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	2^674603-69337	203076	Enzo Doria	12/2015
752	2^674459+74213	203033	Enzo Doria	04/2016
753	2^674116-458879	202930	Enzo Doria	04/2015
754	2^674076-114755	202918	Enzo Doria	04/2015
755	5^289937-4^289937	202658	Jean-Louis Charton	03/2013
756	2^672556-1835519	202460	Enzo Doria	04/2015
757	2^671446-351401	202126	Enzo Doria	07/2015
758	2^671373+77747	202104	Enzo Doria	05/2016
759	2^670726-114845	201909	Enzo Doria	05/2015
760	2^670539-25045	201853	Enzo Doria	09/2013
761	43284^43519-43519^43284	201769	Norbert Schneider	08/2018
762	2^670213+282317	201755	Enzo Doria	09/2016
763	2^669854-113501	201647	Enzo Doria	08/2014
764	2^669718+81619	201606	Enzo Doria	08/2016
765	(145*10^201504-1)/9	201506	Serge Batalov	12/2014
766	2^668938-1839821	201371	Enzo Doria	06/2015
767	2^668492+1879303	201237	Enzo Doria	08/2016
768	6^258413-5^258413	201085	Jean-Louis Charton	03/2013
769	2^667894+1875589	201057	Enzo Doria	06/2016
770	2^667569-1836559	200959	Enzo Doria	05/2015
771	(172*10^200746-1)/9	200748	Serge Batalov	12/2014
772	2^666430+782569	200616	Enzo Doria	10/2016
773	(86^103471+1)/87	200163	Paul Bourdelais	05/2018
775	103(10^100000+20110)^2-4707(10^100000+20110)+50383	200003	Robert Price	05/2017
774	103(10^100000+33798)^2-4707(10^100000+33798)+50383	200003	Robert Price	01/2018
776	numbpart(32235776596)	200002	Serge Batalov	04/2017
777	(10^200001+149)/3	200001	Serge Batalov	12/2014
778	(14*10^199447+73)/3	199448	Robert Price	12/2018
779	2^662103-29287	199313	Enzo Doria	08/2015
780	(2*10^199283+457)/9	199283	Robert Price	01/2018
781	(10^199248-19)/9	199248	Robert Price	01/2018
782	2^660482-2891	198825	Yves Minet	05/2016
783	2^659583+1879223	198555	Enzo Doria	08/2016
784	(53*10^198529+1)/9	198530	Serge Batalov	07/2010
785	2^658828-29819	198327	Enzo Doria	08/2015
786	2^658776-2791229	198312	Enzo Doria	01/2016
787	(35*10^198294-377)/9	198295	Robert Price	07/2018
788	(4*10^198268+137)/3	198269	Robert Price	03/2018
789	2^658544-1854029	198242	Enzo Doria	09/2015
790	(157^90239-1)/156	198154	Alexander Zhirkov	06/2016
791	(4*10^197778+173)/3	197779	Robert Price	02/2018
792	2^656462+1874419	197615	Enzo Doria	06/2016
793	(89^101363+1)/90	197595	Paul Bourdelais	11/2017
794	2^655893-344563	197444	Enzo Doria	07/2015
795	2^655875+71333	197439	Enzo Doria	04/2016
796	2^655845-9	197430	Robert Price	01/2017
797	2^655682-1849121	197380	Enzo Doria	08/2015
798	4*10^197268-89	197269	Robert Price	11/2018
799	2^655045-49603	197189	Enzo Doria	10/2015
800	2^655000-2784089	197175	Enzo Doria	10/2015
801	(18^157051-1)/17	197141	Paul Bourdelais	03/2010
802	2^654400-39719	196995	Enzo Doria	09/2015
803	(14*10^196965-221)/9	196966	Robert Price	04/2018
804	2^654216-459995	196939	Enzo Doria	06/2015
805	(17*10^196921+31)/3	196922	Robert Price	01/2019
806	3*10^196881-59	196882	Robert Price	09/2018
807	2^653851+82295	196829	Enzo Doria	09/2016
808	(38*10^196792+691)/9	196793	Robert Price	10/2018
809	2^653636-29429	196765	Enzo Doria	08/2015
810	2^653601-69673	196754	Enzo Doria	02/2016
811	(44*10^196684+1)/9	196685	Serge Batalov	07/2010
