria	12/2015
880	326^81943-325^81943	205941	Jean-Louis Charton	07/2012
881	(2^684127-1)/23765203727	205933	Jens K. Andersen	04/2009
882	4^341233-3^341233	205443	Jean-Louis Charton	01/2006
883	2^681545+467	205166	Lelio R Paula	11/2013
884	2^681306+81049	205094	Enzo Doria	07/2016
885	2^680697+1877057	204911	Enzo Doria	07/2016
886	2^680415+71783	204826	Enzo Doria	04/2016
887	2^679860-459995	204659	Enzo Doria	06/2015
888	2^679593+1879547	204578	Enzo Doria	09/2016
889	2^678651+1875023	204295	Enzo Doria	07/2016
890	2^678561+678561	204268	Henri Lifchitz	05/2006
891	2^678101-114043	204129	Enzo Doria	11/2014
892	2^678028+1875631	204107	Enzo Doria	06/2016
893	2^676992-59783	203795	Enzo Doria	10/2015
894	2^676972+1866871	203789	Enzo Doria	03/2016
895	2^676761-9	203726	Robert Price	01/2017
896	2^676563-2792407	203666	Enzo Doria	02/2016
897	2^676306-114713	203589	Enzo Doria	04/2015
898	(2^675977-1)/(1686378749257*7171117283326998925471)	203456	Dario Alpern	07/2015
899	2^674627-25161	203083	Enzo Doria	09/2013
900	2^674603-69337	203076	Enzo Doria	12/2015
901	2^674459+74213	203033	Enzo Doria	04/2016
902	2^674116-458879	202930	Enzo Doria	04/2015
903	2^674076-114755	202918	Enzo Doria	04/2015
904	5^289937-4^289937	202658	Jean-Louis Charton	03/2013
905	(467617#+14534)/(2^21343)	202603	Makoto Morimoto	06/2019
906	2^672556-1835519	202460	Enzo Doria	04/2015
907	2^671446-351401	202126	Enzo Doria	07/2015
908	2^671373+77747	202104	Enzo Doria	05/2016
909	2^670726-114845	201909	Enzo Doria	05/2015
910	2^670539-25045	201853	Enzo Doria	09/2013
911	43284^43519-43519^43284	201769	Norbert Schneider	08/2018
912	2^670213+282317	201755	Enzo Doria	09/2016
913	2^669854-113501	201647	Enzo Doria	08/2014
914	2^669718+81619	201606	Enzo Doria	08/2016
915	(145*10^201504-1)/9	201506	Serge Batalov	12/2014
916	2^668938-1839821	201371	Enzo Doria	06/2015
917	2^668492+1879303	201237	Enzo Doria	08/2016
918	6^258413-5^258413	201085	Jean-Louis Charton	03/2013
919	10194^50161-50161^10194	201063	Norbert Schneider	09/2020
920	2^667894+1875589	201057	Enzo Doria	06/2016
921	2^667569-1836559	200959	Enzo Doria	05/2015
922	(172*10^200746-1)/9	200748	Serge Batalov	12/2014
923	2^666430+782569	200616	Enzo Doria	10/2016
924	(86^103471+1)/87	200163	Paul Bourdelais	05/2018
925	103(10^100000+20110)^2-4707(10^100000+20110)+50383	200003	Robert Price	05/2017
926	103(10^100000+33798)^2-4707(10^100000+33798)+50383	200003	Robert Price	01/2018
927	numbpart(32235776596)	200002	Serge Batalov	04/2017
928	(10^200001+149)/3	200001	Serge Batalov	12/2014
929	10^200000+571791	200001	Patrick De Geest	08/2019
930	(3^419180-621444)/3	200000	Stefano Morozzi	06/2019
931	(3^419180-1941384)/3	200000	Stefano Morozzi	08/2019
932	10^200000-45557	200000	Patrick De Geest	08/2019
933	(10^200000-1)/9-10^58838	200000	Akihiko Yoshida	04/2020
934	(299*10^199801-17)/3	199803	Robert Price	04/2020
935	6*10^199788+77	199789	Robert Price	06/2020
936	(14*10^199447+73)/3	199448	Robert Price	12/2018
937	2^662103-29287	199313	Enzo Doria	08/2015
938	(2*10^199283+457)/9	199283	Robert Price	01/2018
939	(10^199248-19)/9	199248	Robert Price	01/2018
