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	2^1688360+233581	508248	Enzo Doria	05/2025
502	2^1688111+217313	508173	Enzo Doria	04/2024
503	(118270^100489-1)/(118270^317-1)	508160	Ryan Propper	11/2023
504	2^1687922+40849	508116	Enzo Doria	01/2025
505	2^1687521+230267	507995	Enzo Doria	01/2025
506	105196^67205+67205^105196	507824	Miklos Levai	09/2023
507	2^1686452+220681	507673	Enzo Doria	04/2024
508	2^1685708+27781	507449	Enzo Doria	01/2024
509	2^1685513+53597	507390	Enzo Doria	01/2026
510	(72^273149-1)/71	507327	Paul Bourdelais	02/2022
511	2^1685092+227191	507264	Enzo Doria	12/2024
512	105154^66373+66373^105154	507052	Miklos Levai	09/2023
513	2^1683331+225413	506734	Enzo Doria	09/2024
514	107890^49423+49423^107890	506429	Miklos Levai	02/2022
515	(14^441697-1)/13	506241	Paul Bourdelais	12/2014
516	2^1681560+244291	506200	Enzo Doria	04/2026
517	101645^94522+94522^101645	505739	Gabor Levai	02/2023
518	3^1059503-2^1059503	505512	Mike Oakes	04/2012
519	2^1678670+21529	505331	Enzo Doria	11/2023
520	101542^92885+92885^101542	504456	Gabor Levai	04/2022
521	2^1675306+227839	504318	Enzo Doria	12/2024
522	2^1674819+42683	504171	Enzo Doria	04/2025
523	2^1673623+42983	503811	Enzo Doria	03/2025
524	105273^60238+60238^105273	503192	Miklos Levai	09/2023
525	105098^61113+61113^105098	503014	Miklos Levai	09/2022
526	2^1670703+60293	502932	Enzo Doria	11/2017
527	(2^1669219-2^834610+1)/5	502485	Borys Jaworski	01/2011
528	101311^90816+90816^101311	502317	Gabor Levai	12/2021
529	101643^87368+87368^101643	502254	Gabor Levai	11/2022
530	(161502^96721-1)/(161502^311-1)	502121	Ryan Propper	11/2023
531	101863^84922+84922^101863	502085	Gabor Levai	10/2022
532	2^1666440+212671	501649	Enzo Doria	09/2023
533	100291^100291+172^172	501582	Serge Batalov	04/2024
534	2^1666177+226697	501570	Enzo Doria	10/2024
535	2^1664940+53821	501197	Enzo Doria	04/2026
536	100207^99856+99856^100207	500973	Gabor Levai	11/2021
537	101839^83028+83028^101839	500969	Gabor Levai	11/2022
538	2^1663461+242357	500752	Enzo Doria	11/2025
539	100263^98600+98600^100263	500702	Gabor Levai	09/2021
540	2^1662045+37607	500326	Enzo Doria	11/2024
541	2^1661503+43553	500163	Enzo Doria	04/2025
542	101761^82168+82168^101761	500126	Gabor Levai	03/2022
543	2^1661176+336631	500064	Tony Prest / Never Odd Or Even	09/2019
544	8603^127088-127088^8603	500047	Norbert Schneider	06/2025
545	101070^88579+88579^101070	500027	Gabor Levai	01/2022
546	(85^259159-1)/84	500025	Paul Bourdelais	11/2021
547	2^1660973+368139	500003	Tony Prest / Never Odd Or Even	08/2020
548	100000^100000+85707^85707	500001	Henri Lifchitz	01/2025
549	2^1660964-382425	500000	Tony Prest / Never Odd Or Even	05/2020
550	2^1660328+226951	499809	Enzo Doria	04/2025
551	(87^257689-1)/86	499791	Paul Bourdelais	01/2021
552	(64*10^499210+53)/9	499211	Serge Batalov	03/2015
553	2^1656126+223227	498544	Enzo Doria	03/2025
554	Tau(631^32370)	498503	Nik Lygeros / Olivier Rozier	05/2015
555	2^1653321+49217	497700	Enzo Doria	09/2025
556	29^339887-28^339887	497051	Jean-Louis Charton	05/2019
557	2^1650975+185225	496993	Stefano Morozzi	09/2024
558	2^1650959+198513	496989	Stefano Morozzi	09/2024
