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	2^644043+1876703	193877	Enzo Doria	07/2016
752	2^643735+1879733	193784	Enzo Doria	09/2016
753	(5^277183+1)/6	193742	Paul Bourdelais	07/2010
754	2^643216-286565	193628	Enzo Doria	07/2015
755	2^642888-24965	193529	Enzo Doria	09/2013
756	2^642448-114825	193397	Enzo Doria	05/2015
757	2^642437-1856623	193393	Enzo Doria	10/2015
758	2^642039-59797	193273	Enzo Doria	11/2015
759	2^641692-286349	193169	Enzo Doria	07/2015
760	2^641690-24737	193168	Enzo Doria	09/2013
761	2^641514+1876549	193115	Enzo Doria	07/2016
762	2^640888-2785619	192927	Enzo Doria	10/2015
763	2^640874-2783741	192923	Enzo Doria	09/2015
764	2^640181+467	192714	Lelio R Paula	08/2013
765	2^639536-1850249	192520	Enzo Doria	08/2015
766	2^639110-2792441	192392	Enzo Doria	02/2016
767	2^638955-29827	192345	Enzo Doria	08/2015
768	2^638713-2784223	192272	Enzo Doria	10/2015
769	2^638490-113507	192205	Enzo Doria	08/2014
770	2^638189-39943	192115	Enzo Doria	09/2015
771	2^638110+1877119	192091	Enzo Doria	07/2016
772	2^638066-2785211	192078	Enzo Doria	10/2015
773	2^637475-115309	191900	Enzo Doria	07/2015
774	2^636661+1876577	191655	Enzo Doria	07/2016
775	2^636177-1855123	191509	Enzo Doria	09/2015
776	2^636158-113627	191503	Enzo Doria	08/2014
777	(37*25^136966+63)/4	191472	Curtis Bright	05/2015
778	2^636035+79823	191466	Enzo Doria	06/2016
779	2^636011-1860847	191459	Enzo Doria	11/2015
780	2^635926-1860611	191433	Enzo Doria	11/2015
781	3*10^191152-7	191153	Robert Price	08/2015
782	2^634883-1865677	191119	Enzo Doria	02/2016
783	2^634801+1871957	191095	Enzo Doria	05/2016
784	(35*10^191073+1)/9	191074	Serge Batalov	07/2010
785	2^634470-59861	190995	Enzo Doria	11/2015
786	2^634368-29519	190964	Enzo Doria	08/2015
787	2^634188-350609	190910	Enzo Doria	06/2015
788	2^633088-113879	190579	Enzo Doria	10/2014
789	2^633064+1874911	190572	Enzo Doria	06/2016
790	2^632795-351205	190491	Enzo Doria	06/2015
791	2^632156+78391	190298	Enzo Doria	06/2016
792	2^632082-1851971	190276	Enzo Doria	08/2015
793	2^632020+1880311	190257	Enzo Doria	09/2016
794	2^631637-462373	190142	Enzo Doria	08/2015
795	2^631122-39251	189987	Enzo Doria	08/2015
796	2^630839-97	189902	Yves Minet	07/2017
797	2^630359+1788953	189757	Enzo Doria	05/2016
798	2^630228+1871971	189718	Enzo Doria	05/2016
799	2^630108+781	189682	Lelio R Paula	08/2013
800	2^629870-1867811	189610	Enzo Doria	04/2016
801	2^629326+2792929	189447	Enzo Doria	02/2016
802	(10^189385-61)/3	189385	Serge Batalov	12/2014
803	2^629036+1874011	189359	Enzo Doria	06/2016
804	2^628930+80779	189327	Enzo Doria	07/2016
805	2^628582+1179439	189223	Enzo Doria	06/2016
806	2^627037-2785843	188757	Enzo Doria	10/2015
807	L(901657)	188436	Renaud Lifchitz	11/2008
808	2^625651+74213	188340	Enzo Doria	04/2016
809	2^625584-460919	188320	Enzo Doria	06/2015
810	(10^188164+359)/9	188164	Serge Batalov	12/2014
811	2^624481-113611	187988	Enzo Doria	08/2014
812	2^624077-112723	187866	Enzo Doria	07/2014
813	2^624008+1874941	187846	Enzo Doria	06/2016
814	2^623870+78679	187804	Enzo Doria	05/2016
