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	2^693462-1847561	208753	Enzo Doria	07/2015
752	2^690890-59981	207979	Enzo Doria	11/2015
753	(38^131591+1)/39	207884	Paul Bourdelais	07/2018
754	2^690163+1877063	207760	Enzo Doria	07/2016
755	2^689286-29381	207496	Enzo Doria	08/2015
756	2^689122-114521	207447	Enzo Doria	04/2015
757	2^688373+6077	207221	Enzo Doria	02/2016
758	2^688201+1875527	207170	Enzo Doria	07/2016
759	(42^127609+1)/43	207140	Paul Bourdelais	07/2018
760	2^687619+81563	206994	Enzo Doria	08/2016
761	2^686572-1845299	206679	Enzo Doria	07/2015
762	(21^156217-1)/20	206552	Paul Bourdelais	04/2010
763	(2^685739+1)/(3*87774593)	206420	Gord Palameta	08/2018
764	2^685578+3	206380	Paul Bourdelais	04/2012
765	2^684836-49349	206157	Enzo Doria	10/2015
766	(73^110603-1)/72	206088	Paul Bourdelais	06/2018
767	2^684163-2790967	205954	Enzo Doria	12/2015
768	326^81943-325^81943	205941	Jean-Louis Charton	07/2012
769	(2^684127-1)/23765203727	205933	Jens K. Andersen	04/2009
770	4^341233-3^341233	205443	Jean-Louis Charton	01/2006
771	2^681545+467	205166	Lelio R Paula	11/2013
772	2^681306+81049	205094	Enzo Doria	07/2016
773	2^680697+1877057	204911	Enzo Doria	07/2016
774	2^680415+71783	204826	Enzo Doria	04/2016
775	2^679860-459995	204659	Enzo Doria	06/2015
776	2^679593+1879547	204578	Enzo Doria	09/2016
777	2^678651+1875023	204295	Enzo Doria	07/2016
778	2^678561+678561	204268	Henri Lifchitz	05/2006
779	2^678101-114043	204129	Enzo Doria	11/2014
780	2^678028+1875631	204107	Enzo Doria	06/2016
781	2^676992-59783	203795	Enzo Doria	10/2015
782	2^676972+1866871	203789	Enzo Doria	03/2016
783	2^676761-9	203726	Robert Price	01/2017
784	2^676563-2792407	203666	Enzo Doria	02/2016
785	2^676306-114713	203589	Enzo Doria	04/2015
786	(2^675977-1)/(1686378749257*7171117283326998925471)	203456	Dario Alpern	07/2015
787	2^674627-25161	203083	Enzo Doria	09/2013
788	2^674603-69337	203076	Enzo Doria	12/2015
789	2^674459+74213	203033	Enzo Doria	04/2016
790	2^674116-458879	202930	Enzo Doria	04/2015
791	2^674076-114755	202918	Enzo Doria	04/2015
792	5^289937-4^289937	202658	Jean-Louis Charton	03/2013
793	(467617#+14534)/(2^21343)	202603	Makoto Morimoto	06/2019
794	2^672556-1835519	202460	Enzo Doria	04/2015
795	2^671446-351401	202126	Enzo Doria	07/2015
796	2^671373+77747	202104	Enzo Doria	05/2016
797	2^670726-114845	201909	Enzo Doria	05/2015
798	2^670539-25045	201853	Enzo Doria	09/2013
799	43284^43519-43519^43284	201769	Norbert Schneider	08/2018
800	2^670213+282317	201755	Enzo Doria	09/2016
801	2^669854-113501	201647	Enzo Doria	08/2014
802	2^669718+81619	201606	Enzo Doria	08/2016
803	(145*10^201504-1)/9	201506	Serge Batalov	12/2014
804	2^668938-1839821	201371	Enzo Doria	06/2015
805	2^668492+1879303	201237	Enzo Doria	08/2016
806	6^258413-5^258413	201085	Jean-Louis Charton	03/2013
807	2^667894+1875589	201057	Enzo Doria	06/2016
808	2^667569-1836559	200959	Enzo Doria	05/2015
809	(172*10^200746-1)/9	200748	Serge Batalov	12/2014
810	2^666430+782569	200616	Enzo Doria	10/2016
811	(86^103471+1)/87	200163	Paul Bourdelais	05/2018