559	2^1650942+181575	496984	Stefano Morozzi	09/2024
560	2^1650940+239581	496983	Enzo Doria	11/2025
561	2^1650905+193947	496972	Stefano Morozzi	09/2024
562	2^1650877+186537	496964	Stefano Morozzi	01/2025
563	2^1650867+192615	496961	Stefano Morozzi	09/2024
564	2^1650854+188973	496957	Stefano Morozzi	01/2025
565	2^1650837+199641	496952	Stefano Morozzi	01/2025
566	2^1650819+198315	496947	Stefano Morozzi	07/2024
567	2^1650788+185823	496937	Stefano Morozzi	09/2024
568	2^1650749+185235	496925	Stefano Morozzi	06/2024
569	2^1650695+183141	496909	Stefano Morozzi	04/2024
570	2^1650640+185311	496893	Stefano Morozzi	03/2024
571	2^1650593+187871	496879	Stefano Morozzi	03/2024
572	2^1650538+196863	496862	Stefano Morozzi	03/2024
573	2^1650484+181413	496846	Stefano Morozzi	03/2024
574	2^1650473+193151	496842	Stefano Morozzi	03/2024
575	2^1650443+193613	496833	Stefano Morozzi	01/2024
576	2^1650426+183543	496828	Stefano Morozzi	01/2024
577	2^1650388+189741	496817	Stefano Morozzi	10/2023
578	2^1650267+193743	496780	Stefano Morozzi	09/2023
579	2^1650196+191835	496759	Stefano Morozzi	07/2023
580	2^1650190+185733	496757	Stefano Morozzi	07/2023
581	2^1650141+189525	496742	Stefano Morozzi	07/2023
582	2^1650103+189519	496731	Stefano Morozzi	05/2023
583	2^1648342+215029	496201	Enzo Doria	01/2024
584	2^1646078+36937	495519	Enzo Doria	10/2024
585	2^1645332+34951	495295	Enzo Doria	12/2024
586	(136688^96721-1)/(136688^311-1)	495136	Ryan Propper	11/2023
587	2^1643411+26213	494717	Enzo Doria	03/2024
588	2^1642987+238853	494589	Enzo Doria	09/2025
589	2^1642104+227491	494323	Enzo Doria	10/2024
590	2^1640056+216241	493707	Enzo Doria	02/2024
591	2^1639019+45113	493394	Enzo Doria	05/2025
592	2^1636027+25763	492494	Enzo Doria	01/2024
593	2^1636012+238741	492489	Enzo Doria	10/2025
594	2^1635235+227693	492255	Enzo Doria	10/2024
595	2^1632498+30397	491431	Enzo Doria	08/2024
596	2^1631030+73519	490989	Enzo Doria	08/2023
597	2^1629568+237541	490549	Enzo Doria	08/2025
598	(2^1629469-1)/644908484660139264379223	490496	Gord Palameta	11/2017
599	2^1627834+225529	490027	Enzo Doria	08/2024
600	2^1626709+30407	489689	Enzo Doria	07/2024
601	2^1626438+38557	489607	Enzo Doria	11/2024
602	2^1621040+39415	487982	Enzo Doria	11/2024
603	2^1619885+28229	487634	Enzo Doria	04/2024
604	10^487291+7	487292	Alfred Reich	06/2021
605	2^1617677+227927	486970	Enzo Doria	10/2024
606	2^1617579+1889543	486940	Enzo Doria	09/2017
607	97481^97481-70^70	486325	Henri Lifchitz	10/2024
608	2^1613665+237257	485762	Enzo Doria	07/2025
609	2^1613632+215011	485752	Enzo Doria	11/2023
610	2^1612600+27331	485441	Enzo Doria	03/2024
611	2^1610146+24739	484703	Enzo Doria	11/2023
612	2^1609596+240481	484537	Enzo Doria	12/2025
613	2^1609360+43711	484466	Enzo Doria	03/2025
614	L(2316773)	484177	Serge Batalov	06/2017
615	(57^275669-1)/56	484039	Paul Bourdelais	04/2021
616	2^1602171+40943	482302	Enzo Doria	01/2025
617	2^1601964+215491	482240	Enzo Doria	11/2023
618	10^482076+9	482077	Boyan Hu	06/2025
619	96672^96672-1825^1825	481939	Henri Lifchitz	12/2024
620	2^1600308+34051	481741	Enzo Doria	09/2024
