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	(3^700897+1)/4	334413	Paul Bourdelais	04/2010
752	2^1104500+22411	332488	Enzo Doria	10/2023
753	2^1104408-114539	332460	Enzo Doria	03/2015
754	2^1101921+82085	331712	Enzo Doria	10/2016
755	2^1101895+29963	331704	Enzo Doria	03/2024
756	2^1100655+683513	331331	Enzo Doria	01/2017
757	(10^330906+71)/9	330906	Serge Batalov	07/2015
758	2^1098346+482899	330636	Enzo Doria	11/2016
759	(2^1096212+19)/5	329992	Stefano Morozzi	09/2022
760	2^1095679+1878713	329833	Enzo Doria	09/2016
761	2^1094874+27499	329590	Enzo Doria	01/2024
762	2^1094740-1851539	329550	Enzo Doria	08/2015
763	2^1092242+19	328798	Stefano Morozzi	10/2022
764	2^1091469-379369	328565	Enzo Doria	03/2014
765	2^1090801+24227	328364	Enzo Doria	10/2023
766	(69^178093-1)/68	327485	Paul Bourdelais	08/2020
767	(10^326884+7)/421	326882	Alfred Reich	12/2021
768	2^1085750+582349	326844	Enzo Doria	11/2016
769	(54308^69169-1)/(54308^263-1)	326261	Ryan Propper	11/2023
770	2^1083596+483061	326195	Enzo Doria	12/2016
771	(2^541456-1)*10^162995+2^541455-1	325990	paolo galliani	01/2019
772	2^1082908+583561	325988	Enzo Doria	05/2017
773	30^220411-29^220411	325574	Jean-Louis Charton	10/2018
774	2^1081308+7	325507	Stefano Morozzi	10/2022
775	2^1080032+25171	325123	Enzo Doria	11/2023
776	2^1078242+1881649	324584	Enzo Doria	11/2016
777	2^1077737+1880117	324432	Enzo Doria	10/2016
778	3^679017-5*2^679017	323974	Jon Grantham	08/2023
779	2^1076006+29539	323911	Enzo Doria	03/2024
780	2^1075425+1880117	323736	Enzo Doria	10/2016
781	(28^223381+1)/29	323267	Paul Bourdelais	12/2020
782	10^322999+187071	323000	Stefano Morozzi	03/2019
783	10^322999-143151	322999	Patrick De Geest	05/2020
784	2^1072146+1886869	322749	Enzo Doria	04/2017
785	2^1072118-7321953	322740	Enzo Doria	02/2015
786	2^1071026+1886869	322411	Enzo Doria	04/2017
787	2^1070539+1880633	322265	Enzo Doria	10/2016
788	2^1069788+26587	322039	Enzo Doria	12/2023
789	2^1069293-1147195	321890	Enzo Doria	05/2015
790	2^1065968+1880941	320889	Enzo Doria	10/2016
791	2^1065897-1147195	320867	Enzo Doria	05/2015
792	2^1063427+1882103	320124	Enzo Doria	12/2016
793	2^1061095-1061095	319422	Henri Lifchitz	10/2013
794	2^1060950+653119	319378	Enzo Doria	12/2016
795	2^1060363+782753	319202	Enzo Doria	11/2016
796	2^1060028+31771	319101	Enzo Doria	04/2024
797	(71^172259-1)/70	318895	Paul Bourdelais	08/2020
798	-30*Bern(85996)/236037521	318354	Sergey Batalov	10/2023
799	2^1055665+30407	317787	Enzo Doria	03/2024
800	2^1054736+483061	317508	Enzo Doria	12/2016
801	2^1053965+1879667	317276	Enzo Doria	10/2016
802	(43^194119-1)/42	317086	Paul Bourdelais	08/2020
803	2^1052186-458165	316740	Enzo Doria	03/2015
804	11^303909+2	316489	Paul Bourdelais	08/2023
805	2^1049026+214609	315789	Enzo Doria	11/2023
806	2^1046613-114685	315062	Enzo Doria	04/2015
807	2^1045625-459373	314765	Enzo Doria	06/2015
808	10^(2157363+1)-810^157363-1	314727	Robert Price	07/2023
809	(7*10^314564-61)/9	314564	Erik Branger	09/2016
810	2^1044206+7	314338	Stefano Morozzi	10/2022
811	(7^371669-1)/6	314096	Paul Bourdelais	02/2010
812	(53^181981-1)/52	313784	Paul Bourdelais	08/2020
813	(8^347437-5^347437)/3	313767	Jon Grantham	08/2023
814	(10^313741+1)/11/11294677	313733	Alfred Reich	04/2024
815	2^1041944+283051	313657	Enzo Doria	12/2016
