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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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	2^676992-59783	203795	Enzo Doria	10/2015
752	2^676972+1866871	203789	Enzo Doria	03/2016
753	2^676761-9	203726	Robert Price	01/2017
754	2^676563-2792407	203666	Enzo Doria	02/2016
755	2^676306-114713	203589	Enzo Doria	04/2015
756	(2^675977-1)/(1686378749257*7171117283326998925471)	203456	Dario Alpern	07/2015
757	2^674627-25161	203083	Enzo Doria	09/2013
758	2^674603-69337	203076	Enzo Doria	12/2015
759	2^674459+74213	203033	Enzo Doria	04/2016
760	2^674116-458879	202930	Enzo Doria	04/2015
761	2^674076-114755	202918	Enzo Doria	04/2015
762	5^289937-4^289937	202658	Jean-Louis Charton	03/2013
763	2^672556-1835519	202460	Enzo Doria	04/2015
764	2^671446-351401	202126	Enzo Doria	07/2015
765	2^671373+77747	202104	Enzo Doria	05/2016
766	2^670726-114845	201909	Enzo Doria	05/2015
767	2^670539-25045	201853	Enzo Doria	09/2013
768	43284^43519-43519^43284	201769	Norbert Schneider	08/2018
769	2^670213+282317	201755	Enzo Doria	09/2016
770	2^669854-113501	201647	Enzo Doria	08/2014
771	2^669718+81619	201606	Enzo Doria	08/2016
772	(145*10^201504-1)/9	201506	Serge Batalov	12/2014
773	2^668938-1839821	201371	Enzo Doria	06/2015
774	2^668492+1879303	201237	Enzo Doria	08/2016
775	6^258413-5^258413	201085	Jean-Louis Charton	03/2013
776	2^667894+1875589	201057	Enzo Doria	06/2016
777	2^667569-1836559	200959	Enzo Doria	05/2015
778	(172*10^200746-1)/9	200748	Serge Batalov	12/2014
779	2^666430+782569	200616	Enzo Doria	10/2016
780	(86^103471+1)/87	200163	Paul Bourdelais	05/2018
781	103(10^100000+20110)^2-4707(10^100000+20110)+50383	200003	Robert Price	05/2017
782	103(10^100000+33798)^2-4707(10^100000+33798)+50383	200003	Robert Price	01/2018
783	numbpart(32235776596)	200002	Serge Batalov	04/2017
784	(10^200001+149)/3	200001	Serge Batalov	12/2014
785	(14*10^199447+73)/3	199448	Robert Price	12/2018
786	2^662103-29287	199313	Enzo Doria	08/2015
787	(2*10^199283+457)/9	199283	Robert Price	01/2018
788	(10^199248-19)/9	199248	Robert Price	01/2018
789	2^660482-2891	198825	Yves Minet	05/2016
790	2^659583+1879223	198555	Enzo Doria	08/2016
791	(53*10^198529+1)/9	198530	Serge Batalov	07/2010
792	2^658828-29819	198327	Enzo Doria	08/2015
793	2^658776-2791229	198312	Enzo Doria	01/2016
794	(35*10^198294-377)/9	198295	Robert Price	07/2018
795	(4*10^198268+137)/3	198269	Robert Price	03/2018
796	2^658544-1854029	198242	Enzo Doria	09/2015
797	(157^90239-1)/156	198154	Alexander Zhirkov	06/2016
798	(4*10^197778+173)/3	197779	Robert Price	02/2018
799	2^656462+1874419	197615	Enzo Doria	06/2016
800	(89^101363+1)/90	197595	Paul Bourdelais	11/2017
801	2^655893-344563	197444	Enzo Doria	07/2015
802	2^655875+71333	197439	Enzo Doria	04/2016
803	2^655845-9	197430	Robert Price	01/2017
804	2^655682-1849121	197380	Enzo Doria	08/2015
805	4*10^197268-89	197269	Robert Price	11/2018
806	2^655045-49603	197189	Enzo Doria	10/2015
807	2^655000-2784089	197175	Enzo Doria	10/2015
808	(18^157051-1)/17	197141	Paul Bourdelais	03/2010
809	2^654400-39719	196995	Enzo Doria	09/2015
