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 (> 30000)	Who ?	When ?
751	2^658776-2791229	198312	Enzo Doria	01/2016
752	(35*10^198294-377)/9	198295	Robert Price	07/2018
753	(4*10^198268+137)/3	198269	Robert Price	03/2018
754	2^658544-1854029	198242	Enzo Doria	09/2015
755	(157^90239-1)/156	198154	Alexander Zhirkov	06/2016
756	(4*10^197778+173)/3	197779	Robert Price	02/2018
757	2^656462+1874419	197615	Enzo Doria	06/2016
758	(89^101363+1)/90	197595	Paul Bourdelais	11/2017
759	2^655893-344563	197444	Enzo Doria	07/2015
760	2^655875+71333	197439	Enzo Doria	04/2016
761	2^655845-9	197430	Robert Price	01/2017
762	2^655682-1849121	197380	Enzo Doria	08/2015
763	2^655045-49603	197189	Enzo Doria	10/2015
764	2^655000-2784089	197175	Enzo Doria	10/2015
765	(18^157051-1)/17	197141	Paul Bourdelais	03/2010
766	2^654400-39719	196995	Enzo Doria	09/2015
767	(14*10^196965-221)/9	196966	Robert Price	04/2018
768	2^654216-459995	196939	Enzo Doria	06/2015
769	2^653851+82295	196829	Enzo Doria	09/2016
770	2^653636-29429	196765	Enzo Doria	08/2015
771	2^653601-69673	196754	Enzo Doria	02/2016
772	(44*10^196684+1)/9	196685	Serge Batalov	07/2010
773	2^652786-1852571	196509	Enzo Doria	08/2015
774	2^652752-1325	196498	Yves Minet	07/2015
775	2^652470-1859141	196414	Enzo Doria	10/2015
776	2^652307+1877483	196364	Enzo Doria	08/2016
777	2^652293-115273	196360	Enzo Doria	06/2015
778	2^651218-1868201	196037	Enzo Doria	04/2016
779	2^651047-49687	195985	Enzo Doria	10/2015
780	2^650285-2785333	195756	Enzo Doria	10/2015
781	(69^106397-1)/68	195647	Paul Bourdelais	10/2017
782	2^649811+1877573	195613	Enzo Doria	08/2016
783	2^649586+182839	195545	Enzo Doria	11/2016
784	2^649537-1867363	195531	Enzo Doria	04/2016
785	2^649536-1861499	195530	Enzo Doria	12/2015
786	(103*10^195478-1)/3	195480	Serge Batalov	12/2014
787	2^649102-59351	195400	Enzo Doria	10/2015
788	(2*10^195399+529)/9	195399	Robert Price	01/2018
789	2^648988+1178971	195365	Enzo Doria	06/2016
790	2^648975-114319	195361	Enzo Doria	02/2015
791	(11*10^195350-137)/9	195351	Robert Price	01/2018
792	2^648619-24835	195254	Enzo Doria	09/2013
793	2^648190-24737	195125	Enzo Doria	09/2013
794	(57^111119+1)/58	195110	Paul Bourdelais	10/2017
795	11^187185-90	194934	Enzo Doria	09/2012
796	2^647068+77281	194787	Enzo Doria	05/2016
797	15^165559-14^165559	194713	Jean-Louis Charton	03/2011
798	F(931517)	194676	Henri Lifchitz	09/2008
799	2^646589+1179407	194643	Enzo Doria	06/2016
800	2^646289-114621	194553	Enzo Doria	05/2015
801	2^646236-39659	194537	Enzo Doria	09/2015
802	2^646161-59833	194514	Enzo Doria	11/2015
803	2*10^194413+3	194414	Robert Price	07/2015
804	2^645360-1848599	194273	Enzo Doria	08/2015
805	(112*10^194150-1)/3	194152	Serge Batalov	12/2014
806	2*10^193981-43	193982	Robert Price	04/2018
807	2^644382+75169	193979	Enzo Doria	04/2016
808	2^644304-1861409	193955	Enzo Doria	11/2015
809	5*10^193907-9	193908	Robert Price	05/2015
810	2^644043+1876703	193877	Enzo Doria	07/2016
811	2^643735+1879733	193784	Enzo Doria	09/2016
812	(5^277183+1)/6	193742	Paul Bourdelais	07/2010
813	2^643216-286565	193628	Enzo Doria	07/2015