815	2^623714-114035	187757	Enzo Doria	11/2014
816	2^623651-1834251	187738	Enzo Doria	07/2015
817	2^623146+1879609	187586	Enzo Doria	09/2016
818	2^622500+81931	187392	Enzo Doria	08/2016
819	2^622300-1861739	187331	Enzo Doria	12/2015
820	2^622052+76771	187257	Enzo Doria	05/2016
821	2^622005-24091	187243	Enzo Doria	08/2013
822	2^621879-351787	187205	Enzo Doria	07/2015
823	2^621700+79411	187151	Enzo Doria	06/2016
824	2^620929-113203	186919	Enzo Doria	07/2014
825	2^620347-1777	186744	Lelio R Paula	07/2013
826	11^179143-4170	186559	Enzo Doria	12/2012
827	(5^266863+1)/6	186529	Paul Bourdelais	07/2010
828	2^619297-2792353	186427	Enzo Doria	02/2016
829	2^618940-460139	186320	Enzo Doria	06/2015
830	2^618046+74179	186051	Enzo Doria	04/2016
831	2*10^185930-3	185931	Robert Price	07/2015
832	2^617250+9385	185811	Lelio R Paula	07/2013
833	39^116749+2	185756	Robert Price	04/2015
834	2^616924-39719	185713	Enzo Doria	09/2015
835	2^616712+1867621	185649	Enzo Doria	04/2016
836	(3^388897+2^388897)/5	185551	Jean-Louis Charton	09/2011
837	4*10^185355+9	185356	Robert Price	05/2015
838	2^615622+76639	185321	Enzo Doria	05/2016
839	2^615591+1879223	185312	Enzo Doria	08/2016
840	2^615503+1876643	185285	Enzo Doria	07/2016
841	5^265007-4^265007	185232	Jean-Louis Charton	02/2013
842	2^614783-2790097	185069	Enzo Doria	12/2015
843	2^614745-29323	185057	Enzo Doria	07/2015
844	(((((((((((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
845	2^614315+81353	184928	Enzo Doria	08/2016
846	2^614294-1849961	184921	Enzo Doria	08/2015
847	2^614266+1877809	184913	Enzo Doria	08/2016
848	2^613715-1860727	184747	Enzo Doria	11/2015
849	2^613487-349987	184678	Enzo Doria	07/2015
850	14^161089-161089^14	184629	Serge Batalov	05/2016
851	2^613033-114621	184542	Enzo Doria	05/2015
852	(9^193247+1)/10	184404	Paul Bourdelais	02/2010
853	2^612341-1604809	184334	Enzo Doria	05/2015
854	(2^611999-1)/18464214225958267477777390354183	184199	Dario Alpern	06/2017
855	3*10^184124-7	184125	Robert Price	08/2015
856	2^611628-24537	184119	Enzo Doria	08/2013
857	2^611460+71881	184068	Enzo Doria	04/2016
858	2^610982-1867301	183924	Enzo Doria	03/2016
859	2^610597+1178897	183809	Enzo Doria	05/2016
860	(28*10^183760-1)/9	183761	Serge Batalov	10/2014
861	2^610401+1277	183750	Lelio R Paula	07/2013
862	2^610356-1849019	183736	Enzo Doria	08/2015
863	2^609846-1834251	183582	Enzo Doria	07/2015
864	11^176176-240	183469	Enzo Doria	11/2012
865	2^608965-113989	183317	Enzo Doria	10/2014
866	A005165(43592)	183312	Serge Batalov	07/2017
867	2^608814-461261	183272	Enzo Doria	06/2015
868	(163*10^183227-1)/9	183229	Serge Batalov	12/2014
869	2^608293+143807	183115	Enzo Doria	10/2016
870	2^608164-462419	183076	Enzo Doria	08/2015
871	2^607950-1862303	183012	Enzo Doria	12/2015
872	2^607101+1871987	182756	Enzo Doria	05/2016
873	2^606869-69175	182686	Enzo Doria	11/2015
874	2^606560-357	182593	Enzo Doria	05/2014
875	2^605687+1866983	182330	Enzo Doria	03/2016
876	2^605655-114445	182321	Enzo Doria	02/2015
877	(20^140053+1)/21	182212	Paul Bourdelais	04/2010
