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	2^730645-2787133	219947	Enzo Doria	11/2015
752	2^730547-25581	219917	Enzo Doria	09/2013
753	2^730460+82291	219891	Enzo Doria	09/2016
754	(2^730339+1)/(3278390620037943469324347)	219831	Gord Palameta	12/2018
755	L(1051849)	219824	Renaud Lifchitz	03/2009
756	11^210961-240	219694	Enzo Doria	01/2013
757	2^729611-113437	219635	Enzo Doria	08/2014
758	F(1049897)	219416	Henri Lifchitz	10/2008
759	2^728604+1879321	219332	Enzo Doria	10/2016
760	33^144412+2	219292	Robert Price	04/2015
761	2^728277-183313	219234	Hans Havermann	10/2018
762	2^727998-1862711	219150	Enzo Doria	12/2015
763	2^727729-114073	219069	Enzo Doria	12/2014
764	2^727496-1851809	218999	Enzo Doria	08/2015
765	2^726591+2793143	218726	Enzo Doria	02/2016
766	2^725534-2791931	218408	Enzo Doria	02/2016
767	2^722184+1877821	217400	Enzo Doria	08/2016
768	(109*10^217360-1)/9	217362	Serge Batalov	12/2014
769	281*499979#/46410-2702372	216849	Robert Smith	08/2016
770	281*499979#/46410+2400766	216849	Robert Smith	08/2016
771	tau(311^15786)	216429	Nik Lygeros / Olivier Rozier / LR team	10/2013
772	2^718756-114107	216368	Enzo Doria	12/2014
773	2^717305+80327	215931	Enzo Doria	07/2016
774	2^717069-59773	215860	Enzo Doria	10/2015
775	30^146021-29^146021	215691	Jean-Louis Charton	09/2018
776	277^88301-276^88301	215674	Jean-Louis Charton	06/2012
777	227^91413-40	215372	Enzo Doria	04/2015
778	2^714717+782897	215152	Enzo Doria	11/2016
779	tau(373^15186)	214796	Nik Lygeros / Olivier Rozier / LR team	10/2013
780	2^713241+1879157	214707	Enzo Doria	08/2016
781	11^206081-10^206081	214612	Jean-Louis Charton	10/2011
782	2^712801-69553	214575	Enzo Doria	01/2016
783	2^712603-25357	214515	Enzo Doria	09/2013
784	2^711721-1846723	214250	Enzo Doria	07/2015
785	2^710730-396765	213952	Enzo Doria	09/2013
786	2^708468-114329	213271	Enzo Doria	02/2015
787	(163*10^212779-1)/9	212781	Serge Batalov	12/2014
788	2^706838-69041	212780	Enzo Doria	11/2015
789	2^704577-113871	212099	Enzo Doria	10/2014
790	2^704110-2792441	211959	Enzo Doria	02/2016
791	2^703943-1862947	211908	Enzo Doria	12/2015
792	(60^119083+1)/61	211746	Paul Bourdelais	10/2018
793	(10^211610-91)/9	211610	Serge Batalov	12/2014
794	227^89797+2	211565	Lelio R Paula	08/2012
795	2^702194-3	211382	Paul Bourdelais	03/2012
796	2^702064+1874911	211343	Enzo Doria	07/2016
797	2^701968-113873	211314	Enzo Doria	10/2014
798	2^701713-113779	211237	Enzo Doria	09/2014
799	2^701449-25201	211158	Enzo Doria	09/2013
800	2^701403-2786977	211144	Enzo Doria	11/2015
801	2^701189-25423	211079	Enzo Doria	09/2013
802	2^701162-459161	211071	Enzo Doria	05/2015
803	(24^152783-1)/23	210872	Paul Bourdelais	04/2018
804	2^700400+9385	210842	Lelio R Paula	01/2014
805	2^700131+1874693	210761	Enzo Doria	06/2016
806	(2^700095+225414)/2	210750	Stefano Morozzi	04/2020
807	(2^700090+278254)/2	210748	Stefano Morozzi	04/2020
808	(2^700075+303666)/2	210744	Stefano Morozzi	04/2020
809	(2^700073+75882)/2	210743	Stefano Morozzi	04/2020
810	(2^700074+328890)/2	210743	Stefano Morozzi	04/2020
811	(2^700052+79162)/2	210737	Stefano Morozzi	04/2020
812	(2^700052+304458)/2	210737	Stefano Morozzi	04/2020