813	103(10^100000+20110)^2-4707(10^100000+20110)+50383	200003	Robert Price	05/2017
812	103(10^100000+33798)^2-4707(10^100000+33798)+50383	200003	Robert Price	01/2018
814	numbpart(32235776596)	200002	Serge Batalov	04/2017
815	(10^200001+149)/3	200001	Serge Batalov	12/2014
816	10^200000+571791	200001	Patrick De Geest	08/2019
817	(3^419180-621444)/3	200000	Stefano Morozzi	06/2019
818	(3^419180-1941384)/3	200000	Stefano Morozzi	08/2019
819	10^200000-45557	200000	Patrick De Geest	08/2019
820	(14*10^199447+73)/3	199448	Robert Price	12/2018
821	2^662103-29287	199313	Enzo Doria	08/2015
822	(2*10^199283+457)/9	199283	Robert Price	01/2018
823	(10^199248-19)/9	199248	Robert Price	01/2018
824	2^660482-2891	198825	Yves Minet	05/2016
825	2^659583+1879223	198555	Enzo Doria	08/2016
826	(53*10^198529+1)/9	198530	Serge Batalov	07/2010
827	(49*10^198403+311)/9	198404	Robert Price	06/2019
828	2^658828-29819	198327	Enzo Doria	08/2015
829	2^658776-2791229	198312	Enzo Doria	01/2016
830	(35*10^198294-377)/9	198295	Robert Price	07/2018
831	(4*10^198268+137)/3	198269	Robert Price	03/2018
832	2^658544-1854029	198242	Enzo Doria	09/2015
833	(157^90239-1)/156	198154	Alexander Zhirkov	06/2016
834	(4*10^197778+173)/3	197779	Robert Price	02/2018
835	2^656462+1874419	197615	Enzo Doria	06/2016
836	(89^101363+1)/90	197595	Paul Bourdelais	11/2017
837	2^655893-344563	197444	Enzo Doria	07/2015
838	2^655875+71333	197439	Enzo Doria	04/2016
839	2^655845-9	197430	Robert Price	01/2017
840	2^655682-1849121	197380	Enzo Doria	08/2015
841	4*10^197268-89	197269	Robert Price	11/2018
842	2^655045-49603	197189	Enzo Doria	10/2015
843	2^655000-2784089	197175	Enzo Doria	10/2015
844	(18^157051-1)/17	197141	Paul Bourdelais	03/2010
845	2^654400-39719	196995	Enzo Doria	09/2015
846	(14*10^196965-221)/9	196966	Robert Price	04/2018
847	2^654216-459995	196939	Enzo Doria	06/2015
848	(17*10^196921+31)/3	196922	Robert Price	01/2019
849	3*10^196881-59	196882	Robert Price	09/2018
850	2^653851+82295	196829	Enzo Doria	09/2016
851	(38*10^196792+691)/9	196793	Robert Price	10/2018
852	2^653636-29429	196765	Enzo Doria	08/2015
853	2^653601-69673	196754	Enzo Doria	02/2016
854	(44*10^196684+1)/9	196685	Serge Batalov	07/2010
855	2^652786-1852571	196509	Enzo Doria	08/2015
856	2^652752-1325	196498	Yves Minet	07/2015
857	2^652470-1859141	196414	Enzo Doria	10/2015
858	2^652307+1877483	196364	Enzo Doria	08/2016
859	2^652293-115273	196360	Enzo Doria	06/2015
860	(47*10^196281+403)/9	196282	Robert Price	03/2019
861	6*10^196070+73	196071	Robert Price	04/2019
862	2^651218-1868201	196037	Enzo Doria	04/2016
863	2^651047-49687	195985	Enzo Doria	10/2015
864	2^650285-2785333	195756	Enzo Doria	10/2015
865	(69^106397-1)/68	195647	Paul Bourdelais	10/2017
866	2^649811+1877573	195613	Enzo Doria	08/2016
867	2^649662-170531	195568	Hans Havermann	10/2018
868	2^649586+182839	195545	Enzo Doria	11/2016
869	2^649537-1867363	195531	Enzo Doria	04/2016
870	2^649536-1861499	195530	Enzo Doria	12/2015
871	(103*10^195478-1)/3	195480	Serge Batalov	12/2014
872	2^649102-59351	195400	Enzo Doria	10/2015
873	(2*10^195399+529)/9	195399	Robert Price	01/2018
