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 ?
501	(77^200657-1)/76	378536	Paul Bourdelais	08/2020
502	(98^189619+1)/99	377573	Paul Bourdelais	02/2021
503	F(1803059)	376817	Henri Lifchitz	06/2009
504	(10^376417-3^376417)/7	376417	Jon Grantham	08/2023
505	2^1246724+213961	375302	Enzo Doria	10/2023
506	2^1245230+19	374852	Stefano Morozzi	10/2022
507	7^442674+4	374103	Paul Bourdelais	02/2021
508	(97^187393-1)/96	372306	Paul Bourdelais	09/2020
509	10^371696+7	371697	Alfred Reich	05/2021
510	2^1234709+883127	371685	Enzo Doria	12/2016
511	2^1234119+21803	371507	Enzo Doria	09/2023
512	(67^203431+1)/68	371479	Paul Bourdelais	09/2021
513	2^1231466+283819	370709	Enzo Doria	07/2017
514	(49627^78961-1)/(49627^281-1)	369460	Ryan Propper	11/2023
515	73^197880+197880	368715	Kellen Shenton	06/2023
516	5*3^771723-2^771723	368207	Jon Grantham	08/2023
517	2^1222211+22703	367923	Enzo Doria	11/2023
518	(2^1222097+19)/3	367888	Stefano Morozzi	09/2022
519	2^1220335+1881263	367358	Enzo Doria	11/2016
520	2^1216694+1884769	366262	Enzo Doria	02/2017
521	2^1215889-3	366020	Paul Bourdelais	06/2019
522	2^1215296+1885441	365841	Enzo Doria	03/2017
523	(80^192133+1)/81	365645	Paul Bourdelais	01/2021
524	2^1214307+1888115	365543	Enzo Doria	05/2017
525	2^1213815+3	365395	Paul Bourdelais	06/2019
526	(80^191953+1)/81	365302	Paul Bourdelais	01/2021
527	2^1213313+215837	365244	Enzo Doria	11/2023
528	2^1208276+22201	363728	Enzo Doria	09/2023
529	2^1207345+1882577	363448	Enzo Doria	12/2016
530	2^1207073+883727	363366	Enzo Doria	03/2017
531	3^761457-2	363308	Ryan Propper	07/2015
532	(10^363030+7)/337/443	363025	Alfred Reich	12/2021
533	2^1200972+141811	361529	Stefano Morozzi	10/2022
534	(2^1200924+324730)/2	361514	Stefano Morozzi	06/2021
535	(2^1200912+274110)/2	361511	Stefano Morozzi	01/2021
536	2^1200906+165249	361509	Stefano Morozzi	07/2022
537	2^1200890+166339	361504	Stefano Morozzi	01/2023
538	(2^1200887+344126)/2	361503	Stefano Morozzi	10/2020
539	2^1200877+186755	361500	Stefano Morozzi	09/2022
540	2^1200861+198521	361495	Stefano Morozzi	11/2021
541	(2^1200856+305790)/2	361494	Stefano Morozzi	10/2020
542	(2^1200853+372822)/2	361493	Stefano Morozzi	06/2021
543	2^1200812+324178)/2	361481	Stefano Morozzi	06/2021
544	(2^1200768+380458)/2	361467	Stefano Morozzi	01/2021
545	2^1200756+140917	361464	Stefano Morozzi	05/2022
546	2^1200741+184781	361460	Stefano Morozzi	09/2022
547	(2^1200741+293402)/2	361459	Stefano Morozzi	07/2021
548	2^1200734+142653	361457	Stefano Morozzi	02/2023
550	2^1200672+1880881	361439	Enzo Doria	10/2016
549	2^1200672+141535	361439	Stefano Morozzi	09/2022
551	2^1200669+178805	361438	Stefano Morozzi	11/2022
552	2^1200660+198555	361435	Stefano Morozzi	12/2021
553	2^1200657+164837	361434	Stefano Morozzi	05/2022
554	2^1200631+166431	361426	Stefano Morozzi	02/2023
555	2^1200627+150669	361425	Stefano Morozzi	02/2023
556	(2^1200603+356030)/2	361418	Stefano Morozzi	10/2020
557	(2^1200590+275854)/2	361414	Stefano Morozzi	03/2021
558	2^1200550+139297	361402	Stefano Morozzi	10/2021
559	2^1200486+172855	361383	Stefano Morozzi	01/2023
560	(2^1200456+320526)/2	361373	Stefano Morozzi	10/2020
561	2^1200443+142121	361370	Stefano Morozzi	01/2023
562	2^1200416+164065	361362	Stefano Morozzi	01/2022