813	(2^700048+376578)/2	210736	Stefano Morozzi	04/2020
814	11^202357-1140	210734	Enzo Doria	12/2012
815	(2^700021+25874)/2	210728	Stefano Morozzi	04/2020
816	(2^700018+377518)/2	210727	Stefano Morozzi	04/2020
817	2^698929-2788423	210399	Enzo Doria	11/2015
818	(5^300893+4^300893)/9	210315	Jean-Louis Charton	11/2011
819	2^698316+1878601	210215	Enzo Doria	08/2016
820	2^697036+1878751	209829	Enzo Doria	08/2016
821	(2^696343-1)/11141489/36009913139329	209600	Tony Prest / Never Odd Or Even	02/2014
822	2^696254-115151	209594	Enzo Doria	06/2015
823	(35^135623+1)/36	209410	Paul Bourdelais	07/2018
824	2^694633+1887257	209106	Enzo Doria	05/2017
825	2^693959+180923	208903	Enzo Doria	07/2016
826	2^693462-1847561	208753	Enzo Doria	07/2015
827	2^690890-59981	207979	Enzo Doria	11/2015
828	(38^131591+1)/39	207884	Paul Bourdelais	07/2018
829	2^690163+1877063	207760	Enzo Doria	07/2016
830	2^689286-29381	207496	Enzo Doria	08/2015
831	2^689122-114521	207447	Enzo Doria	04/2015
832	2^688373+6077	207221	Enzo Doria	02/2016
833	2^688201+1875527	207170	Enzo Doria	07/2016
834	(42^127609+1)/43	207140	Paul Bourdelais	07/2018
835	2^687619+81563	206994	Enzo Doria	08/2016
836	2^686572-1845299	206679	Enzo Doria	07/2015
837	(21^156217-1)/20	206552	Paul Bourdelais	04/2010
838	(2^685739+1)/(3*87774593)	206420	Gord Palameta	08/2018
839	2^685578+3	206380	Paul Bourdelais	04/2012
840	2^684836-49349	206157	Enzo Doria	10/2015
841	(73^110603-1)/72	206088	Paul Bourdelais	06/2018
842	2^684163-2790967	205954	Enzo Doria	12/2015
843	326^81943-325^81943	205941	Jean-Louis Charton	07/2012
844	(2^684127-1)/23765203727	205933	Jens K. Andersen	04/2009
845	4^341233-3^341233	205443	Jean-Louis Charton	01/2006
846	2^681545+467	205166	Lelio R Paula	11/2013
847	2^681306+81049	205094	Enzo Doria	07/2016
848	2^680697+1877057	204911	Enzo Doria	07/2016
849	2^680415+71783	204826	Enzo Doria	04/2016
850	2^679860-459995	204659	Enzo Doria	06/2015
851	2^679593+1879547	204578	Enzo Doria	09/2016
852	2^678651+1875023	204295	Enzo Doria	07/2016
853	2^678561+678561	204268	Henri Lifchitz	05/2006
854	2^678101-114043	204129	Enzo Doria	11/2014
855	2^678028+1875631	204107	Enzo Doria	06/2016
856	2^676992-59783	203795	Enzo Doria	10/2015
857	2^676972+1866871	203789	Enzo Doria	03/2016
858	2^676761-9	203726	Robert Price	01/2017
859	2^676563-2792407	203666	Enzo Doria	02/2016
860	2^676306-114713	203589	Enzo Doria	04/2015
861	(2^675977-1)/(1686378749257*7171117283326998925471)	203456	Dario Alpern	07/2015
862	2^674627-25161	203083	Enzo Doria	09/2013
863	2^674603-69337	203076	Enzo Doria	12/2015
864	2^674459+74213	203033	Enzo Doria	04/2016
865	2^674116-458879	202930	Enzo Doria	04/2015
866	2^674076-114755	202918	Enzo Doria	04/2015
867	5^289937-4^289937	202658	Jean-Louis Charton	03/2013
868	(467617#+14534)/(2^21343)	202603	Makoto Morimoto	06/2019
869	2^672556-1835519	202460	Enzo Doria	04/2015
870	2^671446-351401	202126	Enzo Doria	07/2015
871	2^671373+77747	202104	Enzo Doria	05/2016
872	2^670726-114845	201909	Enzo Doria	05/2015
873	2^670539-25045	201853	Enzo Doria	09/2013
874	43284^43519-43519^43284	201769	Norbert Schneider	08/2018
875	2^670213+282317	201755	Enzo Doria	09/2016
