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	(48^200443-1)/47	336992	Paul Bourdelais	08/2020
752	(2*10^336405+43)/9	336405	Rytis Slatkevicius	01/2023
753	(94^170371-1)/93	336162	Paul Bourdelais	09/2020
754	2^1116184+1883521	336005	Enzo Doria	02/2017
755	2^1115727+27683	335868	Enzo Doria	01/2024
756	2^1114974+28759	335641	Enzo Doria	02/2024
757	2^1114517+1880087	335504	Enzo Doria	10/2016
758	(5*10^335480+31)/9	335480	Serge Batalov	11/2022
759	5*3^701688+2^701688	334791	Jon Grantham	08/2023
760	(101^166849+1)/102	334418	Paul Bourdelais	12/2020
761	(3^700897+1)/4	334413	Paul Bourdelais	04/2010
762	2^1104500+22411	332488	Enzo Doria	10/2023
763	2^1104408-114539	332460	Enzo Doria	03/2015
764	2^1101921+82085	331712	Enzo Doria	10/2016
765	2^1101895+29963	331704	Enzo Doria	03/2024
766	2^1100655+683513	331331	Enzo Doria	01/2017
767	(10^330906+71)/9	330906	Serge Batalov	07/2015
768	2^1098346+482899	330636	Enzo Doria	11/2016
769	(2^1096212+19)/5	329992	Stefano Morozzi	09/2022
770	2^1095679+1878713	329833	Enzo Doria	09/2016
771	2^1094874+27499	329590	Enzo Doria	01/2024
772	2^1094740-1851539	329550	Enzo Doria	08/2015
773	2^1092242+19	328798	Stefano Morozzi	10/2022
774	2^1091469-379369	328565	Enzo Doria	03/2014
775	2^1090801+24227	328364	Enzo Doria	10/2023
776	(69^178093-1)/68	327485	Paul Bourdelais	08/2020
777	(10^326884+7)/421	326882	Alfred Reich	12/2021
778	2^1085750+582349	326844	Enzo Doria	11/2016
779	(54308^69169-1)/(54308^263-1)	326261	Ryan Propper	11/2023
780	2^1083596+483061	326195	Enzo Doria	12/2016
781	(2^541456-1)*10^162995+2^541455-1	325990	paolo galliani	01/2019
782	2^1082908+583561	325988	Enzo Doria	05/2017
783	30^220411-29^220411	325574	Jean-Louis Charton	10/2018
784	2^1081308+7	325507	Stefano Morozzi	10/2022
785	2^1080032+25171	325123	Enzo Doria	11/2023
786	2^1078242+1881649	324584	Enzo Doria	11/2016
787	2^1077737+1880117	324432	Enzo Doria	10/2016
788	3^679017-5*2^679017	323974	Jon Grantham	08/2023
789	2^1076006+29539	323911	Enzo Doria	03/2024
790	2^1075425+1880117	323736	Enzo Doria	10/2016
791	(28^223381+1)/29	323267	Paul Bourdelais	12/2020
792	10^322999+187071	323000	Stefano Morozzi	03/2019
793	10^322999-143151	322999	Patrick De Geest	05/2020
794	2^1072146+1886869	322749	Enzo Doria	04/2017
795	2^1072118-7321953	322740	Enzo Doria	02/2015
796	2^1071026+1886869	322411	Enzo Doria	04/2017
797	2^1070539+1880633	322265	Enzo Doria	10/2016
798	2^1069788+26587	322039	Enzo Doria	12/2023
799	2^1069293-1147195	321890	Enzo Doria	05/2015
800	2^1065968+1880941	320889	Enzo Doria	10/2016
801	2^1065897-1147195	320867	Enzo Doria	05/2015
802	2^1063427+1882103	320124	Enzo Doria	12/2016
803	2^1061095-1061095	319422	Henri Lifchitz	10/2013
804	2^1060950+653119	319378	Enzo Doria	12/2016
805	2^1060363+782753	319202	Enzo Doria	11/2016
806	2^1060028+31771	319101	Enzo Doria	04/2024
807	(71^172259-1)/70	318895	Paul Bourdelais	08/2020
808	-30*Bern(85996)/236037521	318354	Sergey Batalov	10/2023
809	2^1055665+30407	317787	Enzo Doria	03/2024
810	2^1054736+483061	317508	Enzo Doria	12/2016
811	2^1053965+1879667	317276	Enzo Doria	10/2016
812	(43^194119-1)/42	317086	Paul Bourdelais	08/2020
813	2^1052186-458165	316740	Enzo Doria	03/2015
814	11^303909+2	316489	Paul Bourdelais	08/2023
815	2^1049026+214609	315789	Enzo Doria	11/2023
