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	2^1364303+219533	410697	Enzo Doria	03/2024
752	2^1363434+27589	410435	Enzo Doria	02/2024
753	2^1363068+222631	410325	Enzo Doria	06/2024
754	2^1359550+25819	409266	Enzo Doria	12/2023
755	2^1359515+236423	409255	Enzo Doria	05/2025
756	2^1357392+224401	408616	Enzo Doria	06/2024
757	2^1355826+15	408145	Stefano Morozzi	10/2022
758	2^1355790+1888939	408134	Enzo Doria	07/2017
759	2^1355635+1884203	408087	Enzo Doria	01/2017
760	(22071^94249-1)/(22071^307-1)	408068	Ryan Propper	11/2023
761	2^1355083+221603	407921	Enzo Doria	05/2024
762	2^1351989+36587	406990	Enzo Doria	09/2024
763	2^1351675+231083	406895	Enzo Doria	02/2025
764	2^1349535+218783	406251	Enzo Doria	03/2024
765	(55766^85849-1)/(55766^293-1)	406081	Ryan Propper	11/2023
766	2^1348956+24241	406077	Enzo Doria	11/2023
767	(88^208739+1)/89	405888	Paul Bourdelais	12/2020
768	(2^1347781-2^673891+1)/5	405722	Borys Jaworski	10/2008
769	2^1347744-3	405712	Paul Bourdelais	07/2019
770	2^1347546+39133	405652	Enzo Doria	12/2024
771	2^1346431+691203	405317	Boyan Hu	09/2024
772	82358^82358+2025^2025	404848	Henri Lifchitz	01/2025
773	9*10^404644-11	404645	Mischa Rodermond	04/2023
774	2^1343509+237947	404437	Enzo Doria	07/2025
775	1215^131072+242^131072	404302	Kellen Shenton	08/2022
776	2^1341908+212911	403955	Enzo Doria	09/2023
777	2^1341625+226187	403870	Enzo Doria	09/2024
778	2^1340284+43801	403466	Enzo Doria	04/2025
779	1196^131072+595^131072	403405	Kellen Shenton	08/2022
780	2^1339302+29389	403171	Enzo Doria	04/2024
781	2^1335130+31669	401915	Enzo Doria	07/2024
782	2^1330791+46763	400609	Enzo Doria	06/2025
783	2^1330712+45631	400585	Enzo Doria	05/2025
784	2^1330388+38527	400487	Enzo Doria	11/2024
785	2^1330371+28313	400482	Enzo Doria	03/2024
786	10^400310+9	400311	Boyan Hu	06/2025
787	10^400000+1415223	400001	Patrick De Geest	10/2020
788	10^400000-339233	400000	Patrick De Geest	10/2020
789	2^1327766+48019	399698	Enzo Doria	06/2025
790	2^1323373+27317	398375	Enzo Doria	01/2024
791	Tau(863^24630)	397727	Nik Lygeros / Olivier Rozier	01/2016
792	2^1320423+24293	397487	Enzo Doria	11/2023
793	2^1320057+211517	397377	Enzo Doria	08/2023
794	2^1319770+1884949	397291	Enzo Doria	06/2017
795	2^1319616+30091	397244	Enzo Doria	04/2024
796	2^1317657+31367	396655	Enzo Doria	04/2024
797	2^1316848+43021	396411	Enzo Doria	02/2025
798	2^1316687+45983	396363	Enzo Doria	05/2025
799	2^1315753+226187	396082	Enzo Doria	09/2024
800	2^1314741+219257	395777	Enzo Doria	03/2024
801	2^1313062+1888849	395272	Enzo Doria	08/2017
802	(1073516^81920+1)/(1073516^16384+1)	395236	Serge Batalov	01/2017
803	2^1312349+221177	395057	Enzo Doria	04/2024
804	(1059995^81920+1)/(1059995^16384+1)	394875	Serge Batalov	01/2017
805	2^1311618+783529	394837	Enzo Doria	01/2017
806	2^1310192+232531	394408	Enzo Doria	03/2025
807	2^1308992+28111	394046	Enzo Doria	02/2024
808	2^1308000+1883521	393748	Enzo Doria	02/2017
809	2^1307563+232133	393616	Enzo Doria	03/2025
810	2^1307324+224611	393544	Enzo Doria	07/2024
811	2^1307262+28759	393526	Enzo Doria	02/2024
812	(1009565^81920+1)/(1009565^16384+1)	393487	Serge Batalov	01/2017
813	2^1305860+35461	393104	Enzo Doria	08/2024
814	(995042^81920+1)/(995042^16384+1)	393075	Serge Batalov	01/2017