876	2^669854-113501	201647	Enzo Doria	08/2014
877	2^669718+81619	201606	Enzo Doria	08/2016
878	(145*10^201504-1)/9	201506	Serge Batalov	12/2014
879	2^668938-1839821	201371	Enzo Doria	06/2015
880	2^668492+1879303	201237	Enzo Doria	08/2016
881	6^258413-5^258413	201085	Jean-Louis Charton	03/2013
882	10194^50161-50161^10194	201063	Norbert Schneider	09/2020
883	2^667894+1875589	201057	Enzo Doria	06/2016
884	2^667569-1836559	200959	Enzo Doria	05/2015
885	(172*10^200746-1)/9	200748	Serge Batalov	12/2014
886	2^666430+782569	200616	Enzo Doria	10/2016
887	(86^103471+1)/87	200163	Paul Bourdelais	05/2018
889	103(10^100000+20110)^2-4707(10^100000+20110)+50383	200003	Robert Price	05/2017
888	103(10^100000+33798)^2-4707(10^100000+33798)+50383	200003	Robert Price	01/2018
890	numbpart(32235776596)	200002	Serge Batalov	04/2017
891	(10^200001+149)/3	200001	Serge Batalov	12/2014
892	10^200000+571791	200001	Patrick De Geest	08/2019
893	(3^419180-621444)/3	200000	Stefano Morozzi	06/2019
894	(3^419180-1941384)/3	200000	Stefano Morozzi	08/2019
895	10^200000-45557	200000	Patrick De Geest	08/2019
896	(10^200000-1)/9-10^58838	200000	Akihiko Yoshida	04/2020
897	(299*10^199801-17)/3	199803	Robert Price	04/2020
898	6*10^199788+77	199789	Robert Price	06/2020
899	(14*10^199447+73)/3	199448	Robert Price	12/2018
900	2^662103-29287	199313	Enzo Doria	08/2015
901	(2*10^199283+457)/9	199283	Robert Price	01/2018
902	(10^199248-19)/9	199248	Robert Price	01/2018
903	(194*10^199146-17)/3	199148	Robert Price	09/2020
904	(151*10^199003-1)/3	199005	Robert Price	03/2020
905	45*10^198931-7	198933	Robert Price	07/2020
906	2^660482-2891	198825	Yves Minet	05/2016
907	2^659583+1879223	198555	Enzo Doria	08/2016
908	(53*10^198529+1)/9	198530	Serge Batalov	07/2010
909	(49*10^198403+311)/9	198404	Robert Price	06/2019
910	2^658828-29819	198327	Enzo Doria	08/2015
911	2^658776-2791229	198312	Enzo Doria	01/2016
912	(35*10^198294-377)/9	198295	Robert Price	07/2018
913	(4*10^198268+137)/3	198269	Robert Price	03/2018
914	2^658544-1854029	198242	Enzo Doria	09/2015
915	(157^90239-1)/156	198154	Alexander Zhirkov	06/2016
916	(4*10^197778+173)/3	197779	Robert Price	02/2018
917	(29*10^197629-77)/3	197630	Robert Price	02/2020
918	2^656462+1874419	197615	Enzo Doria	06/2016
919	(89^101363+1)/90	197595	Paul Bourdelais	11/2017
920	2^655893-344563	197444	Enzo Doria	07/2015
921	2^655875+71333	197439	Enzo Doria	04/2016
922	2^655845-9	197430	Robert Price	01/2017
923	(299*10^197426+1)/3	197428	Robert Price	04/2020
924	2^655682-1849121	197380	Enzo Doria	08/2015
925	4*10^197268-89	197269	Robert Price	11/2018
926	2^655045-49603	197189	Enzo Doria	10/2015
927	2^655000-2784089	197175	Enzo Doria	10/2015
928	(18^157051-1)/17	197141	Paul Bourdelais	03/2010
929	2^654400-39719	196995	Enzo Doria	09/2015
930	(14*10^196965-221)/9	196966	Robert Price	04/2018
931	2^654216-459995	196939	Enzo Doria	06/2015
932	(17*10^196921+31)/3	196922	Robert Price	01/2019
933	(14*10^196885-89)/3	196886	Robert Price	05/2020
934	3*10^196881-59	196882	Robert Price	09/2018
935	2^653851+82295	196829	Enzo Doria	09/2016
936	(38*10^196792+691)/9	196793	Robert Price	10/2018
937	2^653636-29429	196765	Enzo Doria	08/2015