816	2^1046613-114685	315062	Enzo Doria	04/2015
817	2^1045625-459373	314765	Enzo Doria	06/2015
818	10^(2157363+1)-810^157363-1	314727	Robert Price	07/2023
819	(7*10^314564-61)/9	314564	Erik Branger	09/2016
820	2^1044206+7	314338	Stefano Morozzi	10/2022
821	(7^371669-1)/6	314096	Paul Bourdelais	02/2010
822	(53^181981-1)/52	313784	Paul Bourdelais	08/2020
823	(8^347437-5^347437)/3	313767	Jon Grantham	08/2023
824	(10^313741+1)/11/11294677	313733	Alfred Reich	04/2024
825	2^1041944+283051	313657	Enzo Doria	12/2016
826	(1624^97969-1)/(1624^313-1)	313533	Sergey Batalov	11/2023
827	2^1041153-114391	313419	Enzo Doria	02/2015
828	(2^1039700+9)/5	312981	Stefano Morozzi	09/2022
829	(74^167311+1)/75	312742	Paul Bourdelais	12/2020
830	2^1038871+1866983	312732	Enzo Doria	04/2016
831	2^1038545+71657	312634	Enzo Doria	08/2023
832	(55^179573-1)/54	312521	Paul Bourdelais	08/2020
833	2^1037647+1881263	312363	Enzo Doria	11/2016
834	2^1037226+1879699	312237	Enzo Doria	10/2016
835	2^1036867+1865843	312129	Enzo Doria	02/2016
836	(76^165947+1)/77	312114	Paul Bourdelais	01/2021
837	2^1036020-114539	311874	Enzo Doria	02/2015
838	(90^159463-1)/89	311628	Paul Bourdelais	08/2020
839	2^1034546+28819	311430	Enzo Doria	02/2024
840	2^1032240+1883431	310736	Enzo Doria	01/2017
841	64211^64588+64588^64211	310514	Norbert Schneider	11/2023
842	2^1031450+29629	310498	Enzo Doria	03/2024
843	2^1030352+1870021	310167	Enzo Doria	06/2016
844	2^1030046+1882843	310075	Enzo Doria	11/2016
845	3^648872+16	309591	Robert Price	04/2020
846	(16976^73441-1)/(16976^271-1)	309498	Ryan Propper	11/2023
847	64221^64366+64366^64221	309451	Norbert Schneider	06/2023
848	(11121^76729-1)/(11121^277-1)	309336	Ryan Propper	11/2023
849	2^1027478+219259	309302	Enzo Doria	02/2024
850	2^1026999+20513	309158	Enzo Doria	07/2023
851	5^442281+2	309142	Paul Bourdelais	01/2021
852	2^1026204+22741	308919	Enzo Doria	09/2023
853	2^1026190+15	308914	Stefano Morozzi	10/2022
854	2^1025108+20851	308589	Enzo Doria	08/2023
855	A352736(16)	306985	Kellen Shenton	05/2022
856	2^1019777+213947	306984	Enzo Doria	10/2023
857	(11^293831-1)/10	305993	Paul Bourdelais	03/2010
858	(67^167449-1)/66	305773	Paul Bourdelais	08/2020
859	(62^170539+1)/63	305671	Paul Bourdelais	12/2020
860	2^1015321-1015321	305643	Henri Lifchitz	08/2013
861	2^1014775+27113	305478	Enzo Doria	12/2023
862	2^1014450+7	305380	Stefano Morozzi	10/2022
863	2^1014336+215731	305346	Enzo Doria	12/2023
864	2^1014224-2791229	305312	Enzo Doria	01/2016
865	(10^304986+7)/673	304984	Alfred Reich	11/2021
866	65473^45250+45250^65473	304818	Hans Havermann	02/2022
867	66012^41423+41423^66012	304794	Hans Havermann	03/2022
868	65073^48202+48202^65073	304742	Hans Havermann	04/2022
869	238176^19+19^238176	304569	Hans Havermann	03/2022
870	73122^14615+14615^73122	304539	Hans Havermann	05/2022
871	64492^52639+52639^64492	304487	Hans Havermann	03/2022
872	65955^41288+41288^65955	304437	Hans Havermann	04/2022
873	71729^17530+17530^71729	304403	Hans Havermann	03/2022
874	70170^21733+21733^70170	304336	Hans Havermann	03/2022
875	2^1010751-107709	304267	Enzo Doria	03/2014
876	84473^3994+3994^84473	304222	Hans Havermann	03/2022
877	(2^1010623-1)/12602017578957977	304212	Tony Prest / Never Odd Or Even	02/2014
878	74442^12125+12125^74442	303998	Hans Havermann	02/2022
