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	2^1349535+218783	406251	Enzo Doria	03/2024
752	(55766^85849-1)/(55766^293-1)	406081	Ryan Propper	11/2023
753	2^1348956+24241	406077	Enzo Doria	11/2023
754	(88^208739+1)/89	405888	Paul Bourdelais	12/2020
755	(2^1347781-2^673891+1)/5	405722	Borys Jaworski	10/2008
756	2^1347744-3	405712	Paul Bourdelais	07/2019
757	2^1347546+39133	405652	Enzo Doria	12/2024
758	2^1346431+691203	405317	Boyan Hu	09/2024
759	82358^82358+2025^2025	404848	Henri Lifchitz	01/2025
760	9*10^404644-11	404645	Mischa Rodermond	04/2023
761	1215^131072+242^131072	404302	Kellen Shenton	08/2022
762	2^1341908+212911	403955	Enzo Doria	09/2023
763	2^1341625+226187	403870	Enzo Doria	09/2024
764	2^1340284+43801	403466	Enzo Doria	04/2025
765	1196^131072+595^131072	403405	Kellen Shenton	08/2022
766	2^1339302+29389	403171	Enzo Doria	04/2024
767	2^1335130+31669	401915	Enzo Doria	07/2024
768	2^1330791+46763	400609	Enzo Doria	06/2025
769	2^1330712+45631	400585	Enzo Doria	05/2025
770	2^1330388+38527	400487	Enzo Doria	11/2024
771	2^1330371+28313	400482	Enzo Doria	03/2024
772	10^400310+9	400311	Boyan Hu	06/2025
773	10^400000+1415223	400001	Patrick De Geest	10/2020
774	10^400000-339233	400000	Patrick De Geest	10/2020
775	2^1327766+48019	399698	Enzo Doria	06/2025
776	2^1323373+27317	398375	Enzo Doria	01/2024
777	Tau(863^24630)	397727	Nik Lygeros / Olivier Rozier	01/2016
778	2^1320423+24293	397487	Enzo Doria	11/2023
779	2^1320057+211517	397377	Enzo Doria	08/2023
780	2^1319770+1884949	397291	Enzo Doria	06/2017
781	2^1319616+30091	397244	Enzo Doria	04/2024
782	2^1317657+31367	396655	Enzo Doria	04/2024
783	2^1316848+43021	396411	Enzo Doria	02/2025
784	2^1316687+45983	396363	Enzo Doria	05/2025
785	2^1315753+226187	396082	Enzo Doria	09/2024
786	2^1314741+219257	395777	Enzo Doria	03/2024
787	2^1313062+1888849	395272	Enzo Doria	08/2017
788	(1073516^81920+1)/(1073516^16384+1)	395236	Serge Batalov	01/2017
789	2^1312349+221177	395057	Enzo Doria	04/2024
790	(1059995^81920+1)/(1059995^16384+1)	394875	Serge Batalov	01/2017
791	2^1311618+783529	394837	Enzo Doria	01/2017
792	2^1310192+232531	394408	Enzo Doria	03/2025
793	2^1308992+28111	394046	Enzo Doria	02/2024
794	2^1308000+1883521	393748	Enzo Doria	02/2017
795	2^1307563+232133	393616	Enzo Doria	03/2025
796	2^1307324+224611	393544	Enzo Doria	07/2024
797	2^1307262+28759	393526	Enzo Doria	02/2024
798	(1009565^81920+1)/(1009565^16384+1)	393487	Serge Batalov	01/2017
799	2^1305860+35461	393104	Enzo Doria	08/2024
800	(995042^81920+1)/(995042^16384+1)	393075	Serge Batalov	01/2017
801	2^1305333+47717	392945	Enzo Doria	06/2025
802	(988945^81920+1)/(988945^16384+1)	392900	Serge Batalov	01/2017
803	(988823^81920+1)/(988823^16384+1)	392897	Serge Batalov	01/2017
804	(2^1304983-1)/52199321	392832	Tony Prest / Never Odd Or Even	03/2014
805	(978970^81920+1)/(978970^16384+1)	392612	Serge Batalov	01/2017
806	2^1303816+38251	392488	Enzo Doria	11/2024
807	2^1303102+1866409	392273	Enzo Doria	09/2017
808	2^1302818+283429	392188	Enzo Doria	01/2017
809	2^1301430+22669	391770	Enzo Doria	10/2023
810	2^1301229+222467	391709	Enzo Doria	04/2024
811	2^1300835+232523	391591	Enzo Doria	03/2025
812	(934422^81920+1)/(934422^16384+1)	391286	Serge Batalov	01/2017