563	2^1200331+155429	361336	Stefano Morozzi	10/2021
565	(2^1200289+348366)/2	361323	Stefano Morozzi	10/2020
564	2^1200289+141885	361323	Stefano Morozzi	11/2022
566	(2^1200284+273162)/2	361322	Stefano Morozzi	10/2020
567	2^1200252+194535	361312	Stefano Morozzi	11/2021
568	(2^1200250+364230)/2	361311	Stefano Morozzi	10/2020
569	2^1200227+156881	361305	Stefano Morozzi	05/2022
570	(2^1200209+305990)/2	361299	Stefano Morozzi	10/2020
571	(2^1200210+376278)/2	361299	Stefano Morozzi	10/2020
572	(2^1200182+274462)/2	361291	Stefano Morozzi	01/2021
573	2^1200178+149193	361290	Stefano Morozzi	07/2022
574	2^1200168+140403	361287	Stefano Morozzi	03/2022
575	(2^1200162+275910)/2	361285	Stefano Morozzi	03/2021
576	2^1200157+168927	361284	Stefano Morozzi	02/2023
577	2^1200134+141385	361277	Stefano Morozzi	08/2022
578	(2^1200131+360150)/2	361276	Stefano Morozzi	10/2020
579	(2^1200118+290718)/2	361272	Stefano Morozzi	01/2021
580	2^1200022+192777	361243	Stefano Morozzi	09/2022
581	2^1200021+149777	361243	Stefano Morozzi	10/2022
582	(64*10^360173-1)/243	360173	Serge Batalov	09/2014
583	(59^203309+1)/60	360029	Paul Bourdelais	09/2021
584	(2*10^359860-11)/9	359860	Rytis Slatkevicius	01/2023
585	2^1195093+1882577	359759	Enzo Doria	12/2016
586	3^753451+5*2^753451	359488	Jon Grantham	08/2023
587	(6^461108-11)/5	358812	Paul Bourdelais	04/2019
588	2^1191375+8543	358640	Phil Moore	06/2008
589	2^1190972+1880191	358519	Enzo Doria	11/2016
590	(45^216551-1)/44	358004	Paul Bourdelais	08/2020
591	(50^210319-1)/49	357324	Paul Bourdelais	08/2020
592	(531^131072+25^131072)/2	357184	Kellen Shenton	03/2021
593	2^1184565+21227	356590	Enzo Doria	08/2023
594	2^1180159+22823	355264	Enzo Doria	11/2023
595	2^1179836+1885021	355167	Enzo Doria	02/2017
596	(19*10^353884-91)/9	353885	Alfred Reich	02/2023
597	(10^353884*19-91)/9	353885	Alfred Reich	10/2023
598	20^271951+3	353817	Paul Bourdelais	01/2021
599	2^1173095+21	353137	Stefano Morozzi	10/2022
600	(63^195893-1)/62	352477	Paul Bourdelais	08/2020
601	2^1170326+7	352304	Stefano Morozzi	10/2022
602	numbpart(100000135540)	352269	Serge Batalov	04/2017
603	(10^352237-1)/9/10567111/950335427	352221	Maksym Voznyy	01/2015
604	5*3^737931-2^737931	352084	Jon Grantham	08/2023
605	2^1168554+783529	351770	Enzo Doria	01/2017
606	(2^1168183-1)/54763676838381762583	351639	Matthias Wurtinger	01/2011
607	2^1166152+1882411	351047	Enzo Doria	12/2016
608	2^1163972+20971	350391	Enzo Doria	08/2023
609	2^1163272+22411	350180	Enzo Doria	10/2023
610	10^350071+7	350072	Alfred Reich	05/2021
611	2^1162154+1890207	349844	Enzo Doria	08/2017
612	(7*10^348724-61)/9	348724	Erik Branger	09/2016
613	(4*10^348453+41)/9	348453	Serge Batalov	11/2022
614	(127^165601-1)/126	348390	Alexander Zhirkov	09/2015
615	2^1155085+213377	347716	Enzo Doria	09/2023
616	2^1153083+1883693	347113	Enzo Doria	04/2017
617	(2^1148729+2^574365+1)/5	345802	Borys Jaworski	03/2007
618	2^1145882+80779	344945	Enzo Doria	09/2016
619	2^1136462+1887289	342110	Enzo Doria	05/2017
620	F(1636007)	341905	Henri Lifchitz	03/2009
621	(2^1135567+13)/3	341840	Stefano Morozzi	09/2022
622	2^1133678+782569	341272	Enzo Doria	11/2016
623	(11^327001+1)/12	340536	Paul Bourdelais	09/2013
624	(2^1127239+2^563620+1)/5	339333	Borys Jaworski	11/2006
