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 (> 30000)	Who ?	When ?
501	3^506233-2	241535	Robert Price	11/2013
502	2^802025-25999	241434	Enzo Doria	10/2013
503	(3^505823+3^252912+1)/7	241339	Serge Batalov	03/2014
504	2^801303+1872923	241217	Enzo Doria	05/2016
505	2^800579-1862947	240999	Enzo Doria	12/2015
506	3^504206+2	240568	Luke W. Richards	03/2018
507	2^798973-26283	240515	Enzo Doria	10/2013
508	2^798671-69487	240424	Enzo Doria	12/2015
509	2^797220+79831	239988	Enzo Doria	06/2016
510	2^796910-26001	239894	Enzo Doria	10/2013
511	2^796598+653119	239800	Enzo Doria	12/2016
512	2^796432-1859729	239750	Enzo Doria	11/2015
513	2^796002-1852211	239621	Enzo Doria	08/2015
514	2^795709+75767	239533	Enzo Doria	04/2016
515	2^795708+81721	239532	Enzo Doria	08/2016
516	2^795468-2786249	239460	Enzo Doria	10/2015
517	2^795442+80779	239452	Enzo Doria	07/2016
518	2^795075-1852057	239342	Enzo Doria	08/2015
519	2^794043+1875023	239031	Enzo Doria	06/2016
520	2^793347-69577	238822	Enzo Doria	01/2016
521	2^792988-344429	238714	Enzo Doria	08/2015
522	2^792700-2786369	238627	Enzo Doria	11/2015
523	2^792663-1844797	238616	Enzo Doria	06/2015
524	2^792605-291943	238598	Enzo Doria	07/2015
525	(2^792061-2^396031+1)/5	238434	Thomas Ritschel	03/2014
526	2^789373+1869377	237625	Enzo Doria	05/2016
527	((10^59387+1)^3(10^59387+1+10^29694)-(10^118774+10^59387)(10^29694-1)+10^178161)/27961	237544	Serge Batalov	04/2015
528	2^788942+1866409	237496	Enzo Doria	02/2016
529	2^788844-114329	237466	Enzo Doria	01/2015
530	2^788705-1859713	237424	Enzo Doria	11/2015
531	2^786180+1871971	236664	Enzo Doria	05/2016
532	11^227092-90	236492	Enzo Doria	11/2012
533	2^785260+1866361	236387	Enzo Doria	02/2016
534	2^785220+1880611	236375	Enzo Doria	10/2016
535	19^184650-2	236122	Robert Price	10/2014
536	10^236059+216513	236060	Patrick De Geest	04/2016
537	10^236059-20909	236059	Robert Price	09/2015
538	2^782634-113981	235597	Enzo Doria	11/2014
539	2^782423+1879733	235533	Enzo Doria	09/2016
540	2^781682-2789543	235310	Enzo Doria	12/2015
541	2^780408-113453	234927	Enzo Doria	08/2014
542	2^780368-1864829	234915	Enzo Doria	01/2016
543	2^779593-1836559	234681	Enzo Doria	05/2015
544	(8713#+(549391#)/(8713#))/360295171	234487	Makoto Morimoto	11/2017
545	(5^335429+1)/6	234455	Paul Bourdelais	08/2010
546	2^778395-113617	234321	Enzo Doria	08/2014
547	2^776245-2792353	233674	Enzo Doria	02/2016
548	2^776060-114029	233618	Enzo Doria	11/2014
549	2^775987-2789557	233596	Enzo Doria	12/2015
550	2^775672+1866721	233501	Enzo Doria	03/2016
551	(11^223999+1)/12	233270	Paul Bourdelais	02/2010
552	2^774118+1885789	233033	Enzo Doria	04/2017
553	21^176191-20^176191	232964	Jean-Louis Charton	01/2015
554	2^773679-113425	232901	Enzo Doria	08/2014
555	10^232599+192489	232600	Patrick De Geest	12/2013
556	10^232599-3	232599	Markus Tervooren	10/2010
557	2^772552-458879	232562	Enzo Doria	04/2015
558	2^772214+1874899	232460	Enzo Doria	06/2016
559	2^771994-1862771	232394	Enzo Doria	12/2015
560	2^771889+1876037	232362	Enzo Doria	07/2016
561	2^771660+1866511	232293	Enzo Doria	02/2016
562	5^332150-18188	232163	Enzo Doria	06/2014