813	2^1299181+1886867	391093	Enzo Doria	04/2017
814	(37^249341-1)/36	391016	Paul Bourdelais	08/2020
815	2^1298304+1882891	390829	Enzo Doria	01/2017
816	2^1297732+228721	390657	Enzo Doria	11/2024
817	95196^12497+12497^95196	390000	Hans Havermann	12/2021
818	2^1295539+35633	389997	Enzo Doria	08/2024
819	86206^33381+33381^86206	389953	Hans Havermann	05/2023
820	2^1294976+236731	389827	Enzo Doria	06/2025
821	2^1294324+25171	389631	Enzo Doria	12/2023
822	(874207^81920+1)/(874207^16384+1)	389390	Serge Batalov	01/2017
823	2^1292338+229249	389033	Enzo Doria	11/2024
824	2^1289624+32551	388216	Enzo Doria	05/2024
825	2^1286857+37967	387383	Enzo Doria	10/2024
826	2^1285458+46159	386962	Enzo Doria	06/2025
827	2^1285456+230611	386961	Enzo Doria	01/2025
828	(7^457871-5^457871)/2	386946	Jon Grantham	08/2023
829	79455^73828+73828^79455	386805	Hans Havermann	03/2023
830	81650^54369+54369^81650	386642	Yusuf AttarBashi	06/2021
831	80565^62824+62824^80565	386561	Hans Havermann	08/2021
832	83747^41272+41272^83747	386548	Hans Havermann	08/2021
833	15^328574+328574^15	386434	Serge Batalov	05/2014
834	2^1282676+30493	386124	Enzo Doria	12/2024
835	2^1280078+1885099	385342	Enzo Doria	08/2017
836	2^1279921+17	385295	Stefano Morozzi	10/2022
837	2^1279245+224087	385092	Enzo Doria	07/2024
838	2^1277980+231391	384711	Enzo Doria	01/2025
839	2^1277688+231241	384623	Enzo Doria	01/2025
840	2^1277142+234979	384459	Enzo Doria	04/2025
841	2^1276977+71657	384409	Enzo Doria	08/2023
842	(76803^78961-1)/(76803^281-1)	384382	Ryan Propper	11/2023
843	2^1276571+26213	384287	Enzo Doria	12/2023
844	MillsLike(2,1,4,12,4,22,12,114,4,138,142,2956,6388,5248,17532,96930,83782,1464,897448,300832,26908)	384166	Sergey Batalov	05/2024
845	2^1274941+1880717	383796	Enzo Doria	10/2016
846	2^1272632+383431	383101	Enzo Doria	01/2017
847	2^1271346+1889839	382714	Enzo Doria	08/2017
848	2^1271173+219587	382662	Enzo Doria	03/2024
849	5*3^798534-2^798534	380999	Jon Grantham	08/2023
850	(10^380976-7)/3	380976	Leonid Durman	01/2012
851	2^1264748+23221	380728	Enzo Doria	11/2023
852	(4*10^380056+11)/3	380057	Tyler Busby	03/2023
853	2^1262431+228353	380030	Enzo Doria	11/2024
854	2^1260859+222683	379557	Enzo Doria	06/2024
855	2^1258313+43727	378790	Enzo Doria	03/2025
856	2^1257787+1447761	378632	Makoto Morimoto	10/2013
857	(2^1257787+32270)/(223328122073011)	378620	Makoto Morimoto	12/2016
858	2^1257728+20851	378614	Enzo Doria	08/2023
859	(77^200657-1)/76	378536	Paul Bourdelais	08/2020
860	2^1257107+45413	378427	Enzo Doria	05/2025
861	2^1254797+229487	377732	Enzo Doria	11/2024
862	(98^189619+1)/99	377573	Paul Bourdelais	02/2021
863	F(1803059)	376817	Henri Lifchitz	06/2009
864	2^1250590+29389	376466	Enzo Doria	03/2024
865	(10^376417-3^376417)/7	376417	Jon Grantham	08/2023
866	2^1250116+34951	376323	Enzo Doria	08/2024
867	2^1246724+213961	375302	Enzo Doria	10/2023
868	2^1245610+237919	374966	Enzo Doria	06/2025
869	2^1245230+19	374852	Stefano Morozzi	10/2022
870	2^1244263+230033	374561	Enzo Doria	01/2025
871	7^442674+4	374103	Paul Bourdelais	02/2021
872	2^1239151+35633	373022	Enzo Doria	08/2024
873	2^1238732+39181	372896	Enzo Doria	11/2024
874	2^1237699+34703	372585	Enzo Doria	07/2024
875	(97^187393-1)/96	372306	Paul Bourdelais	09/2020