816	(1624^97969-1)/(1624^313-1)	313533	Sergey Batalov	11/2023
817	2^1041153-114391	313419	Enzo Doria	02/2015
818	(2^1039700+9)/5	312981	Stefano Morozzi	09/2022
819	(74^167311+1)/75	312742	Paul Bourdelais	12/2020
820	2^1038871+1866983	312732	Enzo Doria	04/2016
821	2^1038545+71657	312634	Enzo Doria	08/2023
822	(55^179573-1)/54	312521	Paul Bourdelais	08/2020
823	2^1037647+1881263	312363	Enzo Doria	11/2016
824	2^1037226+1879699	312237	Enzo Doria	10/2016
825	2^1036867+1865843	312129	Enzo Doria	02/2016
826	(76^165947+1)/77	312114	Paul Bourdelais	01/2021
827	2^1036020-114539	311874	Enzo Doria	02/2015
828	(90^159463-1)/89	311628	Paul Bourdelais	08/2020
829	2^1034546+28819	311430	Enzo Doria	02/2024
830	2^1032240+1883431	310736	Enzo Doria	01/2017
831	64211^64588+64588^64211	310514	Norbert Schneider	11/2023
832	2^1031450+29629	310498	Enzo Doria	03/2024
833	2^1030352+1870021	310167	Enzo Doria	06/2016
834	2^1030046+1882843	310075	Enzo Doria	11/2016
835	3^648872+16	309591	Robert Price	04/2020
836	(16976^73441-1)/(16976^271-1)	309498	Ryan Propper	11/2023
837	64221^64366+64366^64221	309451	Norbert Schneider	06/2023
838	(11121^76729-1)/(11121^277-1)	309336	Ryan Propper	11/2023
839	2^1027478+219259	309302	Enzo Doria	02/2024
840	2^1026999+20513	309158	Enzo Doria	07/2023
841	5^442281+2	309142	Paul Bourdelais	01/2021
842	2^1026204+22741	308919	Enzo Doria	09/2023
843	2^1026190+15	308914	Stefano Morozzi	10/2022
844	2^1025108+20851	308589	Enzo Doria	08/2023
845	A352736(16)	306985	Kellen Shenton	05/2022
846	2^1019777+213947	306984	Enzo Doria	10/2023
847	(11^293831-1)/10	305993	Paul Bourdelais	03/2010
848	(67^167449-1)/66	305773	Paul Bourdelais	08/2020
849	(62^170539+1)/63	305671	Paul Bourdelais	12/2020
850	2^1015321-1015321	305643	Henri Lifchitz	08/2013
851	2^1014775+27113	305478	Enzo Doria	12/2023
852	2^1014450+7	305380	Stefano Morozzi	10/2022
853	2^1014336+215731	305346	Enzo Doria	12/2023
854	2^1014224-2791229	305312	Enzo Doria	01/2016
855	(10^304986+7)/673	304984	Alfred Reich	11/2021
856	65473^45250+45250^65473	304818	Hans Havermann	02/2022
857	66012^41423+41423^66012	304794	Hans Havermann	03/2022
858	65073^48202+48202^65073	304742	Hans Havermann	04/2022
859	238176^19+19^238176	304569	Hans Havermann	03/2022
860	73122^14615+14615^73122	304539	Hans Havermann	05/2022
861	64492^52639+52639^64492	304487	Hans Havermann	03/2022
862	65955^41288+41288^65955	304437	Hans Havermann	04/2022
863	71729^17530+17530^71729	304403	Hans Havermann	03/2022
864	70170^21733+21733^70170	304336	Hans Havermann	03/2022
865	2^1010751-107709	304267	Enzo Doria	03/2014
866	84473^3994+3994^84473	304222	Hans Havermann	03/2022
867	(2^1010623-1)/12602017578957977	304212	Tony Prest / Never Odd Or Even	02/2014
868	74442^12125+12125^74442	303998	Hans Havermann	02/2022
869	77842^8039+8039^77842	303989	Hans Havermann	01/2022
870	64209^54140+54140^64209	303935	Hans Havermann	02/2022
871	2^1009577+1869587	303913	Enzo Doria	06/2016
872	67389^32338+32338^67389	303906	Hans Havermann	02/2022
873	8^336419-7^336419	303817	Jean-Louis Charton	01/2008
874	2^1009168+15	303790	Stefano Morozzi	10/2022
875	80766^5771+5771^80766	303782	Hans Havermann	01/2022
876	66094^39385+39385^66094	303724	Hans Havermann	01/2022
877	69147^24574+24574^69147	303589	Hans Havermann	02/2022
