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	2^1200202+216499	361297	Enzo Doria	12/2023
752	(2^1200182+274462)/2	361291	Stefano Morozzi	01/2021
753	2^1200178+149193	361290	Stefano Morozzi	07/2022
754	2^1200168+140403	361287	Stefano Morozzi	03/2022
755	(2^1200162+275910)/2	361285	Stefano Morozzi	03/2021
756	2^1200157+168927	361284	Stefano Morozzi	02/2023
757	2^1200134+141385	361277	Stefano Morozzi	08/2022
758	(2^1200131+360150)/2	361276	Stefano Morozzi	10/2020
759	(2^1200118+290718)/2	361272	Stefano Morozzi	01/2021
760	2^1200022+192777	361243	Stefano Morozzi	09/2022
761	2^1200021+149777	361243	Stefano Morozzi	10/2022
762	(64*10^360173-1)/243	360173	Serge Batalov	09/2014
763	(59^203309+1)/60	360029	Paul Bourdelais	09/2021
764	(2*10^359860-11)/9	359860	Rytis Slatkevicius	01/2023
765	2^1195093+1882577	359759	Enzo Doria	12/2016
766	3^753451+5*2^753451	359488	Jon Grantham	08/2023
767	2^1192258+36739	358906	Enzo Doria	09/2024
768	(6^461108-11)/5	358812	Paul Bourdelais	04/2019
769	2^1191375+8543	358640	Phil Moore	06/2008
770	2^1190972+1880191	358519	Enzo Doria	11/2016
771	2^1189930+28549	358205	Enzo Doria	03/2024
772	(45^216551-1)/44	358004	Paul Bourdelais	08/2020
773	(50^210319-1)/49	357324	Paul Bourdelais	08/2020
774	(531^131072+25^131072)/2	357184	Kellen Shenton	03/2021
775	2^1186366+226747	357132	Enzo Doria	09/2024
776	2^1184565+21227	356590	Enzo Doria	08/2023
777	2^1180159+22823	355264	Enzo Doria	11/2023
778	2^1179836+1885021	355167	Enzo Doria	02/2017
779	2^1178942+32269	354897	Enzo Doria	04/2024
780	2^1177053+28607	354329	Enzo Doria	02/2024
781	(19*10^353884-91)/9	353885	Alfred Reich	02/2023
782	(10^353884*19-91)/9	353885	Alfred Reich	10/2023
783	20^271951+3	353817	Paul Bourdelais	01/2021
784	72722^72722+7^7	353551	Serge Batalov	04/2024
785	2^1173095+21	353137	Stefano Morozzi	10/2022
786	2^1170959+218945	352494	Enzo Doria	03/2024
787	2^1170915+382623	352481	Boyan Hu	08/2024
788	(63^195893-1)/62	352477	Paul Bourdelais	08/2020
789	2^1170331+27293	352305	Enzo Doria	01/2024
790	2^1170326+7	352304	Stefano Morozzi	10/2022
791	numbpart(100000135540)	352269	Serge Batalov	04/2017
792	(10^352237-1)/9/10567111/950335427	352221	Maksym Voznyy	01/2015
793	5*3^737931-2^737931	352084	Jon Grantham	08/2023
794	2^1168851+223613	351860	Enzo Doria	06/2024
795	2^1168554+783529	351770	Enzo Doria	01/2017
796	(2^1168183-1)/54763676838381762583	351639	Matthias Wurtinger	01/2011
797	2^1166950+30409	351287	Enzo Doria	03/2024
798	2^1166563+223103	351171	Enzo Doria	05/2024
799	2^1166152+1882411	351047	Enzo Doria	12/2016
800	2^1163972+20971	350391	Enzo Doria	08/2023
801	2^1163272+22411	350180	Enzo Doria	10/2023
802	10^350071+7	350072	Alfred Reich	05/2021
803	2^1162154+1890207	349844	Enzo Doria	08/2017
804	(7*10^348724-61)/9	348724	Erik Branger	09/2016
805	(4*10^348453+41)/9	348453	Serge Batalov	11/2022
806	(127^165601-1)/126	348390	Alexander Zhirkov	09/2015
807	2^1155085+213377	347716	Enzo Doria	09/2023
808	2^1153083+1883693	347113	Enzo Doria	04/2017
809	2^1152186+225529	346843	Enzo Doria	07/2024
810	(2^1148729+2^574365+1)/5	345802	Borys Jaworski	03/2007
811	2^1145882+80779	344945	Enzo Doria	09/2016
812	2^1143425+221177	344206	Enzo Doria	03/2024