876	2^1235070+46219	371794	Enzo Doria	05/2025
877	10^371696+7	371697	Alfred Reich	05/2021
878	2^1234709+883127	371685	Enzo Doria	12/2016
879	2^1234119+21803	371507	Enzo Doria	09/2023
880	(67^203431+1)/68	371479	Paul Bourdelais	09/2021
881	2^1233971+216593	371463	Enzo Doria	12/2023
882	2^1233212+27301	371234	Enzo Doria	12/2023
883	2^1231529+237557	370728	Enzo Doria	06/2025
884	2^1231466+283819	370709	Enzo Doria	07/2017
885	2^1229766+26659	370197	Enzo Doria	12/2023
886	2^1228899+30713	369936	Enzo Doria	03/2024
887	2^1228892+223831	369934	Enzo Doria	06/2024
888	2^1227635+45413	369555	Enzo Doria	05/2025
889	(49627^78961-1)/(49627^281-1)	369460	Ryan Propper	11/2023
890	2^1227060+226663	369382	Enzo Doria	09/2024
891	2^1226987+28163	369360	Enzo Doria	02/2024
892	2^1226725+234887	369282	Enzo Doria	04/2025
893	2^1226569+30857	369235	Enzo Doria	03/2024
894	2^1225268+46591	368843	Enzo Doria	05/2025
895	73^197880+197880	368715	Kellen Shenton	06/2023
896	5*3^771723-2^771723	368207	Jon Grantham	08/2023
897	2^1222741+231707	368082	Enzo Doria	02/2025
898	2^1222473+221597	368002	Enzo Doria	04/2024
899	2^1222211+22703	367923	Enzo Doria	11/2023
900	(2^1222097+19)/3	367888	Stefano Morozzi	09/2022
901	2^1220335+1881263	367358	Enzo Doria	11/2016
902	2^1218344+215641	366759	Enzo Doria	12/2023
903	2^1217510+220039	366508	Enzo Doria	03/2024
904	2^1217500+226321	366505	Enzo Doria	09/2024
905	(233^154787-1)/232	366434	Anonymous	05/2024
906	2^1216694+1884769	366262	Enzo Doria	02/2017
907	2^1216267+45143	366133	Enzo Doria	05/2025
908	2^1215889-3	366020	Paul Bourdelais	06/2019
909	2^1215296+1885441	365841	Enzo Doria	03/2017
910	(80^192133+1)/81	365645	Paul Bourdelais	01/2021
911	2^1214307+1888115	365543	Enzo Doria	05/2017
912	2^1213815+3	365395	Paul Bourdelais	06/2019
913	(80^191953+1)/81	365302	Paul Bourdelais	01/2021
914	2^1213313+215837	365244	Enzo Doria	11/2023
915	2^1208276+22201	363728	Enzo Doria	09/2023
916	2^1207345+1882577	363448	Enzo Doria	12/2016
917	2^1207336+217801	363445	Enzo Doria	03/2024
918	2^1207073+883727	363366	Enzo Doria	03/2017
919	3^761457-2	363308	Ryan Propper	07/2015
920	(10^363030+7)/337/443	363025	Alfred Reich	12/2021
921	2^1204869+224885	362702	Enzo Doria	07/2024
922	2^1203721+44117	362357	Enzo Doria	04/2025
923	2^1200972+141811	361529	Stefano Morozzi	10/2022
924	(2^1200924+324730)/2	361514	Stefano Morozzi	06/2021
925	(2^1200912+274110)/2	361511	Stefano Morozzi	01/2021
926	2^1200906+165249	361509	Stefano Morozzi	07/2022
927	2^1200890+166339	361504	Stefano Morozzi	01/2023
928	(2^1200887+344126)/2	361503	Stefano Morozzi	10/2020
929	2^1200877+186755	361500	Stefano Morozzi	09/2022
930	2^1200861+198521	361496	Stefano Morozzi	11/2021
931	(2^1200856+305790)/2	361494	Stefano Morozzi	10/2020
932	(2^1200853+372822)/2	361493	Stefano Morozzi	06/2021
933	2^1200812+324178)/2	361481	Stefano Morozzi	06/2021
934	(2^1200768+380458)/2	361467	Stefano Morozzi	01/2021
935	2^1200756+140917	361464	Stefano Morozzi	05/2022
936	2^1200741+184781	361460	Stefano Morozzi	09/2022
937	(2^1200741+293402)/2	361459	Stefano Morozzi	07/2021
938	2^1200734+142653	361457	Stefano Morozzi	02/2023
940	2^1200672+1880881	361439	Enzo Doria	10/2016
939	2^1200672+141535	361439	Stefano Morozzi	09/2022