815	2^1305333+47717	392945	Enzo Doria	06/2025
816	(988945^81920+1)/(988945^16384+1)	392900	Serge Batalov	01/2017
817	(988823^81920+1)/(988823^16384+1)	392897	Serge Batalov	01/2017
818	(2^1304983-1)/52199321	392832	Tony Prest / Never Odd Or Even	03/2014
819	(978970^81920+1)/(978970^16384+1)	392612	Serge Batalov	01/2017
820	2^1303816+38251	392488	Enzo Doria	11/2024
821	2^1303102+1866409	392273	Enzo Doria	09/2017
822	2^1302818+283429	392188	Enzo Doria	01/2017
823	2^1301430+22669	391770	Enzo Doria	10/2023
824	2^1301229+222467	391709	Enzo Doria	04/2024
825	2^1300835+232523	391591	Enzo Doria	03/2025
826	(934422^81920+1)/(934422^16384+1)	391286	Serge Batalov	01/2017
827	2^1299181+1886867	391093	Enzo Doria	04/2017
828	(37^249341-1)/36	391016	Paul Bourdelais	08/2020
829	2^1298304+1882891	390829	Enzo Doria	01/2017
830	2^1297732+228721	390657	Enzo Doria	11/2024
831	95196^12497+12497^95196	390000	Hans Havermann	12/2021
832	2^1295539+35633	389997	Enzo Doria	08/2024
833	86206^33381+33381^86206	389953	Hans Havermann	05/2023
834	2^1294976+236731	389827	Enzo Doria	06/2025
835	2^1294324+25171	389631	Enzo Doria	12/2023
836	(874207^81920+1)/(874207^16384+1)	389390	Serge Batalov	01/2017
837	2^1292338+229249	389033	Enzo Doria	11/2024
838	2^1289624+32551	388216	Enzo Doria	05/2024
839	2^1286857+37967	387383	Enzo Doria	10/2024
840	2^1285458+46159	386962	Enzo Doria	06/2025
841	2^1285456+230611	386961	Enzo Doria	01/2025
842	(7^457871-5^457871)/2	386946	Jon Grantham	08/2023
843	79455^73828+73828^79455	386805	Hans Havermann	03/2023
844	81650^54369+54369^81650	386642	Yusuf AttarBashi	06/2021
845	80565^62824+62824^80565	386561	Hans Havermann	08/2021
846	83747^41272+41272^83747	386548	Hans Havermann	08/2021
847	15^328574+328574^15	386434	Serge Batalov	05/2014
848	2^1282676+30493	386124	Enzo Doria	12/2024
849	2^1280078+1885099	385342	Enzo Doria	08/2017
850	2^1279921+17	385295	Stefano Morozzi	10/2022
851	2^1279245+224087	385092	Enzo Doria	07/2024
852	2^1277980+231391	384711	Enzo Doria	01/2025
853	2^1277688+231241	384623	Enzo Doria	01/2025
854	2^1277142+234979	384459	Enzo Doria	04/2025
855	2^1276977+71657	384409	Enzo Doria	08/2023
856	(76803^78961-1)/(76803^281-1)	384382	Ryan Propper	11/2023
857	2^1276571+26213	384287	Enzo Doria	12/2023
858	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
859	2^1274941+1880717	383796	Enzo Doria	10/2016
860	2^1272632+383431	383101	Enzo Doria	01/2017
861	2^1271346+1889839	382714	Enzo Doria	08/2017
862	2^1271173+219587	382662	Enzo Doria	03/2024
863	5*3^798534-2^798534	380999	Jon Grantham	08/2023
864	(10^380976-7)/3	380976	Leonid Durman	01/2012
865	2^1264748+23221	380728	Enzo Doria	11/2023
866	(4*10^380056+11)/3	380057	Tyler Busby	03/2023
867	2^1262431+228353	380030	Enzo Doria	11/2024
868	2^1260859+222683	379557	Enzo Doria	06/2024
869	2^1258313+43727	378790	Enzo Doria	03/2025
870	2^1257787+1447761	378632	Makoto Morimoto	10/2013
871	(2^1257787+32270)/(223328122073011)	378620	Makoto Morimoto	12/2016
872	2^1257728+20851	378614	Enzo Doria	08/2023
873	(77^200657-1)/76	378536	Paul Bourdelais	08/2020
874	2^1257107+45413	378427	Enzo Doria	05/2025
875	2^1254797+229487	377732	Enzo Doria	11/2024