879	77842^8039+8039^77842	303989	Hans Havermann	01/2022
880	64209^54140+54140^64209	303935	Hans Havermann	02/2022
881	2^1009577+1869587	303913	Enzo Doria	06/2016
882	67389^32338+32338^67389	303906	Hans Havermann	02/2022
883	8^336419-7^336419	303817	Jean-Louis Charton	01/2008
884	2^1009168+15	303790	Stefano Morozzi	10/2022
885	80766^5771+5771^80766	303782	Hans Havermann	01/2022
886	66094^39385+39385^66094	303724	Hans Havermann	01/2022
887	69147^24574+24574^69147	303589	Hans Havermann	02/2022
888	78390^7459+7459^78390	303580	Hans Havermann	01/2022
889	2^1008301+1869377	303529	Enzo Doria	06/2016
890	65008^46615+46615^65008	303492	Hans Havermann	02/2022
891	(2^1007838+5)/3	303389	Serge Batalov	08/2015
892	65018^46293+46293^65018	303343	Hans Havermann	01/2022
893	6^389756+5	303290	Paul Bourdelais	02/2021
894	71016^18649+18649^71016	303285	Hans Havermann	01/2022
895	2^1007065+29231	303157	Enzo Doria	03/2024
896	80160^6047+6047^80160	303129	Hans Havermann	01/2022
897	67434^31237+31237^67434	303094	Hans Havermann	03/2022
898	65537^42102+42102^65537	303063	Hans Havermann	02/2022
899	71790^16553+16553^71790	302874	Hans Havermann	11/2021
900	65208^44129+44129^65208	302874	Hans Havermann	11/2021
901	84181^3960+3960^84181	302858	Hans Havermann	11/2021
902	(13703^73441-1)/(13703^271-1)	302691	Ryan Propper	11/2023
903	71956^16087+16087^71956	302682	Hans Havermann	11/2021
904	2^1005326+383059	302634	Enzo Doria	12/2016
905	2^1004929+1877567	302514	Enzo Doria	08/2016
906	69341^22978+22978^69341	302418	Hans Havermann	12/2021
907	111443^516+516^111443	302306	Hans Havermann	12/2021
908	67638^29387+29387^67638	302218	Hans Havermann	11/2021
909	2^1003494+1874899	302082	Enzo Doria	06/2016
910	75189^10400+10400^75189	302037	Hans Havermann	12/2021
911	67237^31042+31042^67237	302026	Hans Havermann	12/2021
912	64540^47791+47791^64540	302005	Hans Havermann	11/2021
913	2^1003046+60529	301947	Enzo Doria	04/2016
914	83278^4209+4209^83278	301815	Hans Havermann	09/2021
915	64431^48250+48250^64431	301763	Hans Havermann	09/2021
916	67237^30714+30714^67237	301716	Hans Havermann	09/2021
917	64641^46288+46288^64641	301581	Hans Havermann	09/2021
918	71513^16482+16482^71513	301572	Hans Havermann	10/2021
919	72017^15396+15396^72017	301565	Hans Havermann	09/2021
920	65534^39927+39927^65534	301540	Hans Havermann	10/2021
921	(23^221411-1)/22	301501	Paul Bourdelais	08/2020
922	63169^59152+59152^63169	301441	Hans Havermann	09/2021
923	75055^10348+10348^75055	301336	Hans Havermann	09/2021
924	2^1000647+1881353	301225	Enzo Doria	11/2016
925	83686^3961+3961^83686	301086	Hans Havermann	10/2021
926	68529^24742+24742^68529	301078	Hans Havermann	09/2021
927	65207^41416+41416^65207	301072	Hans Havermann	10/2021
929	2^1000000+821751	301030	Tony Prest / Never Odd Or Even	10/2015
928	2^999999+77151	301030	Norman Luhn	09/2023
930	90762^2071+2071^90762	300984	Hans Havermann	06/2021
931	63909^51142+51142^63909	300934	Hans Havermann	08/2021
932	2^999646+1874029	300924	Enzo Doria	06/2016
933	66280^34607+34607^66280	300856	Hans Havermann	06/2021
934	65534^38925+38925^65534	300817	Hans Havermann	07/2021
935	63296^56517+56517^63296	300794	Hans Havermann	06/2021
936	110610^523+523^110610	300694	Hans Havermann	06/2021