810	(14*10^196965-221)/9	196966	Robert Price	04/2018
811	2^654216-459995	196939	Enzo Doria	06/2015
812	(17*10^196921+31)/3	196922	Robert Price	01/2019
813	3*10^196881-59	196882	Robert Price	09/2018
814	2^653851+82295	196829	Enzo Doria	09/2016
815	(38*10^196792+691)/9	196793	Robert Price	10/2018
816	2^653636-29429	196765	Enzo Doria	08/2015
817	2^653601-69673	196754	Enzo Doria	02/2016
818	(44*10^196684+1)/9	196685	Serge Batalov	07/2010
819	2^652786-1852571	196509	Enzo Doria	08/2015
820	2^652752-1325	196498	Yves Minet	07/2015
821	2^652470-1859141	196414	Enzo Doria	10/2015
822	2^652307+1877483	196364	Enzo Doria	08/2016
823	2^652293-115273	196360	Enzo Doria	06/2015
824	(47*10^196281+403)/9	196282	Robert Price	03/2019
825	6*10^196070+73	196071	Robert Price	04/2019
826	2^651218-1868201	196037	Enzo Doria	04/2016
827	2^651047-49687	195985	Enzo Doria	10/2015
828	2^650285-2785333	195756	Enzo Doria	10/2015
829	(69^106397-1)/68	195647	Paul Bourdelais	10/2017
830	2^649811+1877573	195613	Enzo Doria	08/2016
831	2^649662-170531	195568	Hans Havermann	10/2018
832	2^649586+182839	195545	Enzo Doria	11/2016
833	2^649537-1867363	195531	Enzo Doria	04/2016
834	2^649536-1861499	195530	Enzo Doria	12/2015
835	(103*10^195478-1)/3	195480	Serge Batalov	12/2014
836	2^649102-59351	195400	Enzo Doria	10/2015
837	(2*10^195399+529)/9	195399	Robert Price	01/2018
838	2^648988+1178971	195365	Enzo Doria	06/2016
839	2^648975-114319	195361	Enzo Doria	02/2015
840	(11*10^195350-137)/9	195351	Robert Price	01/2018
841	2^648619-24835	195254	Enzo Doria	09/2013
842	(14*10^195234-83)/3	195235	Robert Price	12/2018
843	5*10^195221+81	195222	Robert Price	03/2019
844	2^648190-24737	195125	Enzo Doria	09/2013
845	(57^111119+1)/58	195110	Paul Bourdelais	10/2017
846	11^187185-90	194934	Enzo Doria	09/2012
847	2^647068+77281	194787	Enzo Doria	05/2016
848	15^165559-14^165559	194713	Jean-Louis Charton	03/2011
849	F(931517)	194676	Henri Lifchitz	09/2008
850	4*10^194668+49	194669	Robert Price	01/2019
851	2^646589+1179407	194643	Enzo Doria	06/2016
852	2^646289-114621	194553	Enzo Doria	05/2015
853	2^646236-39659	194537	Enzo Doria	09/2015
854	(16*10^194536+53)/3	194537	Robert Price	03/2019
855	2^646161-59833	194514	Enzo Doria	11/2015
856	(17*10^194502+31)/3	194503	Robert Price	01/2019
857	2*10^194413+3	194414	Robert Price	07/2015
858	2^645360-1848599	194273	Enzo Doria	08/2015
859	(112*10^194150-1)/3	194152	Serge Batalov	12/2014
860	2*10^193981-43	193982	Robert Price	04/2018
861	2^644382+75169	193979	Enzo Doria	04/2016
862	2^644304-1861409	193955	Enzo Doria	11/2015
863	5*10^193907-9	193908	Robert Price	05/2015
864	2^644043+1876703	193877	Enzo Doria	07/2016
865	2^643735+1879733	193784	Enzo Doria	09/2016
866	(5^277183+1)/6	193742	Paul Bourdelais	07/2010
867	2^643216-286565	193628	Enzo Doria	07/2015
868	2^642888-24965	193529	Enzo Doria	09/2013
869	2^642448-114825	193397	Enzo Doria	05/2015
870	2^642437-1856623	193393	Enzo Doria	10/2015
871	2^642039-59797	193273	Enzo Doria	11/2015
872	10^193230+513861	193231	Patrick De Geest	07/2018
873	10^193230-8001	193230	Robert Price	03/2018
874	2^641692-286349	193169	Enzo Doria	07/2015