876	(98^189619+1)/99	377573	Paul Bourdelais	02/2021
877	F(1803059)	376817	Henri Lifchitz	06/2009
878	2^1250590+29389	376466	Enzo Doria	03/2024
879	(10^376417-3^376417)/7	376417	Jon Grantham	08/2023
880	2^1250116+34951	376323	Enzo Doria	08/2024
881	2^1246724+213961	375302	Enzo Doria	10/2023
882	2^1245610+237919	374966	Enzo Doria	06/2025
883	2^1245230+19	374852	Stefano Morozzi	10/2022
884	2^1244263+230033	374561	Enzo Doria	01/2025
885	7^442674+4	374103	Paul Bourdelais	02/2021
886	2^1239151+35633	373022	Enzo Doria	08/2024
887	2^1238732+39181	372896	Enzo Doria	11/2024
888	2^1237699+34703	372585	Enzo Doria	07/2024
889	(97^187393-1)/96	372306	Paul Bourdelais	09/2020
890	2^1235070+46219	371794	Enzo Doria	05/2025
891	10^371696+7	371697	Alfred Reich	05/2021
892	2^1234709+883127	371685	Enzo Doria	12/2016
893	2^1234119+21803	371507	Enzo Doria	09/2023
894	(67^203431+1)/68	371479	Paul Bourdelais	09/2021
895	2^1233971+216593	371463	Enzo Doria	12/2023
896	2^1233212+27301	371234	Enzo Doria	12/2023
897	2^1231529+237557	370728	Enzo Doria	06/2025
898	2^1231466+283819	370709	Enzo Doria	07/2017
899	2^1229766+26659	370197	Enzo Doria	12/2023
900	2^1228899+30713	369936	Enzo Doria	03/2024
901	2^1228892+223831	369934	Enzo Doria	06/2024
902	2^1227635+45413	369555	Enzo Doria	05/2025
903	(49627^78961-1)/(49627^281-1)	369460	Ryan Propper	11/2023
904	2^1227060+226663	369382	Enzo Doria	09/2024
905	2^1226987+28163	369360	Enzo Doria	02/2024
906	2^1226725+234887	369282	Enzo Doria	04/2025
907	2^1226569+30857	369235	Enzo Doria	03/2024
908	2^1225268+46591	368843	Enzo Doria	05/2025
909	73^197880+197880	368715	Kellen Shenton	06/2023
910	5*3^771723-2^771723	368207	Jon Grantham	08/2023
911	2^1222741+231707	368082	Enzo Doria	02/2025
912	2^1222473+221597	368002	Enzo Doria	04/2024
913	2^1222211+22703	367923	Enzo Doria	11/2023
914	(2^1222097+19)/3	367888	Stefano Morozzi	09/2022
915	2^1220335+1881263	367358	Enzo Doria	11/2016
916	2^1218344+215641	366759	Enzo Doria	12/2023
917	2^1217510+220039	366508	Enzo Doria	03/2024
918	2^1217500+226321	366505	Enzo Doria	09/2024
919	(233^154787-1)/232	366434	Anonymous	05/2024
920	2^1216694+1884769	366262	Enzo Doria	02/2017
921	2^1216267+45143	366133	Enzo Doria	05/2025
922	2^1215889-3	366020	Paul Bourdelais	06/2019
923	2^1215296+1885441	365841	Enzo Doria	03/2017
924	(80^192133+1)/81	365645	Paul Bourdelais	01/2021
925	2^1214307+1888115	365543	Enzo Doria	05/2017
926	2^1213815+3	365395	Paul Bourdelais	06/2019
927	(80^191953+1)/81	365302	Paul Bourdelais	01/2021
928	2^1213313+215837	365244	Enzo Doria	11/2023
929	2^1208276+22201	363728	Enzo Doria	09/2023
930	2^1207345+1882577	363448	Enzo Doria	12/2016
931	2^1207336+217801	363445	Enzo Doria	03/2024
932	2^1207073+883727	363366	Enzo Doria	03/2017
933	3^761457-2	363308	Ryan Propper	07/2015
934	(10^363030+7)/337/443	363025	Alfred Reich	12/2021
935	2^1204869+224885	362702	Enzo Doria	07/2024
936	2^1204540+237541	362603	Enzo Doria	07/2025
937	2^1203721+44117	362357	Enzo Doria	04/2025
938	2^1200972+141811	361529	Stefano Morozzi	10/2022
939	(2^1200924+324730)/2	361514	Stefano Morozzi	06/2021
940	(2^1200912+274110)/2	361511	Stefano Morozzi	01/2021
941	2^1200906+165249	361509	Stefano Morozzi	07/2022
942	2^1200890+166339	361504	Stefano Morozzi	01/2023