814	2^642888-24965	193529	Enzo Doria	09/2013
815	2^642448-114825	193397	Enzo Doria	05/2015
816	2^642437-1856623	193393	Enzo Doria	10/2015
817	2^642039-59797	193273	Enzo Doria	11/2015
818	10^193230+513861	193231	Patrick De Geest	07/2018
819	10^193230-8001	193230	Robert Price	03/2018
820	2^641692-286349	193169	Enzo Doria	07/2015
821	2^641690-24737	193168	Enzo Doria	09/2013
822	2^641514+1876549	193115	Enzo Doria	07/2016
823	2^640888-2785619	192927	Enzo Doria	10/2015
824	2^640874-2783741	192923	Enzo Doria	09/2015
825	2^640181+467	192714	Lelio R Paula	08/2013
826	2^639536-1850249	192520	Enzo Doria	08/2015
827	2^639110-2792441	192392	Enzo Doria	02/2016
828	2^638955-29827	192345	Enzo Doria	08/2015
829	2^638713-2784223	192272	Enzo Doria	10/2015
830	2^638490-113507	192205	Enzo Doria	08/2014
831	2^638189-39943	192115	Enzo Doria	09/2015
832	2^638110+1877119	192091	Enzo Doria	07/2016
833	2^638066-2785211	192078	Enzo Doria	10/2015
834	2^637475-115309	191900	Enzo Doria	07/2015
835	2^636661+1876577	191655	Enzo Doria	07/2016
836	(34^125101-1)/33	191589	Paul Bourdelais	11/2017
837	2^636177-1855123	191509	Enzo Doria	09/2015
838	2^636158-113627	191503	Enzo Doria	08/2014
839	(37*25^136966+63)/4	191472	Curtis Bright	05/2015
840	2^636035+79823	191466	Enzo Doria	06/2016
841	2^636011-1860847	191459	Enzo Doria	11/2015
842	2^635926-1860611	191433	Enzo Doria	11/2015
843	3*10^191152-7	191153	Robert Price	08/2015
844	2^634883-1865677	191119	Enzo Doria	02/2016
845	2^634801+1871957	191095	Enzo Doria	05/2016
846	(35*10^191073+1)/9	191074	Serge Batalov	07/2010
847	2^634470-59861	190995	Enzo Doria	11/2015
848	2^634368-29519	190964	Enzo Doria	08/2015
849	2^634188-350609	190910	Enzo Doria	06/2015
850	(7*10^190683+143)/3	190684	Robert Price	03/2018
851	2^633088-113879	190579	Enzo Doria	10/2014
852	2^633064+1874911	190572	Enzo Doria	06/2016
853	2^632795-351205	190491	Enzo Doria	06/2015
854	2^632156+78391	190298	Enzo Doria	06/2016
855	2^632082-1851971	190276	Enzo Doria	08/2015
856	2^632020+1880311	190257	Enzo Doria	09/2016
857	2^631637-462373	190142	Enzo Doria	08/2015
858	2^631122-39251	189987	Enzo Doria	08/2015
859	(26*10^189928-89)/9	189929	Robert Price	06/2018
860	2^630839-97	189902	Yves Minet	07/2017
861	2^630359+1788953	189757	Enzo Doria	05/2016
862	2^630228+1871971	189718	Enzo Doria	05/2016
863	2^630108+781	189682	Lelio R Paula	08/2013
864	2^629870-1867811	189610	Enzo Doria	04/2016
865	(359^74189-1)/358	189558	Alexander Zhirkov	11/2017
866	2^629326+2792929	189447	Enzo Doria	02/2016
867	(10^189385-61)/3	189385	Serge Batalov	12/2014
868	2^629036+1874011	189359	Enzo Doria	06/2016
869	2^628930+80779	189327	Enzo Doria	07/2016
870	2^628582+1179439	189223	Enzo Doria	06/2016
871	2^627037-2785843	188757	Enzo Doria	10/2015
872	L(901657)	188436	Renaud Lifchitz	11/2008
873	2^625651+74213	188340	Enzo Doria	04/2016
874	2^625584-460919	188320	Enzo Doria	06/2015
875	(10^188164+359)/9	188164	Serge Batalov	12/2014
876	2^624481-113611	187988	Enzo Doria	08/2014
877	2^624077-112723	187866	Enzo Doria	07/2014
878	2^624008+1874941	187846	Enzo Doria	06/2016