812	2^652786-1852571	196509	Enzo Doria	08/2015
813	2^652752-1325	196498	Yves Minet	07/2015
814	2^652470-1859141	196414	Enzo Doria	10/2015
815	2^652307+1877483	196364	Enzo Doria	08/2016
816	2^652293-115273	196360	Enzo Doria	06/2015
817	2^651218-1868201	196037	Enzo Doria	04/2016
818	2^651047-49687	195985	Enzo Doria	10/2015
819	2^650285-2785333	195756	Enzo Doria	10/2015
820	(69^106397-1)/68	195647	Paul Bourdelais	10/2017
821	2^649811+1877573	195613	Enzo Doria	08/2016
822	2^649662-170531	195568	Hans Havermann	10/2018
823	2^649586+182839	195545	Enzo Doria	11/2016
824	2^649537-1867363	195531	Enzo Doria	04/2016
825	2^649536-1861499	195530	Enzo Doria	12/2015
826	(103*10^195478-1)/3	195480	Serge Batalov	12/2014
827	2^649102-59351	195400	Enzo Doria	10/2015
828	(2*10^195399+529)/9	195399	Robert Price	01/2018
829	2^648988+1178971	195365	Enzo Doria	06/2016
830	2^648975-114319	195361	Enzo Doria	02/2015
831	(11*10^195350-137)/9	195351	Robert Price	01/2018
832	2^648619-24835	195254	Enzo Doria	09/2013
833	(14*10^195234-83)/3	195235	Robert Price	12/2018
834	2^648190-24737	195125	Enzo Doria	09/2013
835	(57^111119+1)/58	195110	Paul Bourdelais	10/2017
836	11^187185-90	194934	Enzo Doria	09/2012
837	2^647068+77281	194787	Enzo Doria	05/2016
838	15^165559-14^165559	194713	Jean-Louis Charton	03/2011
839	F(931517)	194676	Henri Lifchitz	09/2008
840	4*10^194668+49	194669	Robert Price	01/2019
841	2^646589+1179407	194643	Enzo Doria	06/2016
842	2^646289-114621	194553	Enzo Doria	05/2015
843	2^646236-39659	194537	Enzo Doria	09/2015
844	2^646161-59833	194514	Enzo Doria	11/2015
845	(17*10^194502+31)/3	194503	Robert Price	01/2019
846	2*10^194413+3	194414	Robert Price	07/2015
847	2^645360-1848599	194273	Enzo Doria	08/2015
848	(112*10^194150-1)/3	194152	Serge Batalov	12/2014
849	2*10^193981-43	193982	Robert Price	04/2018
850	2^644382+75169	193979	Enzo Doria	04/2016
851	2^644304-1861409	193955	Enzo Doria	11/2015
852	5*10^193907-9	193908	Robert Price	05/2015
853	2^644043+1876703	193877	Enzo Doria	07/2016
854	2^643735+1879733	193784	Enzo Doria	09/2016
855	(5^277183+1)/6	193742	Paul Bourdelais	07/2010
856	2^643216-286565	193628	Enzo Doria	07/2015
857	2^642888-24965	193529	Enzo Doria	09/2013
858	2^642448-114825	193397	Enzo Doria	05/2015
859	2^642437-1856623	193393	Enzo Doria	10/2015
860	2^642039-59797	193273	Enzo Doria	11/2015
861	10^193230+513861	193231	Patrick De Geest	07/2018
862	10^193230-8001	193230	Robert Price	03/2018
863	2^641692-286349	193169	Enzo Doria	07/2015
864	2^641690-24737	193168	Enzo Doria	09/2013
865	2^641514+1876549	193115	Enzo Doria	07/2016
866	2^640888-2785619	192927	Enzo Doria	10/2015
867	2^640874-2783741	192923	Enzo Doria	09/2015
868	2^640181+467	192714	Lelio R Paula	08/2013
869	2^639536-1850249	192520	Enzo Doria	08/2015
870	5*10^192422-43	192423	Robert Price	01/2019
871	2^639110-2792441	192392	Enzo Doria	02/2016
872	2^638955-29827	192345	Enzo Doria	08/2015
873	2^638713-2784223	192272	Enzo Doria	10/2015
874	2^638490-113507	192205	Enzo Doria	08/2014
875	2^638189-39943	192115	Enzo Doria	09/2015
876	2^638110+1877119	192091	Enzo Doria	07/2016