813	2^1141813+27047	343720	Enzo Doria	12/2023
814	2^1141114+221869	343510	Enzo Doria	04/2024
815	2^1138296+27541	342662	Enzo Doria	01/2024
816	2^1136462+1887289	342110	Enzo Doria	05/2017
817	F(1636007)	341905	Henri Lifchitz	03/2009
818	(2^1135567+13)/3	341840	Stefano Morozzi	09/2022
819	2^1134873+223637	341631	Enzo Doria	06/2024
820	2^1133678+782569	341272	Enzo Doria	11/2016
821	(11^327001+1)/12	340536	Paul Bourdelais	09/2013
822	2^1129965+223667	340154	Enzo Doria	06/2024
823	2^1129361+221597	339972	Enzo Doria	04/2024
824	2^1128706+225529	339775	Enzo Doria	07/2024
825	2^1128621+25919	339749	Enzo Doria	12/2023
826	(2^1127239+2^563620+1)/5	339333	Borys Jaworski	11/2006
827	Tau(907^20848)	339132	Nik Lygeros / Olivier Rozier	01/2016
828	2^1126380-3	339075	Paul Bourdelais	06/2019
829	2^1125784+24331	338895	Enzo Doria	10/2023
830	2^1125446+1885099	338794	Enzo Doria	08/2017
831	(63^188147+1)/64	338539	Paul Bourdelais	12/2020
832	2^1124549+143807	338523	Enzo Doria	10/2016
833	(4*10^338476+23)/9	338476	Serge Batalov	11/2022
834	2^1121187+1886783	337511	Enzo Doria	04/2017
835	(48^200443-1)/47	336992	Paul Bourdelais	08/2020
836	(2*10^336405+43)/9	336405	Rytis Slatkevicius	01/2023
837	(94^170371-1)/93	336162	Paul Bourdelais	09/2020
838	2^1116184+1883521	336005	Enzo Doria	02/2017
839	2^1115727+27683	335868	Enzo Doria	01/2024
840	2^1114974+28759	335641	Enzo Doria	02/2024
841	2^1114517+1880087	335504	Enzo Doria	10/2016
842	(5*10^335480+31)/9	335480	Serge Batalov	11/2022
843	5*3^701688+2^701688	334791	Jon Grantham	08/2023
844	(101^166849+1)/102	334418	Paul Bourdelais	12/2020
845	(3^700897+1)/4	334413	Paul Bourdelais	04/2010
846	2^1109200+223201	333903	Enzo Doria	05/2024
847	2^1108463+32513	333681	Enzo Doria	05/2024
848	2^1104500+22411	332488	Enzo Doria	10/2023
849	2^1104408-114539	332460	Enzo Doria	03/2015
850	2^1101921+82085	331712	Enzo Doria	10/2016
851	2^1101895+29963	331704	Enzo Doria	03/2024
852	2^1101167-1101167^2	331485	Henri Lifchitz	07/2024
853	2^1101091+224153	331462	Enzo Doria	06/2024
854	2^1100655+683513	331331	Enzo Doria	01/2017
855	(10^330906+71)/9	330906	Serge Batalov	07/2015
856	2^1098346+482899	330636	Enzo Doria	11/2016
857	(2^1096212+19)/5	329992	Stefano Morozzi	09/2022
858	2^1095679+1878713	329833	Enzo Doria	09/2016
859	2^1094874+27499	329590	Enzo Doria	01/2024
860	2^1094740-1851539	329550	Enzo Doria	08/2015
861	2^1092242+19	328798	Stefano Morozzi	10/2022
862	2^1091469-379369	328565	Enzo Doria	03/2014
863	2^1090801+24227	328364	Enzo Doria	10/2023
864	(69^178093-1)/68	327485	Paul Bourdelais	08/2020
865	(10^326884+7)/421	326882	Alfred Reich	12/2021
866	2^1085750+582349	326844	Enzo Doria	11/2016
867	(54308^69169-1)/(54308^263-1)	326261	Ryan Propper	11/2023
868	2^1083596+483061	326195	Enzo Doria	12/2016
869	(2^541456-1)*10^162995+2^541455-1	325990	paolo galliani	01/2019
870	2^1082908+583561	325988	Enzo Doria	05/2017
871	30^220411-29^220411	325574	Jean-Louis Charton	10/2018
872	2^1081308+7	325507	Stefano Morozzi	10/2022
873	2^1080151+225413	325158	Enzo Doria	08/2024
874	2^1080032+25171	325123	Enzo Doria	11/2023
875	2^1078242+1881649	324584	Enzo Doria	11/2016
876	2^1077737+1880117	324432	Enzo Doria	10/2016
877	3^679017-5*2^679017	323974	Jon Grantham	08/2023