879	2^623870+78679	187804	Enzo Doria	05/2016
880	2^623714-114035	187757	Enzo Doria	11/2014
881	2^623651-1834251	187738	Enzo Doria	07/2015
882	(7*10^187645+53)/3	187646	Robert Price	05/2018
883	2^623146+1879609	187586	Enzo Doria	09/2016
884	(5*10^187471+91)/3	187472	Robert Price	04/2018
885	2^622500+81931	187392	Enzo Doria	08/2016
886	2^622300-1861739	187331	Enzo Doria	12/2015
887	2^622052+76771	187257	Enzo Doria	05/2016
888	2^622005-24091	187243	Enzo Doria	08/2013
889	2^621879-351787	187205	Enzo Doria	07/2015
890	2^621700+79411	187151	Enzo Doria	06/2016
891	(2*10^187062-71)/3	187062	Robert Price	12/2017
892	2^620929-113203	186919	Enzo Doria	07/2014
893	10^186842+168223	186843	Patrick De Geest	07/2018
894	10^186842-8001	186842	Robert Price	03/2018
895	2^620347-1777	186744	Lelio R Paula	07/2013
896	11^179143-4170	186559	Enzo Doria	12/2012
897	(5^266863+1)/6	186529	Paul Bourdelais	07/2010
898	2^619297-2792353	186427	Enzo Doria	02/2016
899	2^618940-460139	186320	Enzo Doria	06/2015
900	2^618046+74179	186051	Enzo Doria	04/2016
901	3*10^186019+11	186020	Robert Price	07/2018
902	2*10^185930-3	185931	Robert Price	07/2015
903	(82^97151+1)/83	185928	Paul Bourdelais	10/2017
904	2^617250+9385	185811	Lelio R Paula	07/2013
905	39^116749+2	185756	Robert Price	04/2015
906	2^616924-39719	185713	Enzo Doria	09/2015
907	2^616712+1867621	185649	Enzo Doria	04/2016
908	(3^388897+2^388897)/5	185551	Jean-Louis Charton	09/2011
909	4*10^185355+9	185356	Robert Price	05/2015
910	2^615622+76639	185321	Enzo Doria	05/2016
911	2^615591+1879223	185312	Enzo Doria	08/2016
912	2^615503+1876643	185285	Enzo Doria	07/2016
913	5^265007-4^265007	185232	Jean-Louis Charton	02/2013
914	(4*10^185221-91)/3	185222	Robert Price	03/2018
915	2^614783-2790097	185069	Enzo Doria	12/2015
916	2^614745-29323	185057	Enzo Doria	07/2015
917	(((((((((((2^3+3)^3+30)^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+66768)^3+300840	185052	Serge Batalov	07/2013
918	(14*10^184950+211)/9	184951	Robert Price	04/2018
919	2^614315+81353	184928	Enzo Doria	08/2016
920	2^614294-1849961	184921	Enzo Doria	08/2015
921	2^614266+1877809	184913	Enzo Doria	08/2016
922	2^613715-1860727	184747	Enzo Doria	11/2015
923	2*10^184723+41	184724	Robert Price	05/2018
924	2^613487-349987	184678	Enzo Doria	07/2015
925	(95^93377+1)/96	184672	Paul Bourdelais	11/2017
926	14^161089-161089^14	184629	Serge Batalov	05/2016
927	2^613033-114621	184542	Enzo Doria	05/2015
928	(9^193247+1)/10	184404	Paul Bourdelais	02/2010
929	2^612341-1604809	184334	Enzo Doria	05/2015
930	(2^611999-1)/18464214225958267477777390354183	184199	Dario Alpern	06/2017
931	2^611731-4837	184150	Yves Minet	08/2018
932	3*10^184124-7	184125	Robert Price	08/2015
933	2^611628-24537	184119	Enzo Doria	08/2013
934	3*10^184110+13	184111	Robert Price	07/2018
935	2^611460+71881	184068	Enzo Doria	04/2016
936	2^610982-1867301	183924	Enzo Doria	03/2016
937	3*10^183872-49	183873	Robert Price	07/2018
938	2^610597+1178897	183809	Enzo Doria	05/2016
939	(28*10^183760-1)/9	183761	Serge Batalov	10/2014
940	2^610401+1277	183750	Lelio R Paula	07/2013