940	(194*10^199146-17)/3	199148	Robert Price	09/2020
941	(151*10^199003-1)/3	199005	Robert Price	03/2020
942	9*10^198946-73	198947	Robert Price	01/2021
943	45*10^198931-7	198933	Robert Price	07/2020
944	2^660482-2891	198825	Yves Minet	05/2016
945	2^659583+1879223	198555	Enzo Doria	08/2016
946	(53*10^198529+1)/9	198530	Serge Batalov	07/2010
947	(49*10^198403+311)/9	198404	Robert Price	06/2019
948	2^658828-29819	198327	Enzo Doria	08/2015
949	2^658776-2791229	198312	Enzo Doria	01/2016
950	(35*10^198294-377)/9	198295	Robert Price	07/2018
951	(4*10^198268+137)/3	198269	Robert Price	03/2018
952	2^658544-1854029	198242	Enzo Doria	09/2015
953	(157^90239-1)/156	198154	Alexander Zhirkov	06/2016
954	(4*10^197778+173)/3	197779	Robert Price	02/2018
955	78*10^197702-7	197704	Robert Price	10/2020
956	(29*10^197629-77)/3	197630	Robert Price	02/2020
957	2^656462+1874419	197615	Enzo Doria	06/2016
958	(89^101363+1)/90	197595	Paul Bourdelais	11/2017
959	2^655893-344563	197444	Enzo Doria	07/2015
960	2^655875+71333	197439	Enzo Doria	04/2016
961	2^655845-9	197430	Robert Price	01/2017
962	(299*10^197426+1)/3	197428	Robert Price	04/2020
963	2^655682-1849121	197380	Enzo Doria	08/2015
964	4*10^197268-89	197269	Robert Price	11/2018
965	2^655045-49603	197189	Enzo Doria	10/2015
966	2^655000-2784089	197175	Enzo Doria	10/2015
967	(18^157051-1)/17	197141	Paul Bourdelais	03/2010
968	2^654400-39719	196995	Enzo Doria	09/2015
969	(14*10^196965-221)/9	196966	Robert Price	04/2018
970	2^654216-459995	196939	Enzo Doria	06/2015
971	(17*10^196921+31)/3	196922	Robert Price	01/2019
972	(14*10^196885-89)/3	196886	Robert Price	05/2020
973	3*10^196881-59	196882	Robert Price	09/2018
974	2^653851+82295	196829	Enzo Doria	09/2016
975	(38*10^196792+691)/9	196793	Robert Price	10/2018
976	2^653636-29429	196765	Enzo Doria	08/2015
977	2^653601-69673	196754	Enzo Doria	02/2016
978	(44*10^196684+1)/9	196685	Serge Batalov	07/2010
979	2^652786-1852571	196509	Enzo Doria	08/2015
980	2^652752-1325	196498	Yves Minet	07/2015
981	2^652470-1859141	196414	Enzo Doria	10/2015
982	2^652307+1877483	196364	Enzo Doria	08/2016
983	2^652293-115273	196360	Enzo Doria	06/2015
984	(47*10^196281+403)/9	196282	Robert Price	03/2019
985	6*10^196070+73	196071	Robert Price	04/2019
986	2^651218-1868201	196037	Enzo Doria	04/2016
987	2^651047-49687	195985	Enzo Doria	10/2015
988	2^650285-2785333	195756	Enzo Doria	10/2015
989	(69^106397-1)/68	195647	Paul Bourdelais	10/2017
990	2^649811+1877573	195613	Enzo Doria	08/2016
991	2^649662-170531	195568	Hans Havermann	10/2018
992	2^649586+182839	195545	Enzo Doria	11/2016
993	2^649537-1867363	195531	Enzo Doria	04/2016
994	2^649536-1861499	195530	Enzo Doria	12/2015
995	(103*10^195478-1)/3	195480	Serge Batalov	12/2014
996	2^649102-59351	195400	Enzo Doria	10/2015
997	(2*10^195399+529)/9	195399	Robert Price	01/2018
998	(202*10^195383-13)/9	195385	Robert Price	01/2020
999	2^648988+1178971	195365	Enzo Doria	06/2016
1000	2^648975-114319	195361	Enzo Doria	02/2015

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Probable Primes Top 10000

(277054 PRPs in the top)