877	2^638066-2785211	192078	Enzo Doria	10/2015
878	2^637475-115309	191900	Enzo Doria	07/2015
879	2^636661+1876577	191655	Enzo Doria	07/2016
880	(34^125101-1)/33	191589	Paul Bourdelais	11/2017
881	2^636177-1855123	191509	Enzo Doria	09/2015
882	2^636158-113627	191503	Enzo Doria	08/2014
883	(37*25^136966+63)/4	191472	Curtis Bright	05/2015
884	2^636035+79823	191466	Enzo Doria	06/2016
885	2^636011-1860847	191459	Enzo Doria	11/2015
886	2^635926-1860611	191433	Enzo Doria	11/2015
887	3*10^191152-7	191153	Robert Price	08/2015
888	2^634883-1865677	191119	Enzo Doria	02/2016
889	2^634801+1871957	191095	Enzo Doria	05/2016
890	(35*10^191073+1)/9	191074	Serge Batalov	07/2010
891	2^634470-59861	190995	Enzo Doria	11/2015
892	2^634368-29519	190964	Enzo Doria	08/2015
893	2^634188-350609	190910	Enzo Doria	06/2015
894	(13*10^190732-61)/3	190733	Robert Price	11/2018
895	(7*10^190683+143)/3	190684	Robert Price	03/2018
896	2^633088-113879	190579	Enzo Doria	10/2014
897	2^633064+1874911	190572	Enzo Doria	06/2016
898	(43*10^190547+83)/9	190548	Robert Price	11/2018
899	2^632795-351205	190491	Enzo Doria	06/2015
900	(43*10^190351+101)/9	190352	Robert Price	11/2018
901	2^632156+78391	190298	Enzo Doria	06/2016
902	2^632082-1851971	190276	Enzo Doria	08/2015
903	2^632020+1880311	190257	Enzo Doria	09/2016
904	2^631637-462373	190142	Enzo Doria	08/2015
905	2^631122-39251	189987	Enzo Doria	08/2015
906	(26*10^189928-89)/9	189929	Robert Price	06/2018
907	2^630839-97	189902	Yves Minet	07/2017
908	2^630359+1788953	189757	Enzo Doria	05/2016
909	2^630228+1871971	189718	Enzo Doria	05/2016
910	2^630108+781	189682	Lelio R Paula	08/2013
911	2^629870-1867811	189610	Enzo Doria	04/2016
912	(359^74189-1)/358	189558	Alexander Zhirkov	11/2017
913	2^629326+2792929	189447	Enzo Doria	02/2016
914	(10^189385-61)/3	189385	Serge Batalov	12/2014
915	2^629036+1874011	189359	Enzo Doria	06/2016
916	2^628930+80779	189327	Enzo Doria	07/2016
917	2^628582+1179439	189223	Enzo Doria	06/2016
918	(44*10^188999-503)/9	189000	Robert Price	12/2018
919	2^627037-2785843	188757	Enzo Doria	10/2015
920	L(901657)	188436	Renaud Lifchitz	11/2008
921	2^625651+74213	188340	Enzo Doria	04/2016
922	2^625584-460919	188320	Enzo Doria	06/2015
923	(10^188164+359)/9	188164	Serge Batalov	12/2014
924	2^624481-113611	187988	Enzo Doria	08/2014
925	2^624077-112723	187866	Enzo Doria	07/2014
926	2^624008+1874941	187846	Enzo Doria	06/2016
927	2^623870+78679	187804	Enzo Doria	05/2016
928	2^623714-114035	187757	Enzo Doria	11/2014
929	2^623651-1834251	187738	Enzo Doria	07/2015
930	(7*10^187645+53)/3	187646	Robert Price	05/2018
931	2^623146+1879609	187586	Enzo Doria	09/2016
932	(5*10^187471+91)/3	187472	Robert Price	04/2018
933	2^622500+81931	187392	Enzo Doria	08/2016
934	2^622300-1861739	187331	Enzo Doria	12/2015
935	(38*10^187281+349)/9	187282	Robert Price	10/2018
936	2^622052+76771	187257	Enzo Doria	05/2016
937	2^622005-24091	187243	Enzo Doria	08/2013
938	2^621879-351787	187205	Enzo Doria	07/2015
939	2^621700+79411	187151	Enzo Doria	06/2016
940	(2*10^187062-71)/3	187062	Robert Price	12/2017