941	2^610356-1849019	183736	Enzo Doria	08/2015
942	(63^102103+1)/64	183717	Paul Bourdelais	10/2017
943	(2^610289+1)/(3*528882550291)	183704	Gord Palameta	08/2018
944	(4*10^183659+149)/9	183659	Robert Price	04/2018
945	2^609846-1834251	183582	Enzo Doria	07/2015
946	11^176176-240	183469	Enzo Doria	11/2012
947	(41^113749+1)/42	183451	Paul Bourdelais	11/2017
948	(101^91463+1)/102	183320	Paul Bourdelais	11/2017
949	2^608965-113989	183317	Enzo Doria	10/2014
950	A005165(43592)	183312	Serge Batalov	07/2017
951	2^608814-461261	183272	Enzo Doria	06/2015
952	(163*10^183227-1)/9	183229	Serge Batalov	12/2014
953	2^608541-608541^2	183190	Henri Lifchitz	02/2018
954	2^608293+143807	183115	Enzo Doria	10/2016
955	2^608164-462419	183076	Enzo Doria	08/2015
956	2^607950-1862303	183012	Enzo Doria	12/2015
957	2^607101+1871987	182756	Enzo Doria	05/2016
958	2^606869-69175	182686	Enzo Doria	11/2015
959	3*10^182614-11	182615	Robert Price	07/2018
960	2^606560-357	182593	Enzo Doria	05/2014
961	2^605687+1866983	182330	Enzo Doria	03/2016
962	2^605655-114445	182321	Enzo Doria	02/2015
963	(20^140053+1)/21	182212	Paul Bourdelais	04/2010
964	(14*10^182177-221)/9	182178	Robert Price	04/2018
965	2^605174-112751	182176	Enzo Doria	06/2014
966	2^604761+1874507	182052	Enzo Doria	06/2016
967	2^604705+1871957	182035	Enzo Doria	05/2016
968	(14*10^182000+229)/9	182001	Robert Price	03/2018
969	(10^181996+41)/3	181996	Robert Price	12/2017
970	(5*10^181950-101)/3	181951	Robert Price	04/2018
971	2^603915+75233	181797	Enzo Doria	04/2016
972	11^174145-360	181354	Enzo Doria	10/2012
973	2^602351-396765	181326	Enzo Doria	08/2013
974	2^601957-113833	181208	Enzo Doria	09/2014
975	66^99581-65^99581	181193	Robert Price	09/2013
976	10^181182+383973	181183	Patrick De Geest	04/2016
977	10^181182-21	181182	Serge Batalov	12/2014
978	(5*10^181127-29)/3	181128	Robert Price	03/2018
979	2^601521-29143	181076	Enzo Doria	07/2015
980	2^601442-2797811	181053	Enzo Doria	04/2016
981	5*10^180992-9	180993	Robert Price	05/2015
982	10^180979+79477	180980	Patrick De Geest	04/2016
983	10^180979+107739	180980	Patrick De Geest	04/2016
984	10^180979-11	180979	Serge Batalov	12/2014
985	2^601023-113851	180926	Enzo Doria	10/2014
986	3*10^180852+29	180853	Robert Price	05/2018
987	2^600300-1852559	180709	Enzo Doria	08/2015
988	(10^180689+71)/9	180689	Serge Batalov	07/2015
989	2^600209+76487	180681	Enzo Doria	05/2016
990	2^599702-369885	180529	Enzo Doria	11/2013
991	Tau(643^11688)	180524	Nik Lygeros / Olivier Rozier	05/2015
992	(2951*29^123418-3)/4	180490	Curtis Bright	05/2015
993	4*10^180360+93	180361	Robert Price	08/2018
994	2^598942+80779	180300	Enzo Doria	07/2016
995	2^598591-1844797	180194	Enzo Doria	06/2015
996	(100^90089+1)/101	180176	Paul Bourdelais	08/2017
997	(4*10^179963-79)/3	179964	Robert Price	02/2018
998	Gamma-Prime(179849)	179849	Eric W. Weisstein	06/2011
999	2^597424-1859729	179843	Enzo Doria	11/2015
1000	Phi(180683,10)	179760	Maksym Voznyy	09/2015

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Probable Primes Top 10000

(218736 PRPs in the top)