563	3^485977-2^485977	231870	Mike Oakes	09/2009
564	2^770082-114161	231818	Enzo Doria	01/2015
565	(20^177967+1)/21	231540	Paul Bourdelais	05/2013
566	2^767622-9221	231078	Lelio R Paula	01/2016
567	2^767344+1880311	230994	Enzo Doria	09/2016
568	(3^483611-1)/2	230741	Paul Bourdelais	02/2010
569	(10^230706+179)/9	230706	Serge Batalov	12/2014
570	2^766309+1875257	230682	Enzo Doria	06/2016
571	2^765635+1879883	230480	Enzo Doria	09/2016
572	2^764348-113697	230092	Enzo Doria	09/2014
573	2^764131+78863	230027	Enzo Doria	05/2016
574	2^763701+60197	229897	Enzo Doria	03/2016
575	2^762841-25905	229639	Enzo Doria	10/2013
576	2^761117-113569	229120	Enzo Doria	08/2014
577	2^757985-2790013	228177	Enzo Doria	12/2015
578	2^757038-1862081	227892	Enzo Doria	12/2015
579	2^756839+95849	227832	Makoto Morimoto	10/2013
580	(2^756839+6989)/756091	227826	Makoto Morimoto	09/2016
581	2^756773-112723	227812	Enzo Doria	07/2014
582	524309#+616367	227431	Makoto Morimoto	02/2016
583	2^755097-114193	227307	Enzo Doria	12/2014
584	2^754473-2791513	227120	Enzo Doria	01/2016
585	2^751426-764321	226202	Enzo Doria	12/2013
586	(18^180181-1)/17	226176	Andy Steward	04/2007
587	2^750740-3	225996	Paul Bourdelais	03/2012
588	2^750725+60227	225991	Enzo Doria	02/2016
589	2^750525-113743	225931	Enzo Doria	09/2014
590	(2^750151-1)/(4299340426317590093831289397764574647511836143783478715117383638888678527263)	225744	Dario Alpern	10/2014
591	2^749444-1861889	225606	Enzo Doria	12/2015
592	tau(311^16452)	225560	Nik Lygeros / Olivier Rozier / LR team	10/2013
593	2^749096+1876861	225501	Enzo Doria	07/2016
594	2^748657+79607	225369	Enzo Doria	06/2016
595	2^746653-291583	224765	Enzo Doria	07/2015
596	2^746461-114043	224708	Enzo Doria	11/2014
597	2^745098-350471	224297	Enzo Doria	06/2015
598	(154*10^224061-1)/9	224063	Serge Batalov	12/2014
599	2^744211-1845787	224030	Enzo Doria	07/2015
600	234178^9+9^234178	223463	Anatoly F. Selevich	07/2011
601	2^741651-461197	223260	Enzo Doria	07/2015
602	2^741362-1845251	223173	Enzo Doria	07/2015
603	2^740455-1863877	222900	Enzo Doria	12/2015
604	2^739636-2792219	222653	Enzo Doria	02/2016
605	11^213654-180	222498	Enzo Doria	01/2013
606	2^738957-1859743	222449	Enzo Doria	11/2015
607	(10^221654+179)/9	221654	Serge Batalov	12/2014
608	2^736281+79817	221643	Enzo Doria	06/2016
609	10^221631+247617	221632	Patrick De Geest	10/2013
610	10^221631-9	221631	Alexander Gramolin	02/2011
611	2^735970-1839821	221550	Enzo Doria	06/2015
612	2^735367+60293	221368	Enzo Doria	03/2016
613	(29^151153+1)/30	221045	Paul Bourdelais	09/2017
614	2^733264-2784089	220735	Enzo Doria	10/2015
615	2^733114-24555	220690	Enzo Doria	09/2013
616	2^731891-636259	220322	Enzo Doria	12/2013
617	2^731124-25539	220091	Enzo Doria	09/2013
618	2^730972-462029	220045	Enzo Doria	07/2015
619	2^730833+1868627	220003	Enzo Doria	04/2016
620	2^730645-2787133	219947	Enzo Doria	11/2015
621	2^730547-25581	219917	Enzo Doria	09/2013
622	2^730460+82291	219891	Enzo Doria	09/2016
623	L(1051849)	219824	Renaud Lifchitz	03/2009
624	11^210961-240	219694	Enzo Doria	01/2013
625	2^729611-113437	219635	Enzo Doria	08/2014
626	F(1049897)	219416	Henri Lifchitz	10/2008