878	2^1076006+29539	323911	Enzo Doria	03/2024
879	2^1075573+32417	323780	Enzo Doria	05/2024
880	2^1075425+1880117	323736	Enzo Doria	10/2016
881	(28^223381+1)/29	323267	Paul Bourdelais	12/2020
882	10^322999+187071	323000	Stefano Morozzi	03/2019
883	10^322999-143151	322999	Patrick De Geest	05/2020
884	2^1072744+32641	322929	Enzo Doria	05/2024
885	2^1072146+1886869	322749	Enzo Doria	04/2017
886	2^1072118-7321953	322740	Enzo Doria	02/2015
887	2^1071026+1886869	322411	Enzo Doria	04/2017
888	2^1070539+1880633	322265	Enzo Doria	10/2016
889	2^1069788+26587	322039	Enzo Doria	12/2023
890	2^1069293-1147195	321890	Enzo Doria	05/2015
891	2^1065968+1880941	320889	Enzo Doria	10/2016
892	2^1065897-1147195	320867	Enzo Doria	05/2015
893	2^1063427+1882103	320124	Enzo Doria	12/2016
894	2^1061095-1061095	319422	Henri Lifchitz	10/2013
895	2^1060950+653119	319378	Enzo Doria	12/2016
896	2^1060363+782753	319202	Enzo Doria	11/2016
897	2^1060028+31771	319101	Enzo Doria	04/2024
898	(71^172259-1)/70	318895	Paul Bourdelais	08/2020
899	-30*Bern(85996)/236037521	318354	Sergey Batalov	10/2023
900	2^1055665+30407	317787	Enzo Doria	03/2024
901	2^1054736+483061	317508	Enzo Doria	12/2016
902	2^1053965+1879667	317276	Enzo Doria	10/2016
903	(43^194119-1)/42	317086	Paul Bourdelais	08/2020
904	2^1052899+225413	316955	Enzo Doria	08/2024
905	2^1052186-458165	316740	Enzo Doria	03/2015
906	11^303909+2	316489	Paul Bourdelais	08/2023
907	2^1049026+214609	315789	Enzo Doria	11/2023
908	2^1048576+69661	315653	Boyan Hu	08/2024
909	2^1046613-114685	315062	Enzo Doria	04/2015
910	2^1045625-459373	314765	Enzo Doria	06/2015
911	10^(2157363+1)-810^157363-1	314727	Robert Price	07/2023
912	(7*10^314564-61)/9	314564	Erik Branger	09/2016
913	2^1044206+7	314338	Stefano Morozzi	10/2022
914	(7^371669-1)/6	314096	Paul Bourdelais	02/2010
915	(53^181981-1)/52	313784	Paul Bourdelais	08/2020
916	(8^347437-5^347437)/3	313767	Jon Grantham	08/2023
917	(10^313741+1)/11/11294677	313733	Alfred Reich	04/2024
918	2^1041944+283051	313657	Enzo Doria	12/2016
919	(1624^97969-1)/(1624^313-1)	313533	Sergey Batalov	11/2023
920	2^1041153-114391	313419	Enzo Doria	02/2015
921	(2^1039700+9)/5	312981	Stefano Morozzi	09/2022
922	(74^167311+1)/75	312742	Paul Bourdelais	12/2020
923	2^1038871+1866983	312732	Enzo Doria	04/2016
924	2^1038545+71657	312634	Enzo Doria	08/2023
925	(55^179573-1)/54	312521	Paul Bourdelais	08/2020
926	2^1037647+1881263	312363	Enzo Doria	11/2016
927	2^1037226+1879699	312237	Enzo Doria	10/2016
928	2^1036867+1865843	312129	Enzo Doria	02/2016
929	(76^165947+1)/77	312114	Paul Bourdelais	01/2021
930	2^1036020-114539	311874	Enzo Doria	02/2015
931	(90^159463-1)/89	311628	Paul Bourdelais	08/2020
932	2^1034546+28819	311430	Enzo Doria	02/2024
933	2^1032240+1883431	310736	Enzo Doria	01/2017
934	64211^64588+64588^64211	310514	Norbert Schneider	11/2023
935	2^1031450+29629	310498	Enzo Doria	03/2024
936	2^1030352+1870021	310167	Enzo Doria	06/2016
937	2^1030046+1882843	310075	Enzo Doria	11/2016
938	3^648872+16	309591	Robert Price	04/2020
939	(16976^73441-1)/(16976^271-1)	309498	Ryan Propper	11/2023
940	64221^64366+64366^64221	309451	Norbert Schneider	06/2023
941	(11121^76729-1)/(11121^277-1)	309336	Ryan Propper	11/2023