941	2^620929-113203	186919	Enzo Doria	07/2014
942	10^186842+168223	186843	Patrick De Geest	07/2018
943	10^186842-8001	186842	Robert Price	03/2018
944	2^620347-1777	186744	Lelio R Paula	07/2013
945	11^179143-4170	186559	Enzo Doria	12/2012
946	(5^266863+1)/6	186529	Paul Bourdelais	07/2010
947	2^619297-2792353	186427	Enzo Doria	02/2016
948	2^618940-460139	186320	Enzo Doria	06/2015
949	2^618046+74179	186051	Enzo Doria	04/2016
950	3*10^186019+11	186020	Robert Price	07/2018
951	2*10^185930-3	185931	Robert Price	07/2015
952	(82^97151+1)/83	185928	Paul Bourdelais	10/2017
953	4*10^185905+91	185906	Robert Price	08/2018
954	(37*10^185811+377)/9	185812	Robert Price	11/2018
955	2^617250+9385	185811	Lelio R Paula	07/2013
956	39^116749+2	185756	Robert Price	04/2015
957	2^616924-39719	185713	Enzo Doria	09/2015
958	2^616712+1867621	185649	Enzo Doria	04/2016
959	(3^388897+2^388897)/5	185551	Jean-Louis Charton	09/2011
960	4*10^185355+9	185356	Robert Price	05/2015
961	2^615622+76639	185321	Enzo Doria	05/2016
962	2^615591+1879223	185312	Enzo Doria	08/2016
963	2^615503+1876643	185285	Enzo Doria	07/2016
964	5^265007-4^265007	185232	Jean-Louis Charton	02/2013
965	(4*10^185221-91)/3	185222	Robert Price	03/2018
966	2^614783-2790097	185069	Enzo Doria	12/2015
967	2^614745-29323	185057	Enzo Doria	07/2015
968	(((((((((((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
969	(14*10^184950+211)/9	184951	Robert Price	04/2018
970	2^614315+81353	184928	Enzo Doria	08/2016
971	2^614294-1849961	184921	Enzo Doria	08/2015
972	2^614266+1877809	184913	Enzo Doria	08/2016
973	2^613715-1860727	184747	Enzo Doria	11/2015
974	2*10^184723+41	184724	Robert Price	05/2018
975	2^613487-349987	184678	Enzo Doria	07/2015
976	(95^93377+1)/96	184672	Paul Bourdelais	11/2017
977	14^161089-161089^14	184629	Serge Batalov	05/2016
978	2^613033-114621	184542	Enzo Doria	05/2015
979	(9^193247+1)/10	184404	Paul Bourdelais	02/2010
980	2^612341-1604809	184334	Enzo Doria	05/2015
981	(2^611999-1)/18464214225958267477777390354183	184199	Dario Alpern	06/2017
982	(14*10^184150+37)/3	184151	Robert Price	12/2018
983	2^611731-4837	184150	Yves Minet	08/2018
984	3*10^184124-7	184125	Robert Price	08/2015
985	2^611628-24537	184119	Enzo Doria	08/2013
986	3*10^184110+13	184111	Robert Price	07/2018
987	2^611460+71881	184068	Enzo Doria	04/2016
988	4*10^184004-63	184005	Robert Price	10/2018
989	2^610982-1867301	183924	Enzo Doria	03/2016
990	3*10^183872-49	183873	Robert Price	07/2018
991	2^610597+1178897	183809	Enzo Doria	05/2016
992	(17*10^183764+31)/3	183765	Robert Price	01/2019
993	(28*10^183760-1)/9	183761	Serge Batalov	10/2014
994	2^610401+1277	183750	Lelio R Paula	07/2013
995	2^610356-1849019	183736	Enzo Doria	08/2015
996	(63^102103+1)/64	183717	Paul Bourdelais	10/2017
997	(2^610289+1)/(3*528882550291)	183704	Gord Palameta	08/2018
998	(4*10^183659+149)/9	183659	Robert Price	04/2018
999	2^609846-1834251	183582	Enzo Doria	07/2015
1000	11^176176-240	183469	Enzo Doria	11/2012

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PRP Records

Probable Primes Top 10000

(252538 PRPs in the top)