878	78390^7459+7459^78390	303580	Hans Havermann	01/2022
879	2^1008301+1869377	303529	Enzo Doria	06/2016
880	65008^46615+46615^65008	303492	Hans Havermann	02/2022
881	(2^1007838+5)/3	303389	Serge Batalov	08/2015
882	65018^46293+46293^65018	303343	Hans Havermann	01/2022
883	6^389756+5	303290	Paul Bourdelais	02/2021
884	71016^18649+18649^71016	303285	Hans Havermann	01/2022
885	2^1007065+29231	303157	Enzo Doria	03/2024
886	80160^6047+6047^80160	303129	Hans Havermann	01/2022
887	67434^31237+31237^67434	303094	Hans Havermann	03/2022
888	65537^42102+42102^65537	303063	Hans Havermann	02/2022
889	71790^16553+16553^71790	302874	Hans Havermann	11/2021
890	65208^44129+44129^65208	302874	Hans Havermann	11/2021
891	84181^3960+3960^84181	302858	Hans Havermann	11/2021
892	(13703^73441-1)/(13703^271-1)	302691	Ryan Propper	11/2023
893	71956^16087+16087^71956	302682	Hans Havermann	11/2021
894	2^1005326+383059	302634	Enzo Doria	12/2016
895	2^1004929+1877567	302514	Enzo Doria	08/2016
896	69341^22978+22978^69341	302418	Hans Havermann	12/2021
897	111443^516+516^111443	302306	Hans Havermann	12/2021
898	67638^29387+29387^67638	302218	Hans Havermann	11/2021
899	2^1003494+1874899	302082	Enzo Doria	06/2016
900	75189^10400+10400^75189	302037	Hans Havermann	12/2021
901	67237^31042+31042^67237	302026	Hans Havermann	12/2021
902	64540^47791+47791^64540	302005	Hans Havermann	11/2021
903	2^1003046+60529	301947	Enzo Doria	04/2016
904	83278^4209+4209^83278	301815	Hans Havermann	09/2021
905	64431^48250+48250^64431	301763	Hans Havermann	09/2021
906	67237^30714+30714^67237	301716	Hans Havermann	09/2021
907	64641^46288+46288^64641	301581	Hans Havermann	09/2021
908	71513^16482+16482^71513	301572	Hans Havermann	10/2021
909	72017^15396+15396^72017	301565	Hans Havermann	09/2021
910	65534^39927+39927^65534	301540	Hans Havermann	10/2021
911	(23^221411-1)/22	301501	Paul Bourdelais	08/2020
912	63169^59152+59152^63169	301441	Hans Havermann	09/2021
913	75055^10348+10348^75055	301336	Hans Havermann	09/2021
914	2^1000647+1881353	301225	Enzo Doria	11/2016
915	83686^3961+3961^83686	301086	Hans Havermann	10/2021
916	68529^24742+24742^68529	301078	Hans Havermann	09/2021
917	65207^41416+41416^65207	301072	Hans Havermann	10/2021
919	2^1000000+821751	301030	Tony Prest / Never Odd Or Even	10/2015
918	2^999999+77151	301030	Norman Luhn	09/2023
920	90762^2071+2071^90762	300984	Hans Havermann	06/2021
921	63909^51142+51142^63909	300934	Hans Havermann	08/2021
922	2^999646+1874029	300924	Enzo Doria	06/2016
923	66280^34607+34607^66280	300856	Hans Havermann	06/2021
924	65534^38925+38925^65534	300817	Hans Havermann	07/2021
925	63296^56517+56517^63296	300794	Hans Havermann	06/2021
926	110610^523+523^110610	300694	Hans Havermann	06/2021
927	66428^33609+33609^66428	300684	Hans Havermann	06/2021
928	74247^11210+11210^74247	300672	Hans Havermann	06/2021
929	(59^169777-1)/58	300649	Paul Bourdelais	08/2020
930	10^300476+3	300477	Ed Trice	10/2012
931	10^300476-530913	300476	Patrick De Geest	03/2016
932	66703^31960+31960^66703	300471	Hans Havermann	06/2021
933	63722^51915+51915^63722	300468	Hans Havermann	06/2021
934	2^998053+1879667	300444	Enzo Doria	09/2016
935	77018^7959+7959^77018	300437	Hans Havermann	07/2021
936	314738^9+9^314738	300337	Anatoly F. Selevich	02/2011
937	2^997689+217787	300335	Enzo Doria	01/2024