878	2^605174-112751	182176	Enzo Doria	06/2014
879	2^604761+1874507	182052	Enzo Doria	06/2016
880	2^604705+1871957	182035	Enzo Doria	05/2016
881	2^603915+75233	181797	Enzo Doria	04/2016
882	11^174145-360	181354	Enzo Doria	10/2012
883	2^602351-396765	181326	Enzo Doria	08/2013
884	2^601957-113833	181208	Enzo Doria	09/2014
885	66^99581-65^99581	181193	Robert Price	09/2013
886	10^181182+383973	181183	Patrick De Geest	04/2016
887	10^181182-21	181182	Serge Batalov	12/2014
888	2^601521-29143	181076	Enzo Doria	07/2015
889	2^601442-2797811	181053	Enzo Doria	04/2016
890	5*10^180992-9	180993	Robert Price	05/2015
891	10^180979+79477	180980	Patrick De Geest	04/2016
892	10^180979+107739	180980	Patrick De Geest	04/2016
893	10^180979-11	180979	Serge Batalov	12/2014
894	2^601023-113851	180926	Enzo Doria	10/2014
895	2^600300-1852559	180709	Enzo Doria	08/2015
896	(10^180689+71)/9	180689	Serge Batalov	07/2015
897	2^600209+76487	180681	Enzo Doria	05/2016
898	2^599702-369885	180529	Enzo Doria	11/2013
899	Tau(643^11688)	180524	Nik Lygeros / Olivier Rozier	05/2015
900	(2951*29^123418-3)/4	180490	Curtis Bright	05/2015
901	2^598942+80779	180300	Enzo Doria	07/2016
902	2^598591-1844797	180194	Enzo Doria	06/2015
903	(100^90089+1)/101	180176	Paul Bourdelais	08/2017
904	Gamma-Prime(179849)	179849	Eric W. Weisstein	06/2011
905	2^597424-1859729	179843	Enzo Doria	11/2015
906	Phi(180683,10)	179760	Maksym Voznyy	09/2015
907	(10^180683-1)*9/(10^643-1)/(10^281-1)	179760	Robert Price	07/2016
908	(3^376657-2^376657)/22301107657	179701	Mike Oakes	04/2017
909	2^596690-461261	179622	Enzo Doria	07/2015
910	2^596684-113939	179620	Enzo Doria	10/2014
911	3^375887-112696	179344	Enzo Doria	07/2014
912	2^595144-1850429	179157	Enzo Doria	08/2015
913	2^594531+82253	178972	Enzo Doria	09/2016
914	2^594260-2787899	178891	Enzo Doria	11/2015
915	10^178695+136719	178696	Patrick De Geest	05/2016
916	10^178695-71	178695	Serge Batalov	12/2014
917	(2^148330+1)^4-2	178608	Cletus Emmanuel	12/2003
918	2^593178+1867219	178565	Enzo Doria	03/2016
919	(18^142031-1)/17	178287	Paul Bourdelais	03/2010
920	2^591872-291929	178172	Enzo Doria	07/2015
921	2^591682-286871	178115	Enzo Doria	07/2015
922	4*10^178091+9	178092	Robert Price	05/2015
923	410747#+478483	178007	Makoto Morimoto	02/2016
924	2^590762-396765	177838	Enzo Doria	08/2013
925	(136*10^177754-1)/9	177756	Serge Batalov	12/2014
926	ReverseConsecutiveIntegerPrime(37765)	177719	Eric W. Weisstein	04/2010
927	2^589204+1881151	177369	Enzo Doria	11/2016
928	2^589132-69479	177347	Enzo Doria	01/2016
929	2^588912-113519	177281	Enzo Doria	08/2014
930	15^150706+2	177245	Robert Price	06/2015
931	2^588194-1861001	177065	Enzo Doria	11/2015
932	2^587560-113699	176874	Enzo Doria	09/2014
933	5^252763-12862	176674	Enzo Doria	05/2014
934	2^586804+81721	176646	Enzo Doria	08/2016
935	2^586570+1874419	176576	Enzo Doria	06/2016
936	2^585994-3311	176402	Yves Minet	12/2014
937	2^585832-112799	176354	Enzo Doria	07/2014
938	2^585336-461039	176204	Enzo Doria	06/2015
939	2^585095-1848127	176132	Enzo Doria	08/2015