874	2^648988+1178971	195365	Enzo Doria	06/2016
875	2^648975-114319	195361	Enzo Doria	02/2015
876	(11*10^195350-137)/9	195351	Robert Price	01/2018
877	2^648619-24835	195254	Enzo Doria	09/2013
878	(14*10^195234-83)/3	195235	Robert Price	12/2018
879	5*10^195221+81	195222	Robert Price	03/2019
880	2^648190-24737	195125	Enzo Doria	09/2013
881	(57^111119+1)/58	195110	Paul Bourdelais	10/2017
882	11^187185-90	194934	Enzo Doria	09/2012
883	2^647068+77281	194787	Enzo Doria	05/2016
884	15^165559-14^165559	194713	Jean-Louis Charton	03/2011
885	F(931517)	194676	Henri Lifchitz	09/2008
886	4*10^194668+49	194669	Robert Price	01/2019
887	2^646589+1179407	194643	Enzo Doria	06/2016
888	2^646289-114621	194553	Enzo Doria	05/2015
889	2^646236-39659	194537	Enzo Doria	09/2015
890	(16*10^194536+53)/3	194537	Robert Price	03/2019
891	2^646161-59833	194514	Enzo Doria	11/2015
892	(17*10^194502+31)/3	194503	Robert Price	01/2019
893	2*10^194413+3	194414	Robert Price	07/2015
894	2^645360-1848599	194273	Enzo Doria	08/2015
895	(112*10^194150-1)/3	194152	Serge Batalov	12/2014
896	2*10^193981-43	193982	Robert Price	04/2018
897	2^644382+75169	193979	Enzo Doria	04/2016
898	2^644304-1861409	193955	Enzo Doria	11/2015
899	5*10^193907-9	193908	Robert Price	05/2015
900	2^644043+1876703	193877	Enzo Doria	07/2016
901	2^643735+1879733	193784	Enzo Doria	09/2016
902	(5^277183+1)/6	193742	Paul Bourdelais	07/2010
903	2^643216-286565	193628	Enzo Doria	07/2015
904	2^642888-24965	193529	Enzo Doria	09/2013
905	2^642448-114825	193397	Enzo Doria	05/2015
906	2^642437-1856623	193393	Enzo Doria	10/2015
907	2^642039-59797	193273	Enzo Doria	11/2015
908	10^193230+513861	193231	Patrick De Geest	07/2018
909	10^193230-8001	193230	Robert Price	03/2018
910	2^641692-286349	193169	Enzo Doria	07/2015
911	2^641690-24737	193168	Enzo Doria	09/2013
912	2^641514+1876549	193115	Enzo Doria	07/2016
913	2^640888-2785619	192927	Enzo Doria	10/2015
914	2^640874-2783741	192923	Enzo Doria	09/2015
915	(46*10^192841+683)/9	192842	Robert Price	03/2019
916	2^640181+467	192714	Lelio R Paula	08/2013
917	2^639536-1850249	192520	Enzo Doria	08/2015
918	5*10^192422-43	192423	Robert Price	01/2019
919	2^639110-2792441	192392	Enzo Doria	02/2016
920	2^638955-29827	192345	Enzo Doria	08/2015
921	2^638713-2784223	192272	Enzo Doria	10/2015
922	2^638490-113507	192205	Enzo Doria	08/2014
923	2^638189-39943	192115	Enzo Doria	09/2015
924	2^638110+1877119	192091	Enzo Doria	07/2016
925	2^638066-2785211	192078	Enzo Doria	10/2015
926	2^637475-115309	191900	Enzo Doria	07/2015
927	2^636661+1876577	191655	Enzo Doria	07/2016
928	(34^125101-1)/33	191589	Paul Bourdelais	11/2017
929	2^636177-1855123	191509	Enzo Doria	09/2015
930	2^636158-113627	191503	Enzo Doria	08/2014
931	(37*25^136966+63)/4	191472	Curtis Bright	05/2015
932	2^636035+79823	191466	Enzo Doria	06/2016
933	2^636011-1860847	191459	Enzo Doria	11/2015
934	2^635926-1860611	191433	Enzo Doria	11/2015
935	3*10^191152-7	191153	Robert Price	08/2015
936	2^634883-1865677	191119	Enzo Doria	02/2016
937	2^634801+1871957	191095	Enzo Doria	05/2016
938	(35*10^191073+1)/9	191074	Serge Batalov	07/2010