625	Tau(907^20848)	339132	Nik Lygeros / Olivier Rozier	01/2016
626	2^1126380-3	339075	Paul Bourdelais	06/2019
627	2^1125784+24331	338895	Enzo Doria	10/2023
628	2^1125446+1885099	338794	Enzo Doria	08/2017
629	(63^188147+1)/64	338539	Paul Bourdelais	12/2020
630	2^1124549+143807	338523	Enzo Doria	10/2016
631	(4*10^338476+23)/9	338476	Serge Batalov	11/2022
632	2^1121187+1886783	337511	Enzo Doria	04/2017
633	(48^200443-1)/47	336992	Paul Bourdelais	08/2020
634	(2*10^336405+43)/9	336405	Rytis Slatkevicius	01/2023
635	(94^170371-1)/93	336162	Paul Bourdelais	09/2020
636	2^1116184+1883521	336005	Enzo Doria	02/2017
637	2^1114517+1880087	335504	Enzo Doria	10/2016
638	(5*10^335480+31)/9	335480	Serge Batalov	11/2022
639	5*3^701688+2^701688	334791	Jon Grantham	08/2023
640	(101^166849+1)/102	334418	Paul Bourdelais	12/2020
641	(3^700897+1)/4	334413	Paul Bourdelais	04/2010
642	2^1104500+22411	332488	Enzo Doria	10/2023
643	2^1104408-114539	332460	Enzo Doria	03/2015
644	2^1101921+82085	331712	Enzo Doria	10/2016
645	2^1100655+683513	331331	Enzo Doria	01/2017
646	(10^330906+71)/9	330906	Serge Batalov	07/2015
647	2^1098346+482899	330636	Enzo Doria	11/2016
648	(2^1096212+19)/5	329992	Stefano Morozzi	09/2022
649	2^1095679+1878713	329833	Enzo Doria	09/2016
650	2^1094740-1851539	329550	Enzo Doria	08/2015
651	2^1092242+19	328798	Stefano Morozzi	10/2022
652	2^1091469-379369	328565	Enzo Doria	03/2014
653	2^1090801+24227	328364	Enzo Doria	10/2023
654	(69^178093-1)/68	327485	Paul Bourdelais	08/2020
655	(10^326884+7)/421	326882	Alfred Reich	12/2021
656	2^1085750+582349	326844	Enzo Doria	11/2016
657	(54308^69169-1)/(54308^263-1)	326261	Ryan Propper	11/2023
658	2^1083596+483061	326195	Enzo Doria	12/2016
659	(2^541456-1)*10^162995+2^541455-1	325990	paolo galliani	01/2019
660	2^1082908+583561	325988	Enzo Doria	05/2017
661	30^220411-29^220411	325574	Jean-Louis Charton	10/2018
662	2^1081308+7	325507	Stefano Morozzi	10/2022
663	2^1080032+25171	325123	Enzo Doria	11/2023
664	2^1078242+1881649	324584	Enzo Doria	11/2016
665	2^1077737+1880117	324432	Enzo Doria	10/2016
666	3^679017-5*2^679017	323974	Jon Grantham	08/2023
667	2^1075425+1880117	323736	Enzo Doria	10/2016
668	(28^223381+1)/29	323267	Paul Bourdelais	12/2020
669	10^322999+187071	323000	Stefano Morozzi	03/2019
670	10^322999-143151	322999	Patrick De Geest	05/2020
671	2^1072146+1886869	322749	Enzo Doria	04/2017
672	2^1072118-7321953	322740	Enzo Doria	02/2015
673	2^1071026+1886869	322411	Enzo Doria	04/2017
674	2^1070539+1880633	322265	Enzo Doria	10/2016
675	2^1069293-1147195	321890	Enzo Doria	05/2015
676	2^1065968+1880941	320889	Enzo Doria	10/2016
677	2^1065897-1147195	320867	Enzo Doria	05/2015
678	2^1063427+1882103	320124	Enzo Doria	12/2016
679	2^1061095-1061095	319422	Henri Lifchitz	10/2013
680	2^1060950+653119	319378	Enzo Doria	12/2016
681	2^1060363+782753	319202	Enzo Doria	11/2016
682	(71^172259-1)/70	318895	Paul Bourdelais	08/2020
683	-30*Bern(85996)/236037521	318354	Sergey Batalov	10/2023
684	2^1054736+483061	317508	Enzo Doria	12/2016
685	2^1053965+1879667	317276	Enzo Doria	10/2016
686	(43^194119-1)/42	317086	Paul Bourdelais	08/2020
687	2^1052186-458165	316740	Enzo Doria	03/2015
688	11^303909+2	316489	Paul Bourdelais	08/2023
689	2^1049026+214609	315789	Enzo Doria	11/2023