621	2^1599674+43909	481550	Enzo Doria	04/2025
622	2^1599624+20011	481535	Enzo Doria	07/2023
623	2^1599281+237557	481432	Enzo Doria	08/2025
624	2^1599238+234559	481419	Enzo Doria	04/2025
625	2^1599205+27047	481409	Enzo Doria	03/2024
626	2^1599120-5	481384	Stefano Morozzi	12/2022
627	10^480684-3	480684	Paul Bourdelais	01/2021
628	2^1595483+184133	480289	Enzo Doria	07/2017
629	2^1594947+3	480127	Paul Bourdelais	07/2019
630	2^1594420+36781	479969	Enzo Doria	10/2024
631	2^1594135+225893	479883	Enzo Doria	10/2024
632	2^1594129+22697	479881	Enzo Doria	11/2023
633	2^1593922+213289	479819	Enzo Doria	10/2023
634	2^1592677+228257	479444	Enzo Doria	11/2024
635	2^1592625+234041	479428	Enzo Doria	04/2025
636	2^1592234+26809	479311	Enzo Doria	03/2024
637	2^1590797+34967	478878	Enzo Doria	10/2024
638	2^1590424+54061	478766	Enzo Doria	03/2026
639	(94^241993-1)/93	477482	Paul Bourdelais	09/2020
640	2^1585195+1888373	477192	Enzo Doria	08/2017
641	2^1585021+43427	477139	Enzo Doria	03/2025
642	2^1583403+242513	476652	Enzo Doria	12/2025
643	2^1583251+244223	476607	Enzo Doria	03/2026
644	(33^313553+1)/34	476134	Paul Bourdelais	02/2021
645	2^1581306+220309	476021	Enzo Doria	03/2024
646	2^1579739+50783	475549	Enzo Doria	10/2025
647	2^1578654+215029	475223	Enzo Doria	01/2024
648	(84615^96721-1)/(84615^311-1)	475056	Ryan Propper	11/2023
649	3^994536+16	474515	Robert Price	10/2020
650	2^1576219+233663	474490	Enzo Doria	03/2025
651	2^1575391+71483	474240	Enzo Doria	04/2018
652	(2^1572882+5)/3	473485	Serge Batalov	08/2015
653	2^1572882+50239	473485	Enzo Doria	09/2025
654	2^1572813+240791	473464	Enzo Doria	11/2025
655	2^1572728+45421	473439	Enzo Doria	07/2025
656	(6^608099-1)/5	473193	Paul Bourdelais	05/2010
657	2^1570431+41183	472747	Enzo Doria	02/2025
658	2^1569708+20371	472530	Enzo Doria	09/2023
659	2^1569375+29153	472429	Enzo Doria	05/2024
660	3^989124+16	471933	Robert Price	10/2020
661	2^1567518+51289	471870	Enzo Doria	01/2026
662	2^1567006+1888099	471716	Enzo Doria	05/2017
663	-E(107194)/47	471629	Serge Batalov	07/2025
664	2^1564510+45709	470965	Enzo Doria	06/2025
665	2^1563462+39919	470649	Enzo Doria	12/2024
666	2^1563067+1889813	470531	Enzo Doria	08/2017
667	2^1562428+215851	470338	Enzo Doria	02/2024
668	2^1557036+226321	468715	Enzo Doria	09/2024
669	2^1556730+222829	468623	Enzo Doria	07/2024
670	2^1554175+228353	467854	Enzo Doria	12/2024
671	2^1554078+53359	467825	Enzo Doria	12/2025
672	2^1551415+215813	467023	Enzo Doria	02/2024
673	2^1551411+212933	467022	Enzo Doria	09/2023
674	2^1550887+36743	466864	Enzo Doria	11/2024
675	2^1549797+60197	466536	Enzo Doria	02/2018
676	2^1549030+1887619	466305	Enzo Doria	05/2017
677	2^1545920+41467	465369	Enzo Doria	02/2025
678	2^1544971+43403	465083	Enzo Doria	03/2025
679	416^177481-415^177481	464840	Jean-Louis Charton	12/2016
680	2^1541374+226729	464000	Enzo Doria	09/2024
681	(78^245183-1)/77	463908	Paul Bourdelais	02/2021
682	93331^93331-90^90	463858	Henri Lifchitz	10/2024
683	2^1540755+236603	463814	Enzo Doria	08/2025
684	2^1540117+31907	463622	Enzo Doria	04/2024
685	2^1538959-25	463273	Boyan Hu	01/2025
686	2^1537058+29839	462701	Enzo Doria	07/2024