938	2^653601-69673	196754	Enzo Doria	02/2016
939	(44*10^196684+1)/9	196685	Serge Batalov	07/2010
940	2^652786-1852571	196509	Enzo Doria	08/2015
941	2^652752-1325	196498	Yves Minet	07/2015
942	2^652470-1859141	196414	Enzo Doria	10/2015
943	2^652307+1877483	196364	Enzo Doria	08/2016
944	2^652293-115273	196360	Enzo Doria	06/2015
945	(47*10^196281+403)/9	196282	Robert Price	03/2019
946	6*10^196070+73	196071	Robert Price	04/2019
947	2^651218-1868201	196037	Enzo Doria	04/2016
948	2^651047-49687	195985	Enzo Doria	10/2015
949	2^650285-2785333	195756	Enzo Doria	10/2015
950	(69^106397-1)/68	195647	Paul Bourdelais	10/2017
951	2^649811+1877573	195613	Enzo Doria	08/2016
952	2^649662-170531	195568	Hans Havermann	10/2018
953	2^649586+182839	195545	Enzo Doria	11/2016
954	2^649537-1867363	195531	Enzo Doria	04/2016
955	2^649536-1861499	195530	Enzo Doria	12/2015
956	(103*10^195478-1)/3	195480	Serge Batalov	12/2014
957	2^649102-59351	195400	Enzo Doria	10/2015
958	(2*10^195399+529)/9	195399	Robert Price	01/2018
959	(202*10^195383-13)/9	195385	Robert Price	01/2020
960	2^648988+1178971	195365	Enzo Doria	06/2016
961	2^648975-114319	195361	Enzo Doria	02/2015
962	(11*10^195350-137)/9	195351	Robert Price	01/2018
963	2^648619-24835	195254	Enzo Doria	09/2013
964	(14*10^195234-83)/3	195235	Robert Price	12/2018
965	5*10^195221+81	195222	Robert Price	03/2019
966	2^648190-24737	195125	Enzo Doria	09/2013
967	(57^111119+1)/58	195110	Paul Bourdelais	10/2017
968	10^195060-40000000001	195060	Robert Price	09/2020
969	56*10^195032-3	195034	Robert Price	03/2020
970	11^187185-90	194934	Enzo Doria	09/2012
971	2^647068+77281	194787	Enzo Doria	05/2016
972	15^165559-14^165559	194713	Jean-Louis Charton	03/2011
973	F(931517)	194676	Henri Lifchitz	09/2008
974	4*10^194668+49	194669	Robert Price	01/2019
975	2^646589+1179407	194643	Enzo Doria	06/2016
976	2^646289-114621	194553	Enzo Doria	05/2015
977	2^646236-39659	194537	Enzo Doria	09/2015
978	(16*10^194536+53)/3	194537	Robert Price	03/2019
979	2^646161-59833	194514	Enzo Doria	11/2015
980	(17*10^194502+31)/3	194503	Robert Price	01/2019
981	2*10^194413+3	194414	Robert Price	07/2015
982	2^645360-1848599	194273	Enzo Doria	08/2015
983	(112*10^194150-1)/3	194152	Serge Batalov	12/2014
984	2*10^193981-43	193982	Robert Price	04/2018
985	2^644382+75169	193979	Enzo Doria	04/2016
986	2^644304-1861409	193955	Enzo Doria	11/2015
987	5*10^193907-9	193908	Robert Price	05/2015
988	2^644043+1876703	193877	Enzo Doria	07/2016
989	2^643735+1879733	193784	Enzo Doria	09/2016
990	(5^277183+1)/6	193742	Paul Bourdelais	07/2010
991	9*10^193712+71	193713	Robert Price	08/2020
992	2^643216-286565	193628	Enzo Doria	07/2015
993	2^642888-24965	193529	Enzo Doria	09/2013
994	2^642448-114825	193397	Enzo Doria	05/2015
995	2^642437-1856623	193393	Enzo Doria	10/2015
996	2^642039-59797	193273	Enzo Doria	11/2015
997	10^193230+513861	193231	Patrick De Geest	07/2018
998	10^193230-8001	193230	Robert Price	03/2018
999	2^641692-286349	193169	Enzo Doria	07/2015
1000	2^641690-24737	193168	Enzo Doria	09/2013

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PRP Records

Probable Primes Top 10000

(271067 PRPs in the top)