627	2^728604+1879321	219332	Enzo Doria	10/2016
628	33^144412+2	219292	Robert Price	04/2015
629	2^727998-1862711	219150	Enzo Doria	12/2015
630	2^727729-114073	219069	Enzo Doria	12/2014
631	2^727496-1851809	218999	Enzo Doria	08/2015
632	2^726591+2793143	218726	Enzo Doria	02/2016
633	2^725534-2791931	218408	Enzo Doria	02/2016
634	2^722184+1877821	217400	Enzo Doria	08/2016
635	(109*10^217360-1)/9	217362	Serge Batalov	12/2014
636	281*499979#/46410-2702372	216849	Robert Smith	08/2016
637	281*499979#/46410+2400766	216849	Robert Smith	08/2016
638	tau(311^15786)	216429	Nik Lygeros / Olivier Rozier / LR team	10/2013
639	2^718756-114107	216368	Enzo Doria	12/2014
640	2^717305+80327	215931	Enzo Doria	07/2016
641	2^717069-59773	215860	Enzo Doria	10/2015
642	277^88301-276^88301	215674	Jean-Louis Charton	06/2012
643	227^91413-40	215372	Enzo Doria	04/2015
644	2^714717+782897	215152	Enzo Doria	11/2016
645	tau(373^15186)	214796	Nik Lygeros / Olivier Rozier / LR team	10/2013
646	2^713241+1879157	214707	Enzo Doria	08/2016
647	11^206081-10^206081	214612	Jean-Louis Charton	10/2011
648	2^712801-69553	214575	Enzo Doria	01/2016
649	2^712603-25357	214515	Enzo Doria	09/2013
650	2^711721-1846723	214250	Enzo Doria	07/2015
651	2^710730-396765	213952	Enzo Doria	09/2013
652	2^708468-114329	213271	Enzo Doria	02/2015
653	(163*10^212779-1)/9	212781	Serge Batalov	12/2014
654	2^706838-69041	212780	Enzo Doria	11/2015
655	2^704577-113871	212099	Enzo Doria	10/2014
656	2^704110-2792441	211959	Enzo Doria	02/2016
657	2^703943-1862947	211908	Enzo Doria	12/2015
658	(10^211610-91)/9	211610	Serge Batalov	12/2014
659	227^89797+2	211565	Lelio R Paula	08/2012
660	2^702194-3	211382	Paul Bourdelais	03/2012
661	2^702064+1874911	211343	Enzo Doria	07/2016
662	2^701968-113873	211314	Enzo Doria	10/2014
663	2^701713-113779	211237	Enzo Doria	09/2014
664	2^701449-25201	211158	Enzo Doria	09/2013
665	2^701403-2786977	211144	Enzo Doria	11/2015
666	2^701189-25423	211079	Enzo Doria	09/2013
667	2^701162-459161	211071	Enzo Doria	05/2015
668	(24^152783-1)/23	210872	Paul Bourdelais	04/2018
669	2^700400+9385	210842	Lelio R Paula	01/2014
670	2^700131+1874693	210761	Enzo Doria	06/2016
671	11^202357-1140	210734	Enzo Doria	12/2012
672	2^698929-2788423	210399	Enzo Doria	11/2015
673	(5^300893+4^300893)/9	210315	Jean-Louis Charton	11/2011
674	2^698316+1878601	210215	Enzo Doria	08/2016
675	2^697036+1878751	209829	Enzo Doria	08/2016
676	(2^696343-1)/11141489/36009913139329	209600	Tony Prest / Never Odd Or Even	02/2014
677	2^696254-115151	209594	Enzo Doria	06/2015
678	(35^135623+1)/36	209410	Paul Bourdelais	07/2018
679	2^694633+1887257	209106	Enzo Doria	05/2017
680	2^693959+180923	208903	Enzo Doria	07/2016
681	2^693462-1847561	208753	Enzo Doria	07/2015
682	2^690890-59981	207979	Enzo Doria	11/2015
683	(38^131591+1)/39	207884	Paul Bourdelais	07/2018
684	2^690163+1877063	207760	Enzo Doria	07/2016
685	2^689286-29381	207496	Enzo Doria	08/2015
686	2^689122-114521	207447	Enzo Doria	04/2015
687	2^688373+6077	207221	Enzo Doria	02/2016
688	2^688201+1875527	207170	Enzo Doria	07/2016
689	(42^127609+1)/43	207140	Paul Bourdelais	07/2018
690	2^687619+81563	206994	Enzo Doria	08/2016