687	2^1534770+20809	462012	Enzo Doria	08/2023
688	2^1531286+24799	460964	Enzo Doria	11/2023
689	2^1530725+38267	460795	Enzo Doria	10/2024
690	2^1530380+38011	460691	Enzo Doria	11/2024
691	2^1527857+225269	459931	Enzo Doria	11/2024
692	2^1527070+47659	459694	Enzo Doria	07/2025
693	10^459480-11	459480	Mischa Rodermond	04/2023
694	2^1526274+44629	459455	Enzo Doria	05/2025
695	(5^656657-2^656657)/3	458984	Jon Grantham	08/2023
696	2^1522569+71657	458339	Enzo Doria	04/2018
697	2^1521240+54061	457939	Enzo Doria	03/2026
698	2^1520990+35257	457864	Enzo Doria	10/2024
699	2^1520920+38251	457843	Enzo Doria	11/2024
700	(55814^96721-1)/(55814^311-1)	457634	Ryan Propper	11/2023
701	2^1518191+75353	457022	Ben Maloney / Five or Bust	01/2009
702	2^1515700+243481	456272	Enzo Doria	03/2026
703	2^1513244+44641	455532	Enzo Doria	04/2025
704	2^1512733+227027	455379	Enzo Doria	10/2024
705	2^1510915+223463	454831	Enzo Doria	06/2024
706	6^584279-5	454658	Paul Bourdelais	02/2021
707	2^1509037-13	454266	Stefano Morozzi	12/2022
708	(52^264697-1)/51	454220	Paul Bourdelais	10/2021
709	2^1507525+53837	453811	Enzo Doria	02/2026
710	2^1507169+29027	453704	Enzo Doria	05/2024
711	2^1506029+1890167	453360	Enzo Doria	02/2018
712	2^1505887+246893	453318	Enzo Doria	04/2026
713	2^1504232+26101	452819	Enzo Doria	01/2024
714	-E(103274)/8318971	452706	Serge Batalov	07/2025
715	2^1502037+51287	452159	Enzo Doria	11/2025
716	2^1501670+41629	452048	Enzo Doria	02/2025
717	2^1499357+244577	451352	Enzo Doria	02/2026
718	2^1498015+219113	450948	Enzo Doria	03/2024
719	2^1497532+220471	450803	Enzo Doria	04/2024
720	2^1497523+230873	450800	Enzo Doria	01/2025
721	2^1497466+241489	450783	Enzo Doria	10/2025
722	2^1497369+216977	450753	Enzo Doria	01/2024
723	(34^294277+1)/35	450678	Paul Bourdelais	06/2018
724	2^1496854+232399	450598	Enzo Doria	02/2025
725	2^1496449+42587	450477	Enzo Doria	02/2025
726	2^1495434+1890439	450171	Enzo Doria	12/2017
727	2^1495078+227779	450064	Enzo Doria	10/2024
728	2^1494634+7	449930	Stefano Morozzi	10/2022
729	2^1494534+48319	449900	Enzo Doria	09/2025
730	2^1493170+784129	449489	Enzo Doria	08/2017
731	2^1490332-229043	448635	Enzo Doria	01/2025
732	2^1489873+1888277	448497	Enzo Doria	06/2017
733	2^1489543+55463	448398	Enzo Doria	03/2026
734	2^1487582+242059	447807	Enzo Doria	12/2025
735	2^1487389+32417	447749	Enzo Doria	06/2024
736	2^1486846+36019	447586	Enzo Doria	11/2024
737	2^1485952+241741	447317	Enzo Doria	11/2025
738	2^1485471+224789	447172	Enzo Doria	09/2024
739	2^1485203+71663	447091	Enzo Doria	09/2023
740	2^1484671+1888463	446931	Enzo Doria	06/2017
741	2^1483112+23961	446462	Enzo Doria	12/2023
742	2^1482867+1886783	446388	Enzo Doria	04/2017
743	2^1482148+284011	446172	Enzo Doria	04/2017
744	2^1481363+215843	445935	Enzo Doria	12/2023
745	2^1480415+217643	445650	Enzo Doria	02/2024
746	2^1480400+225013	445645	Enzo Doria	10/2024
747	2^1479356+1888291	445331	Enzo Doria	06/2017
748	(157742^85849-1)/(157742^293-1)	444716	Ryan Propper	11/2023
749	2^1477225+50147	444690	Enzo Doria	09/2025
750	2^1476810+23299	444565	Enzo Doria	12/2023

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