875	2^641690-24737	193168	Enzo Doria	09/2013
876	2^641514+1876549	193115	Enzo Doria	07/2016
877	2^640888-2785619	192927	Enzo Doria	10/2015
878	2^640874-2783741	192923	Enzo Doria	09/2015
879	(46*10^192841+683)/9	192842	Robert Price	03/2019
880	2^640181+467	192714	Lelio R Paula	08/2013
881	2^639536-1850249	192520	Enzo Doria	08/2015
882	5*10^192422-43	192423	Robert Price	01/2019
883	2^639110-2792441	192392	Enzo Doria	02/2016
884	2^638955-29827	192345	Enzo Doria	08/2015
885	2^638713-2784223	192272	Enzo Doria	10/2015
886	2^638490-113507	192205	Enzo Doria	08/2014
887	2^638189-39943	192115	Enzo Doria	09/2015
888	2^638110+1877119	192091	Enzo Doria	07/2016
889	2^638066-2785211	192078	Enzo Doria	10/2015
890	2^637475-115309	191900	Enzo Doria	07/2015
891	2^636661+1876577	191655	Enzo Doria	07/2016
892	(34^125101-1)/33	191589	Paul Bourdelais	11/2017
893	2^636177-1855123	191509	Enzo Doria	09/2015
894	2^636158-113627	191503	Enzo Doria	08/2014
895	(37*25^136966+63)/4	191472	Curtis Bright	05/2015
896	2^636035+79823	191466	Enzo Doria	06/2016
897	2^636011-1860847	191459	Enzo Doria	11/2015
898	2^635926-1860611	191433	Enzo Doria	11/2015
899	3*10^191152-7	191153	Robert Price	08/2015
900	2^634883-1865677	191119	Enzo Doria	02/2016
901	2^634801+1871957	191095	Enzo Doria	05/2016
902	(35*10^191073+1)/9	191074	Serge Batalov	07/2010
903	2^634470-59861	190995	Enzo Doria	11/2015
904	2^634368-29519	190964	Enzo Doria	08/2015
905	2^634188-350609	190910	Enzo Doria	06/2015
906	(13*10^190732-61)/3	190733	Robert Price	11/2018
907	(7*10^190683+143)/3	190684	Robert Price	03/2018
908	2^633088-113879	190579	Enzo Doria	10/2014
909	2^633064+1874911	190572	Enzo Doria	06/2016
910	(43*10^190547+83)/9	190548	Robert Price	11/2018
911	2^632795-351205	190491	Enzo Doria	06/2015
912	(16*10^190420-19)/3	190421	Robert Price	02/2019
913	(43*10^190351+101)/9	190352	Robert Price	11/2018
914	2^632156+78391	190298	Enzo Doria	06/2016
915	2^632082-1851971	190276	Enzo Doria	08/2015
916	2^632020+1880311	190257	Enzo Doria	09/2016
917	2^631637-462373	190142	Enzo Doria	08/2015
918	2^631122-39251	189987	Enzo Doria	08/2015
919	(26*10^189928-89)/9	189929	Robert Price	06/2018
920	2^630839-97	189902	Yves Minet	07/2017
921	2^630359+1788953	189757	Enzo Doria	05/2016
922	2^630228+1871971	189718	Enzo Doria	05/2016
923	2^630108+781	189682	Lelio R Paula	08/2013
924	2^629870-1867811	189610	Enzo Doria	04/2016
925	(359^74189-1)/358	189558	Alexander Zhirkov	11/2017
926	2^629326+2792929	189447	Enzo Doria	02/2016
927	(10^189385-61)/3	189385	Serge Batalov	12/2014
928	2^629036+1874011	189359	Enzo Doria	06/2016
929	2^628930+80779	189327	Enzo Doria	07/2016
930	2^628582+1179439	189223	Enzo Doria	06/2016
931	(44*10^188999-503)/9	189000	Robert Price	12/2018
932	2^627037-2785843	188757	Enzo Doria	10/2015
933	(16*10^188457+161)/3	188458	Robert Price	02/2019
934	L(901657)	188436	Renaud Lifchitz	11/2008
935	2^625651+74213	188340	Enzo Doria	04/2016
936	2^625584-460919	188320	Enzo Doria	06/2015
937	(10^188164+359)/9	188164	Serge Batalov	12/2014
938	2^624481-113611	187988	Enzo Doria	08/2014
939	2^624077-112723	187866	Enzo Doria	07/2014