939	2^634470-59861	190995	Enzo Doria	11/2015
940	2^634368-29519	190964	Enzo Doria	08/2015
941	2^634188-350609	190910	Enzo Doria	06/2015
942	(13*10^190732-61)/3	190733	Robert Price	11/2018
943	(7*10^190683+143)/3	190684	Robert Price	03/2018
944	2^633088-113879	190579	Enzo Doria	10/2014
945	2^633064+1874911	190572	Enzo Doria	06/2016
946	(43*10^190547+83)/9	190548	Robert Price	11/2018
947	2^632795-351205	190491	Enzo Doria	06/2015
948	(16*10^190420-19)/3	190421	Robert Price	02/2019
949	(43*10^190351+101)/9	190352	Robert Price	11/2018
950	2^632156+78391	190298	Enzo Doria	06/2016
951	2^632082-1851971	190276	Enzo Doria	08/2015
952	2^632020+1880311	190257	Enzo Doria	09/2016
953	2^631637-462373	190142	Enzo Doria	08/2015
954	2^631122-39251	189987	Enzo Doria	08/2015
955	(26*10^189928-89)/9	189929	Robert Price	06/2018
956	2^630839-97	189902	Yves Minet	07/2017
957	2^630359+1788953	189757	Enzo Doria	05/2016
958	2^630228+1871971	189718	Enzo Doria	05/2016
959	2^630108+781	189682	Lelio R Paula	08/2013
960	2^629870-1867811	189610	Enzo Doria	04/2016
961	(359^74189-1)/358	189558	Alexander Zhirkov	11/2017
962	2^629326+2792929	189447	Enzo Doria	02/2016
963	(10^189385-61)/3	189385	Serge Batalov	12/2014
964	2^629036+1874011	189359	Enzo Doria	06/2016
965	2^628930+80779	189327	Enzo Doria	07/2016
966	2^628582+1179439	189223	Enzo Doria	06/2016
967	(44*10^188999-503)/9	189000	Robert Price	12/2018
968	(16*10^188823+167)/3	188824	Robert Price	06/2019
969	2^627037-2785843	188757	Enzo Doria	10/2015
970	(16*10^188457+161)/3	188458	Robert Price	02/2019
971	L(901657)	188436	Renaud Lifchitz	11/2008
972	2^625651+74213	188340	Enzo Doria	04/2016
973	2^625584-460919	188320	Enzo Doria	06/2015
974	(10^188164+359)/9	188164	Serge Batalov	12/2014
975	2^624481-113611	187988	Enzo Doria	08/2014
976	2^624077-112723	187866	Enzo Doria	07/2014
977	2^624008+1874941	187846	Enzo Doria	06/2016
978	2^623870+78679	187804	Enzo Doria	05/2016
979	2^623714-114035	187757	Enzo Doria	11/2014
980	2^623651-1834251	187738	Enzo Doria	07/2015
981	(7*10^187645+53)/3	187646	Robert Price	05/2018
982	2^623146+1879609	187586	Enzo Doria	09/2016
983	(5*10^187471+91)/3	187472	Robert Price	04/2018
984	2^622500+81931	187392	Enzo Doria	08/2016
985	2^622300-1861739	187331	Enzo Doria	12/2015
986	(38*10^187281+349)/9	187282	Robert Price	10/2018
987	2^622052+76771	187257	Enzo Doria	05/2016
988	2^622005-24091	187243	Enzo Doria	08/2013
989	2^621879-351787	187205	Enzo Doria	07/2015
990	2^621700+79411	187151	Enzo Doria	06/2016
991	(2*10^187062-71)/3	187062	Robert Price	12/2017
992	2^620929-113203	186919	Enzo Doria	07/2014
993	10^186842+168223	186843	Patrick De Geest	07/2018
994	10^186842-8001	186842	Robert Price	03/2018
995	2^620347-1777	186744	Lelio R Paula	07/2013
996	11^179143-4170	186559	Enzo Doria	12/2012
997	(5^266863+1)/6	186529	Paul Bourdelais	07/2010
998	2^619297-2792353	186427	Enzo Doria	02/2016
999	(49*10^186409+383)/9	186410	Robert Price	04/2019
1000	2^618940-460139	186320	Enzo Doria	06/2015

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PRP Records

Probable Primes Top 10000

(253476 PRPs in the top)