690	2^1046613-114685	315062	Enzo Doria	04/2015
691	2^1045625-459373	314765	Enzo Doria	06/2015
692	10^(2157363+1)-810^157363-1	314727	Robert Price	07/2023
693	(7*10^314564-61)/9	314564	Erik Branger	09/2016
694	2^1044206+7	314338	Stefano Morozzi	10/2022
695	(7^371669-1)/6	314096	Paul Bourdelais	02/2010
696	(53^181981-1)/52	313784	Paul Bourdelais	08/2020
697	(8^347437-5^347437)/3	313767	Jon Grantham	08/2023
698	2^1041944+283051	313657	Enzo Doria	12/2016
699	(1624^97969-1)/(1624^313-1)	313533	Sergey Batalov	11/2023
700	2^1041153-114391	313419	Enzo Doria	02/2015
701	(2^1039700+9)/5	312981	Stefano Morozzi	09/2022
702	(74^167311+1)/75	312742	Paul Bourdelais	12/2020
703	2^1038871+1866983	312732	Enzo Doria	04/2016
704	2^1038545+71657	312634	Enzo Doria	08/2023
705	(55^179573-1)/54	312521	Paul Bourdelais	08/2020
706	2^1037647+1881263	312363	Enzo Doria	11/2016
707	2^1037226+1879699	312237	Enzo Doria	10/2016
708	2^1036867+1865843	312129	Enzo Doria	02/2016
709	(76^165947+1)/77	312114	Paul Bourdelais	01/2021
710	2^1036020-114539	311874	Enzo Doria	02/2015
711	(90^159463-1)/89	311628	Paul Bourdelais	08/2020
712	2^1032240+1883431	310736	Enzo Doria	01/2017
713	64211^64588+64588^64211	310514	Norbert Schneider	11/2023
714	2^1030352+1870021	310167	Enzo Doria	06/2016
715	2^1030046+1882843	310075	Enzo Doria	11/2016
716	3^648872+16	309591	Robert Price	04/2020
717	(16976^73441-1)/(16976^271-1)	309498	Ryan Propper	11/2023
718	64221^64366+64366^64221	309451	Norbert Schneider	06/2023
719	(11121^76729-1)/(11121^277-1)	309336	Ryan Propper	11/2023
720	2^1026999+20513	309158	Enzo Doria	07/2023
721	5^442281+2	309142	Paul Bourdelais	01/2021
722	2^1026204+22741	308919	Enzo Doria	09/2023
723	2^1026190+15	308914	Stefano Morozzi	10/2022
724	2^1025108+20851	308589	Enzo Doria	08/2023
725	A352736(16)	306985	Kellen Shenton	05/2022
726	2^1019777+213947	306984	Enzo Doria	10/2023
727	(11^293831-1)/10	305993	Paul Bourdelais	03/2010
728	(67^167449-1)/66	305773	Paul Bourdelais	08/2020
729	(62^170539+1)/63	305671	Paul Bourdelais	12/2020
730	2^1015321-1015321	305643	Henri Lifchitz	08/2013
731	2^1014450+7	305380	Stefano Morozzi	10/2022
732	2^1014224-2791229	305312	Enzo Doria	01/2016
733	(10^304986+7)/673	304984	Alfred Reich	11/2021
734	65473^45250+45250^65473	304818	Hans Havermann	02/2022
735	66012^41423+41423^66012	304794	Hans Havermann	03/2022
736	65073^48202+48202^65073	304742	Hans Havermann	04/2022
737	238176^19+19^238176	304569	Hans Havermann	03/2022
738	73122^14615+14615^73122	304539	Hans Havermann	05/2022
739	64492^52639+52639^64492	304487	Hans Havermann	03/2022
740	65955^41288+41288^65955	304437	Hans Havermann	04/2022
741	71729^17530+17530^71729	304403	Hans Havermann	03/2022
742	70170^21733+21733^70170	304336	Hans Havermann	03/2022
743	2^1010751-107709	304267	Enzo Doria	03/2014
744	84473^3994+3994^84473	304222	Hans Havermann	03/2022
745	(2^1010623-1)/12602017578957977	304212	Tony Prest / Never Odd Or Even	02/2014
746	74442^12125+12125^74442	303998	Hans Havermann	02/2022
747	77842^8039+8039^77842	303989	Hans Havermann	01/2022
748	64209^54140+54140^64209	303935	Hans Havermann	02/2022
749	2^1009577+1869587	303913	Enzo Doria	06/2016
750	67389^32338+32338^67389	303906	Hans Havermann	02/2022

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