940	2^624008+1874941	187846	Enzo Doria	06/2016
941	2^623870+78679	187804	Enzo Doria	05/2016
942	2^623714-114035	187757	Enzo Doria	11/2014
943	2^623651-1834251	187738	Enzo Doria	07/2015
944	(7*10^187645+53)/3	187646	Robert Price	05/2018
945	2^623146+1879609	187586	Enzo Doria	09/2016
946	(5*10^187471+91)/3	187472	Robert Price	04/2018
947	2^622500+81931	187392	Enzo Doria	08/2016
948	2^622300-1861739	187331	Enzo Doria	12/2015
949	(38*10^187281+349)/9	187282	Robert Price	10/2018
950	2^622052+76771	187257	Enzo Doria	05/2016
951	2^622005-24091	187243	Enzo Doria	08/2013
952	2^621879-351787	187205	Enzo Doria	07/2015
953	2^621700+79411	187151	Enzo Doria	06/2016
954	(2*10^187062-71)/3	187062	Robert Price	12/2017
955	2^620929-113203	186919	Enzo Doria	07/2014
956	10^186842+168223	186843	Patrick De Geest	07/2018
957	10^186842-8001	186842	Robert Price	03/2018
958	2^620347-1777	186744	Lelio R Paula	07/2013
959	11^179143-4170	186559	Enzo Doria	12/2012
960	(5^266863+1)/6	186529	Paul Bourdelais	07/2010
961	2^619297-2792353	186427	Enzo Doria	02/2016
962	(49*10^186409+383)/9	186410	Robert Price	04/2019
963	2^618940-460139	186320	Enzo Doria	06/2015
964	2^618046+74179	186051	Enzo Doria	04/2016
965	3*10^186019+11	186020	Robert Price	07/2018
966	(16*10^185978-19)/3	185979	Robert Price	02/2019
967	2*10^185930-3	185931	Robert Price	07/2015
968	(82^97151+1)/83	185928	Paul Bourdelais	10/2017
969	4*10^185905+91	185906	Robert Price	08/2018
970	(37*10^185811+377)/9	185812	Robert Price	11/2018
971	2^617250+9385	185811	Lelio R Paula	07/2013
972	39^116749+2	185756	Robert Price	04/2015
973	2^616924-39719	185713	Enzo Doria	09/2015
974	2^616712+1867621	185649	Enzo Doria	04/2016
975	(3^388897+2^388897)/5	185551	Jean-Louis Charton	09/2011
976	4*10^185355+9	185356	Robert Price	05/2015
977	2^615622+76639	185321	Enzo Doria	05/2016
978	2^615591+1879223	185312	Enzo Doria	08/2016
979	2^615503+1876643	185285	Enzo Doria	07/2016
980	5^265007-4^265007	185232	Jean-Louis Charton	02/2013
981	(4*10^185221-91)/3	185222	Robert Price	03/2018
982	2^614783-2790097	185069	Enzo Doria	12/2015
983	2^614745-29323	185057	Enzo Doria	07/2015
984	(((((((((((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
985	(49*10^184993-67)/9	184994	Robert Price	03/2019
986	(14*10^184950+211)/9	184951	Robert Price	04/2018
987	2^614315+81353	184928	Enzo Doria	08/2016
988	2^614294-1849961	184921	Enzo Doria	08/2015
989	2^614266+1877809	184913	Enzo Doria	08/2016
990	2^613715-1860727	184747	Enzo Doria	11/2015
991	2*10^184723+41	184724	Robert Price	05/2018
992	2^613487-349987	184678	Enzo Doria	07/2015
993	(95^93377+1)/96	184672	Paul Bourdelais	11/2017
994	14^161089-161089^14	184629	Serge Batalov	05/2016
995	2^613033-114621	184542	Enzo Doria	05/2015
996	(9^193247+1)/10	184404	Paul Bourdelais	02/2010
997	2^612341-1604809	184334	Enzo Doria	05/2015
998	(2^611999-1)/18464214225958267477777390354183	184199	Dario Alpern	06/2017
999	(14*10^184150+37)/3	184151	Robert Price	12/2018
1000	2^611731-4837	184150	Yves Minet	08/2018

Find by discoverer :

PRP Records

Probable Primes Top 10000

(252675 PRPs in the top)