691	2^686572-1845299	206679	Enzo Doria	07/2015
692	(21^156217-1)/20	206552	Paul Bourdelais	04/2010
693	(2^685739+1)/(3*87774593)	206420	Gord Palameta	08/2018
694	2^685578+3	206380	Paul Bourdelais	04/2012
695	2^684836-49349	206157	Enzo Doria	10/2015
696	(73^110603-1)/72	206088	Paul Bourdelais	06/2018
697	2^684163-2790967	205954	Enzo Doria	12/2015
698	326^81943-325^81943	205941	Jean-Louis Charton	07/2012
699	(2^684127-1)/23765203727	205933	Jens K. Andersen	04/2009
700	4^341233-3^341233	205443	Jean-Louis Charton	01/2006
701	2^681545+467	205166	Lelio R Paula	11/2013
702	2^681306+81049	205094	Enzo Doria	07/2016
703	2^680697+1877057	204911	Enzo Doria	07/2016
704	2^680415+71783	204826	Enzo Doria	04/2016
705	2^679860-459995	204659	Enzo Doria	06/2015
706	2^679593+1879547	204578	Enzo Doria	09/2016
707	2^678651+1875023	204295	Enzo Doria	07/2016
708	2^678561+678561	204268	Henri Lifchitz	05/2006
709	2^678101-114043	204129	Enzo Doria	11/2014
710	2^678028+1875631	204107	Enzo Doria	06/2016
711	2^676992-59783	203795	Enzo Doria	10/2015
712	2^676972+1866871	203789	Enzo Doria	03/2016
713	2^676761-9	203726	Robert Price	01/2017
714	2^676563-2792407	203666	Enzo Doria	02/2016
715	2^676306-114713	203589	Enzo Doria	04/2015
716	(2^675977-1)/(1686378749257*7171117283326998925471)	203456	Dario Alpern	07/2015
717	2^674627-25161	203083	Enzo Doria	09/2013
718	2^674603-69337	203076	Enzo Doria	12/2015
719	2^674459+74213	203033	Enzo Doria	04/2016
720	2^674116-458879	202930	Enzo Doria	04/2015
721	2^674076-114755	202918	Enzo Doria	04/2015
722	5^289937-4^289937	202658	Jean-Louis Charton	03/2013
723	2^672556-1835519	202460	Enzo Doria	04/2015
724	2^671446-351401	202126	Enzo Doria	07/2015
725	2^671373+77747	202104	Enzo Doria	05/2016
726	2^670726-114845	201909	Enzo Doria	05/2015
727	2^670539-25045	201853	Enzo Doria	09/2013
728	2^670213+282317	201755	Enzo Doria	09/2016
729	2^669854-113501	201647	Enzo Doria	08/2014
730	2^669718+81619	201606	Enzo Doria	08/2016
731	(145*10^201504-1)/9	201506	Serge Batalov	12/2014
732	2^668938-1839821	201371	Enzo Doria	06/2015
733	2^668492+1879303	201237	Enzo Doria	08/2016
734	6^258413-5^258413	201085	Jean-Louis Charton	03/2013
735	2^667894+1875589	201057	Enzo Doria	06/2016
736	2^667569-1836559	200959	Enzo Doria	05/2015
737	(172*10^200746-1)/9	200748	Serge Batalov	12/2014
738	2^666430+782569	200616	Enzo Doria	10/2016
739	(86^103471+1)/87	200163	Paul Bourdelais	05/2018
740	103(10^100000+20110)^2-4707(10^100000+20110)+50383	200003	Robert Price	05/2017
741	103(10^100000+33798)^2-4707(10^100000+33798)+50383	200003	Robert Price	01/2018
742	numbpart(32235776596)	200002	Serge Batalov	04/2017
743	(10^200001+149)/3	200001	Serge Batalov	12/2014
744	2^662103-29287	199313	Enzo Doria	08/2015
745	(2*10^199283+457)/9	199283	Robert Price	01/2018
746	(10^199248-19)/9	199248	Robert Price	01/2018
747	2^660482-2891	198825	Yves Minet	05/2016
748	2^659583+1879223	198555	Enzo Doria	08/2016
749	(53*10^198529+1)/9	198530	Serge Batalov	07/2010
750	2^658828-29819	198327	Enzo Doria	08/2015

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PRP Records

Probable Primes Top 10000

(218736 PRPs in the top)