943	(2^1200887+344126)/2	361503	Stefano Morozzi	10/2020
944	2^1200877+186755	361500	Stefano Morozzi	09/2022
945	2^1200861+198521	361496	Stefano Morozzi	11/2021
946	(2^1200856+305790)/2	361494	Stefano Morozzi	10/2020
947	(2^1200853+372822)/2	361493	Stefano Morozzi	06/2021
948	2^1200812+324178)/2	361481	Stefano Morozzi	06/2021
949	(2^1200768+380458)/2	361467	Stefano Morozzi	01/2021
950	2^1200756+140917	361464	Stefano Morozzi	05/2022
951	2^1200741+184781	361460	Stefano Morozzi	09/2022
952	(2^1200741+293402)/2	361459	Stefano Morozzi	07/2021
953	2^1200734+142653	361457	Stefano Morozzi	02/2023
955	2^1200672+1880881	361439	Enzo Doria	10/2016
954	2^1200672+141535	361439	Stefano Morozzi	09/2022
956	2^1200669+178805	361438	Stefano Morozzi	11/2022
957	2^1200660+198555	361435	Stefano Morozzi	12/2021
958	2^1200657+164837	361434	Stefano Morozzi	05/2022
959	2^1200631+166431	361426	Stefano Morozzi	02/2023
960	2^1200627+150669	361425	Stefano Morozzi	02/2023
961	(2^1200603+356030)/2	361418	Stefano Morozzi	10/2020
962	(2^1200590+275854)/2	361414	Stefano Morozzi	03/2021
963	2^1200550+139297	361402	Stefano Morozzi	10/2021
964	2^1200486+172855	361383	Stefano Morozzi	01/2023
965	(2^1200456+320526)/2	361373	Stefano Morozzi	10/2020
966	2^1200443+142121	361370	Stefano Morozzi	01/2023
967	2^1200416+164065	361362	Stefano Morozzi	01/2022
968	2^1200331+155429	361336	Stefano Morozzi	10/2021
970	(2^1200289+348366)/2	361323	Stefano Morozzi	10/2020
969	2^1200289+141885	361323	Stefano Morozzi	11/2022
971	(2^1200284+273162)/2	361322	Stefano Morozzi	10/2020
972	2^1200252+194535	361312	Stefano Morozzi	11/2021
973	(2^1200250+364230)/2	361311	Stefano Morozzi	10/2020
974	2^1200227+156881	361305	Stefano Morozzi	05/2022
975	(2^1200209+305990)/2	361299	Stefano Morozzi	10/2020
976	(2^1200210+376278)/2	361299	Stefano Morozzi	10/2020
977	2^1200202+216499	361297	Enzo Doria	12/2023
978	(2^1200182+274462)/2	361291	Stefano Morozzi	01/2021
979	2^1200178+149193	361290	Stefano Morozzi	07/2022
980	2^1200168+140403	361287	Stefano Morozzi	03/2022
981	(2^1200162+275910)/2	361285	Stefano Morozzi	03/2021
982	2^1200157+168927	361284	Stefano Morozzi	02/2023
983	2^1200134+141385	361277	Stefano Morozzi	08/2022
984	(2^1200131+360150)/2	361276	Stefano Morozzi	10/2020
985	(2^1200118+290718)/2	361272	Stefano Morozzi	01/2021
986	2^1200022+192777	361243	Stefano Morozzi	09/2022
987	2^1200021+149777	361243	Stefano Morozzi	10/2022
988	(64*10^360173-1)/243	360173	Serge Batalov	09/2014
989	(59^203309+1)/60	360029	Paul Bourdelais	09/2021
990	(2*10^359860-11)/9	359860	Rytis Slatkevicius	01/2023
991	2^1195093+1882577	359759	Enzo Doria	12/2016
992	3^753451+5*2^753451	359488	Jon Grantham	08/2023
993	2^1193505+238397	359281	Enzo Doria	07/2025
994	2^1192258+36739	358906	Enzo Doria	09/2024
995	2^1192251+47183	358904	Enzo Doria	06/2025
996	(6^461108-11)/5	358812	Paul Bourdelais	04/2019
997	2^1191375+8543	358640	Phil Moore	06/2008
998	2^1190972+1880191	358519	Enzo Doria	11/2016
999	2^1189930+28549	358205	Enzo Doria	03/2024
1000	(45^216551-1)/44	358004	Paul Bourdelais	08/2020

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Probable Primes Top 10000

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