938	69478^20987+20987^69478	300281	Hans Havermann	07/2021
939	64088^48393+48393^64088	300239	Hans Havermann	07/2021
940	64605^44146+44146^64605	300084	Hans Havermann	08/2021
941	2^996845+29027	300081	Enzo Doria	02/2024
942	7^355039-6^355039	300043	Jean-Louis Charton	05/2011
943	67594^27465+27465^67594	300035	Hans Havermann	06/2021
944	10^300000+287389	300001	Patrick De Geest	10/2019
945	10^300000-83657	300000	Patrick De Geest	10/2019
946	70599^17756+17756^70599	300000	Hans Havermann	06/2021
947	numbpart(72526161452)	299999	Serge Batalov	04/2017
948	2^996182-114431	299881	Enzo Doria	02/2015
949	3*2^996126+5	299865	Jon Grantham	07/2023
950	2^996034-17	299837	Stefano Morozzi	07/2022
951	(19*10^299640+77)/3	299641	Robert Price	03/2023
952	2^995214-2788361	299590	Enzo Doria	12/2015
953	2^994791-114319	299462	Enzo Doria	01/2015
954	2^994490-1863791	299372	Enzo Doria	01/2016
955	2^993322+1885729	299020	Enzo Doria	03/2017
956	(36395^65536+36393^65536)/2	298913	Kellen Shenton	04/2022
957	2^992711-2788807	298836	Enzo Doria	12/2015
958	2^992525-114199	298780	Enzo Doria	12/2014
959	(7^353501-3^353501)/4	298743	Jon Grantham	08/2023
960	2^992329+1884707	298721	Enzo Doria	02/2017
961	2^992052+215491	298638	Enzo Doria	11/2023
962	2^991968-23	298613	Stefano Morozzi	07/2022
963	2^991715-19	298536	Stefano Morozzi	07/2022
964	(10^298414+7)/191/823/56921/1334467	298398	Alfred Reich	10/2021
965	2^989562+25	297888	Stefano Morozzi	05/2021
966	2^988580+214051	297593	Enzo Doria	10/2023
967	2^988537+218837	297580	Enzo Doria	03/2024
968	(19*10^297497+77)/3	297498	Robert Price	03/2023
969	(2*10^297488-23)/3	297488	Robert Price	10/2022
970	(2^986191+1)/3	296873	Vincent Diepeveen	06/2008
971	2^985217-114553	296580	Enzo Doria	03/2015
972	(76^157649-1)/75	296507	Paul Bourdelais	07/2019
973	2^984650+21529	296410	Enzo Doria	08/2023
974	2^984131-1828009	296253	Enzo Doria	01/2015
975	2^983620+60451	296100	Phil Moore	03/2008
976	2^982721-2683	295829	Yves Minet	02/2016
977	(23*10^295581+7)/3	295582	Robert Price	05/2023
978	2^981298-2788421	295401	Enzo Doria	12/2015
979	2^981163-2790967	295360	Enzo Doria	12/2015
980	2^981016-15	295316	Stefano Morozzi	07/2022
981	8*10^295160-13	295161	Robert Price	08/2023
982	2^979594+1865839	294888	Enzo Doria	02/2016
983	2^979502+221029	294860	Enzo Doria	03/2024
984	2*10^294527-91	294528	Robert Price	02/2023
985	(49363^63001-1)/(49363^251-1)	294511	Ryan Propper	11/2023
986	10^294475+49	294476	Robert Price	02/2023
987	(11*10^294308+91)/3	294309	Robert Price	03/2023
988	2^976760+1885021	294035	Enzo Doria	02/2017
989	3*2^976518+5	293962	Jon Grantham	07/2023
990	2^975798+218599	293745	Enzo Doria	01/2024
991	2^974441+1878407	293336	Enzo Doria	08/2016
992	2^974180+1876831	293258	Enzo Doria	07/2016
993	2^974170+453319	293255	Enzo Doria	01/2017
994	2^972744-114419	292826	Enzo Doria	03/2015
995	11^281143+6	292781	Paul Bourdelais	03/2021
996	(4*10^292619-91)/3	292620	Robert Price	12/2022
997	E(69468)/13247122135	292549	Sergey Batalov	10/2023
998	CopelandErdos(292447)	292447	Mark Rodenkirch	12/2015
999	3*10^292344-97	292345	Robert Price	01/2023
1000	2^970911+1873373	292274	Enzo Doria	07/2016

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Probable Primes Top 10000

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