937	66428^33609+33609^66428	300684	Hans Havermann	06/2021
938	74247^11210+11210^74247	300672	Hans Havermann	06/2021
939	(59^169777-1)/58	300649	Paul Bourdelais	08/2020
940	10^300476+3	300477	Ed Trice	10/2012
941	10^300476-530913	300476	Patrick De Geest	03/2016
942	66703^31960+31960^66703	300471	Hans Havermann	06/2021
943	63722^51915+51915^63722	300468	Hans Havermann	06/2021
944	2^998053+1879667	300444	Enzo Doria	09/2016
945	77018^7959+7959^77018	300437	Hans Havermann	07/2021
946	314738^9+9^314738	300337	Anatoly F. Selevich	02/2011
947	2^997689+217787	300335	Enzo Doria	01/2024
948	69478^20987+20987^69478	300281	Hans Havermann	07/2021
949	64088^48393+48393^64088	300239	Hans Havermann	07/2021
950	64605^44146+44146^64605	300084	Hans Havermann	08/2021
951	2^996845+29027	300081	Enzo Doria	02/2024
952	7^355039-6^355039	300043	Jean-Louis Charton	05/2011
953	67594^27465+27465^67594	300035	Hans Havermann	06/2021
954	10^300000+287389	300001	Patrick De Geest	10/2019
955	10^300000-83657	300000	Patrick De Geest	10/2019
956	70599^17756+17756^70599	300000	Hans Havermann	06/2021
957	numbpart(72526161452)	299999	Serge Batalov	04/2017
958	2^996182-114431	299881	Enzo Doria	02/2015
959	3*2^996126+5	299865	Jon Grantham	07/2023
960	2^996034-17	299837	Stefano Morozzi	07/2022
961	(19*10^299640+77)/3	299641	Robert Price	03/2023
962	2^995214-2788361	299590	Enzo Doria	12/2015
963	2^994791-114319	299462	Enzo Doria	01/2015
964	2^994490-1863791	299372	Enzo Doria	01/2016
965	2^993322+1885729	299020	Enzo Doria	03/2017
966	(36395^65536+36393^65536)/2	298913	Kellen Shenton	04/2022
967	2^992711-2788807	298836	Enzo Doria	12/2015
968	2^992525-114199	298780	Enzo Doria	12/2014
969	(7^353501-3^353501)/4	298743	Jon Grantham	08/2023
970	2^992329+1884707	298721	Enzo Doria	02/2017
971	2^992052+215491	298638	Enzo Doria	11/2023
972	2^991968-23	298613	Stefano Morozzi	07/2022
973	2^991715-19	298536	Stefano Morozzi	07/2022
974	(10^298414+7)/191/823/56921/1334467	298398	Alfred Reich	10/2021
975	2^989562+25	297888	Stefano Morozzi	05/2021
976	2^988580+214051	297593	Enzo Doria	10/2023
977	2^988537+218837	297580	Enzo Doria	03/2024
978	(19*10^297497+77)/3	297498	Robert Price	03/2023
979	(2*10^297488-23)/3	297488	Robert Price	10/2022
980	(2^986191+1)/3	296873	Vincent Diepeveen	06/2008
981	2^985217-114553	296580	Enzo Doria	03/2015
982	(76^157649-1)/75	296507	Paul Bourdelais	07/2019
983	2^984650+21529	296410	Enzo Doria	08/2023
984	2^984131-1828009	296253	Enzo Doria	01/2015
985	2^983620+60451	296100	Phil Moore	03/2008
986	2^982721-2683	295829	Yves Minet	02/2016
987	(23*10^295581+7)/3	295582	Robert Price	05/2023
988	2^981298-2788421	295401	Enzo Doria	12/2015
989	2^981163-2790967	295360	Enzo Doria	12/2015
990	2^981016-15	295316	Stefano Morozzi	07/2022
991	8*10^295160-13	295161	Robert Price	08/2023
992	2^979594+1865839	294888	Enzo Doria	02/2016
993	2^979502+221029	294860	Enzo Doria	03/2024
994	2*10^294527-91	294528	Robert Price	02/2023
995	(49363^63001-1)/(49363^251-1)	294511	Ryan Propper	11/2023
996	10^294475+49	294476	Robert Price	02/2023
997	(11*10^294308+91)/3	294309	Robert Price	03/2023
998	2^976760+1885021	294035	Enzo Doria	02/2017
999	3*2^976518+5	293962	Jon Grantham	07/2023
1000	2^975798+218599	293745	Enzo Doria	01/2024

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