940	2^584950-115451	176088	Enzo Doria	07/2015
941	2^584671-3697	176004	Yves Minet	03/2017
942	10^175608+2971	175609	Mike Oakes	05/2010
943	10^175608-55829	175608	Patrick De Geest	09/2013
944	2^583051+1879793	175516	Enzo Doria	09/2016
945	2^582860-23829	175459	Enzo Doria	08/2013
946	2^582670-23913	175402	Enzo Doria	08/2013
947	2^582573-29563	175372	Enzo Doria	08/2015
948	2^582435-1862767	175331	Enzo Doria	12/2015
949	2^582072-1848599	175222	Enzo Doria	08/2015
950	2^581560+1874911	175068	Enzo Doria	06/2016
951	(75^93307-1)/74	174955	Paul Bourdelais	09/2017
952	2^580528-114035	174757	Enzo Doria	11/2014
953	2^580046-459161	174612	Enzo Doria	05/2015
954	2^579992-39779	174595	Enzo Doria	09/2015
955	(2^578696+1)/257	174203	Lelio R Paula	09/2015
956	2^578656-1851809	174193	Enzo Doria	08/2015
957	2^578583-113917	174171	Enzo Doria	10/2014
958	2^578434-83	174126	Yves Minet	07/2017
959	15^148048-2	174118	Robert Price	06/2015
960	2^578346+2794249	174100	Enzo Doria	03/2016
961	(L!41532)/2	173772	Serge Batalov	07/2017
962	2^577146-49877	173739	Enzo Doria	10/2015
963	2^576889+49727	173661	Enzo Doria	09/2016
964	(2^576551-1)/4612409/64758208321/242584327930759	173528	Dario Alpern	06/2014
965	2^576016-113919	173399	Enzo Doria	11/2014
966	2^575911-1849387	173367	Enzo Doria	08/2015
967	2^575196-114053	173152	Enzo Doria	11/2014
968	2^574591-115387	172970	Enzo Doria	07/2015
969	2^574328+81121	172890	Enzo Doria	07/2016
970	(115*10^172862-1)/3	172864	Serge Batalov	12/2014
971	4*5^247217-9	172798	Lelio R Paula	10/2015
972	2^573668-2782319	172692	Enzo Doria	09/2015
973	2^573444-1855109	172624	Enzo Doria	09/2015
974	3^361608+2	172531	Robert Price	08/2014
975	2^572592-114893	172368	Enzo Doria	05/2015
976	5^246497-4^246497	172295	Jean-Louis Charton	11/2008
977	(36^110503+1)/37	171975	Lelio R Paula	04/2017
978	2^570980-2782289	171883	Enzo Doria	09/2015
979	(2^(12*47563+13)-9)/7	171818	Kevin Acres	11/2013
980	2^569563-1854607	171456	Enzo Doria	09/2015
981	2^568642+1876129	171179	Enzo Doria	07/2016
982	(58*10^170842+221)/9	170843	Robert Price	02/2017
983	11^164009-270	170798	Enzo Doria	10/2012
984	3^357706-112358	170670	Enzo Doria	07/2014
985	TheodorusPrime(170657)	170657	Eric W. Weisstein	08/2013
986	2^566871+1876163	170646	Enzo Doria	07/2016
987	2^566496+7	170533	Donovan Johnson	07/2006
988	(7^201653+1)/8	170416	Paul Bourdelais	02/2010
989	2^565183-352021	170138	Enzo Doria	07/2015
990	2^565143-114457	170125	Enzo Doria	02/2015
991	2^564976-49869	170075	Enzo Doria	10/2015
992	2^564526-351401	169940	Enzo Doria	07/2015
993	21^128327-20^128327	169677	Jean-Louis Charton	11/2014
994	2^562749+2793047	169405	Enzo Doria	02/2016
995	(154*10^169337-1)/9	169339	Serge Batalov	12/2014
996	2^562369-29503	169290	Enzo Doria	08/2015
997	2^560405-39943	168699	Enzo Doria	09/2015
998	2^559686-350471	168483	Enzo Doria	06/2015
999	2^559672-1855889	168479	Enzo Doria	09/2015
1000	2^559000-59939	168276	Enzo Doria	11/2015

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PRP Records

Probable Primes Top 10000

(183432 PRPs in the top)