941	2^1200669+178805	361438	Stefano Morozzi	11/2022
942	2^1200660+198555	361435	Stefano Morozzi	12/2021
943	2^1200657+164837	361434	Stefano Morozzi	05/2022
944	2^1200631+166431	361426	Stefano Morozzi	02/2023
945	2^1200627+150669	361425	Stefano Morozzi	02/2023
946	(2^1200603+356030)/2	361418	Stefano Morozzi	10/2020
947	(2^1200590+275854)/2	361414	Stefano Morozzi	03/2021
948	2^1200550+139297	361402	Stefano Morozzi	10/2021
949	2^1200486+172855	361383	Stefano Morozzi	01/2023
950	(2^1200456+320526)/2	361373	Stefano Morozzi	10/2020
951	2^1200443+142121	361370	Stefano Morozzi	01/2023
952	2^1200416+164065	361362	Stefano Morozzi	01/2022
953	2^1200331+155429	361336	Stefano Morozzi	10/2021
955	(2^1200289+348366)/2	361323	Stefano Morozzi	10/2020
954	2^1200289+141885	361323	Stefano Morozzi	11/2022
956	(2^1200284+273162)/2	361322	Stefano Morozzi	10/2020
957	2^1200252+194535	361312	Stefano Morozzi	11/2021
958	(2^1200250+364230)/2	361311	Stefano Morozzi	10/2020
959	2^1200227+156881	361305	Stefano Morozzi	05/2022
960	(2^1200209+305990)/2	361299	Stefano Morozzi	10/2020
961	(2^1200210+376278)/2	361299	Stefano Morozzi	10/2020
962	2^1200202+216499	361297	Enzo Doria	12/2023
963	(2^1200182+274462)/2	361291	Stefano Morozzi	01/2021
964	2^1200178+149193	361290	Stefano Morozzi	07/2022
965	2^1200168+140403	361287	Stefano Morozzi	03/2022
966	(2^1200162+275910)/2	361285	Stefano Morozzi	03/2021
967	2^1200157+168927	361284	Stefano Morozzi	02/2023
968	2^1200134+141385	361277	Stefano Morozzi	08/2022
969	(2^1200131+360150)/2	361276	Stefano Morozzi	10/2020
970	(2^1200118+290718)/2	361272	Stefano Morozzi	01/2021
971	2^1200022+192777	361243	Stefano Morozzi	09/2022
972	2^1200021+149777	361243	Stefano Morozzi	10/2022
973	(64*10^360173-1)/243	360173	Serge Batalov	09/2014
974	(59^203309+1)/60	360029	Paul Bourdelais	09/2021
975	(2*10^359860-11)/9	359860	Rytis Slatkevicius	01/2023
976	2^1195093+1882577	359759	Enzo Doria	12/2016
977	3^753451+5*2^753451	359488	Jon Grantham	08/2023
978	2^1192258+36739	358906	Enzo Doria	09/2024
979	2^1192251+47183	358904	Enzo Doria	06/2025
980	(6^461108-11)/5	358812	Paul Bourdelais	04/2019
981	2^1191375+8543	358640	Phil Moore	06/2008
982	2^1190972+1880191	358519	Enzo Doria	11/2016
983	2^1189930+28549	358205	Enzo Doria	03/2024
984	(45^216551-1)/44	358004	Paul Bourdelais	08/2020
985	2^1187473+237257	357465	Enzo Doria	06/2025
986	2^1187356+44641	357430	Enzo Doria	06/2025
987	2^1187005+230807	357325	Enzo Doria	01/2025
988	(50^210319-1)/49	357324	Paul Bourdelais	08/2020
989	(531^131072+25^131072)/2	357184	Kellen Shenton	03/2021
990	2^1186366+226747	357132	Enzo Doria	09/2024
991	2^1184565+21227	356590	Enzo Doria	08/2023
992	2^1180312+44173	355310	Enzo Doria	04/2025
993	2^1180159+22823	355264	Enzo Doria	11/2023
994	2^1179836+1885021	355167	Enzo Doria	02/2017
995	2^1178942+32269	354897	Enzo Doria	04/2024
996	2^1178474+43369	354757	Enzo Doria	03/2025
997	2^1177053+28607	354329	Enzo Doria	02/2024
998	2^1177027+234863	354321	Enzo Doria	04/2025
999	(19*10^353884-91)/9	353885	Alfred Reich	02/2023
1000	(10^353884*19-91)/9	353885	Alfred Reich	10/2023

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Probable Primes Top 10000

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