942	2^1027478+219259	309302	Enzo Doria	02/2024
943	2^1026999+20513	309158	Enzo Doria	07/2023
944	5^442281+2	309142	Paul Bourdelais	01/2021
945	2^1026204+22741	308919	Enzo Doria	09/2023
946	2^1026190+15	308914	Stefano Morozzi	10/2022
947	2^1025108+20851	308589	Enzo Doria	08/2023
948	A352736(16)	306985	Kellen Shenton	05/2022
949	2^1019777+213947	306984	Enzo Doria	10/2023
950	(11^293831-1)/10	305993	Paul Bourdelais	03/2010
951	(67^167449-1)/66	305773	Paul Bourdelais	08/2020
952	(62^170539+1)/63	305671	Paul Bourdelais	12/2020
953	2^1015321-1015321	305643	Henri Lifchitz	08/2013
954	2^1014775+27113	305478	Enzo Doria	12/2023
955	2^1014450+7	305380	Stefano Morozzi	10/2022
956	2^1014336+215731	305346	Enzo Doria	12/2023
957	2^1014224-2791229	305312	Enzo Doria	01/2016
958	(10^304986+7)/673	304984	Alfred Reich	11/2021
959	65473^45250+45250^65473	304818	Hans Havermann	02/2022
960	66012^41423+41423^66012	304794	Hans Havermann	03/2022
961	65073^48202+48202^65073	304742	Hans Havermann	04/2022
962	2^1012054+31669	304659	Enzo Doria	06/2024
963	238176^19+19^238176	304569	Hans Havermann	03/2022
964	73122^14615+14615^73122	304539	Hans Havermann	05/2022
965	64492^52639+52639^64492	304487	Hans Havermann	03/2022
966	65955^41288+41288^65955	304437	Hans Havermann	04/2022
967	71729^17530+17530^71729	304403	Hans Havermann	03/2022
968	70170^21733+21733^70170	304336	Hans Havermann	03/2022
969	2^1010751-107709	304267	Enzo Doria	03/2014
970	84473^3994+3994^84473	304222	Hans Havermann	03/2022
971	(2^1010623-1)/12602017578957977	304212	Tony Prest / Never Odd Or Even	02/2014
972	74442^12125+12125^74442	303998	Hans Havermann	02/2022
973	77842^8039+8039^77842	303989	Hans Havermann	01/2022
974	64209^54140+54140^64209	303935	Hans Havermann	02/2022
975	2^1009577+1869587	303913	Enzo Doria	06/2016
976	67389^32338+32338^67389	303906	Hans Havermann	02/2022
977	8^336419-7^336419	303817	Jean-Louis Charton	01/2008
978	2^1009168+15	303790	Stefano Morozzi	10/2022
979	80766^5771+5771^80766	303782	Hans Havermann	01/2022
980	66094^39385+39385^66094	303724	Hans Havermann	01/2022
981	69147^24574+24574^69147	303589	Hans Havermann	02/2022
982	78390^7459+7459^78390	303580	Hans Havermann	01/2022
983	2^1008301+1869377	303529	Enzo Doria	06/2016
984	65008^46615+46615^65008	303492	Hans Havermann	02/2022
985	(2^1007838+5)/3	303389	Serge Batalov	08/2015
986	65018^46293+46293^65018	303343	Hans Havermann	01/2022
987	6^389756+5	303290	Paul Bourdelais	02/2021
988	71016^18649+18649^71016	303285	Hans Havermann	01/2022
989	2^1007065+29231	303157	Enzo Doria	03/2024
990	80160^6047+6047^80160	303129	Hans Havermann	01/2022
991	67434^31237+31237^67434	303094	Hans Havermann	03/2022
992	65537^42102+42102^65537	303063	Hans Havermann	02/2022
993	71790^16553+16553^71790	302874	Hans Havermann	11/2021
994	65208^44129+44129^65208	302874	Hans Havermann	11/2021
995	84181^3960+3960^84181	302858	Hans Havermann	11/2021
996	(13703^73441-1)/(13703^271-1)	302691	Ryan Propper	11/2023
997	71956^16087+16087^71956	302682	Hans Havermann	11/2021
998	2^1005326+383059	302634	Enzo Doria	12/2016
999	2^1004929+1877567	302514	Enzo Doria	08/2016
1000	69341^22978+22978^69341	302418	Hans Havermann	12/2021

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