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	21^190632-2	252058	Robert Price	07/2015
502	2^837242+1873297	252035	Enzo Doria	06/2016
503	2^836656-2787929	251859	Enzo Doria	11/2015
504	2^836380+1875541	251776	Enzo Doria	07/2016
505	(359^98327-1)/358	251233	Alexander Zhirkov	11/2017
506	tau(41^28288)	250924	Nik Lygeros / Olivier Rozier	10/2013
507	2^832511-461197	250611	Enzo Doria	07/2015
508	2^832505+1881137	250609	Enzo Doria	11/2016
509	2^832363+583295	250567	Enzo Doria	12/2016
510	2^832244-403635	250531	Enzo Doria	01/2014
511	2^831157+1880657	250204	Enzo Doria	11/2016
512	2^831088-7200899	250183	Enzo Doria	01/2015
513	2^830956-1349	250143	Yves Minet	07/2015
514	2^830037+282317	249867	Enzo Doria	09/2016
515	2^829589-113653	249732	Enzo Doria	09/2014
516	2^828281-3193	249338	Yves Minet	08/2016
517	2^828064-2785619	249273	Enzo Doria	10/2015
518	2^827602+60409	249134	Enzo Doria	03/2016
519	10^249010+348861	249011	Patrick De Geest	04/2016
520	10^249010-21	249010	Serge Batalov	12/2014
521	2^826733+1882907	248872	Enzo Doria	12/2016
522	2^825682+1876549	248556	Enzo Doria	07/2016
523	2^824991-114121	248348	Enzo Doria	12/2014
524	2^824642-362727	248242	Enzo Doria	12/2013
525	2^824565-114265	248219	Enzo Doria	01/2015
526	(73*10^248145-1)/9	248146	Robert Price	01/2015
527	(2^823337+1)/(3*362268281)	247841	Gord Palameta	08/2018
528	(2^822971-1)/6583769/28211445881/21255852651726486149207	247700	Robert Kinser	09/2016
529	2^822296+76501	247536	Enzo Doria	05/2016
530	2^821590-114167	247324	Enzo Doria	12/2014
531	2^821512-2790659	247300	Enzo Doria	12/2015
532	2^820077+382847	246868	Enzo Doria	11/2016
533	2^820001+81269	246845	Enzo Doria	07/2016
534	2^819463-59197	246683	Enzo Doria	10/2015
535	2^819296+80581	246633	Enzo Doria	07/2016
536	2^817160-350369	245990	Enzo Doria	06/2015
537	88093#+(653879#)/(88093#)	245374	Makoto Morimoto	11/2017
538	2^815111-113857	245373	Enzo Doria	10/2014
539	2^814914-4001	245314	Yves Minet	05/2017
540	846^83761-845^83761	245200	Jean-Louis Charton	12/2012
541	2^814356-2790449	245146	Enzo Doria	12/2015
542	2^814276-459029	245122	Enzo Doria	04/2015
543	2^814023+180923	245046	Enzo Doria	07/2016
544	(3^513059-2^513059)/(1026119*5430216457)	244776	Mike Oakes	03/2017
545	2^811842-113675	244389	Enzo Doria	09/2014
546	2^811132-2787929	244176	Enzo Doria	11/2015
547	2^809746-2790971	243758	Enzo Doria	01/2016
548	2^808767-3295	243464	Yves Minet	12/2016
549	2^808621-113809	243420	Enzo Doria	09/2014
550	2^807724+1879621	243150	Enzo Doria	09/2016
551	2^805843-113611	242583	Enzo Doria	08/2014
552	2^805745-459763	242554	Enzo Doria	05/2015
553	2^805353+782687	242436	Enzo Doria	11/2016
554	2^804277-417933	242112	Enzo Doria	01/2014
555	2^803468-269039	241868	Enzo Doria	10/2013
556	2^803172+80851	241779	Enzo Doria	07/2016
557	3^506233-2	241535	Robert Price	11/2013
558	2^802025-25999	241434	Enzo Doria	10/2013
559	(3^505823+3^252912+1)/7	241339	Serge Batalov	03/2014
560	2^801303+1872923	241217	Enzo Doria	05/2016
561	2^800579-1862947	240999	Enzo Doria	12/2015
562	3^504206+2	240568	Luke W. Richards	03/2018
563	2^798973-26283	240515	Enzo Doria	10/2013
564	2^798671-69487	240424	Enzo Doria	12/2015
565	2^797220+79831	239988	Enzo Doria	06/2016
566	2^796910-26001	239894	Enzo Doria	10/2013
567	2^796598+653119	239800	Enzo Doria	12/2016
568	2^796432-1859729	239750	Enzo Doria	11/2015
569	2^796002-1852211	239621	Enzo Doria	08/2015
570	2^795709+75767	239533	Enzo Doria	04/2016
571	2^795708+81721	239532	Enzo Doria	08/2016
572	2^795468-2786249	239460	Enzo Doria	10/2015
573	2^795442+80779	239452	Enzo Doria	07/2016
574	2^795075-1852057	239342	Enzo Doria	08/2015
575	(86^123677+1)/87	239252	Paul Bourdelais	01/2019
576	2^794043+1875023	239031	Enzo Doria	06/2016
577	2^793347-69577	238822	Enzo Doria	01/2016
578	2^792988-344429	238714	Enzo Doria	08/2015
579	2^792700-2786369	238627	Enzo Doria	11/2015
580	2^792663-1844797	238616	Enzo Doria	06/2015
581	2^792605-291943	238598	Enzo Doria	07/2015
582	(2^792061-2^396031+1)/5	238434	Thomas Ritschel	03/2014
583	2^789373+1869377	237625	Enzo Doria	05/2016
584	((10^59387+1)^3(10^59387+1+10^29694)-(10^118774+10^59387)(10^29694-1)+10^178161)/27961	237544	Serge Batalov	04/2015
585	2^788942+1866409	237496	Enzo Doria	02/2016
586	2^788844-114329	237466	Enzo Doria	01/2015
587	2^788705-1859713	237424	Enzo Doria	11/2015
588	2^786180+1871971	236664	Enzo Doria	05/2016
589	11^227092-90	236492	Enzo Doria	11/2012
590	2^785260+1866361	236387	Enzo Doria	02/2016
591	2^785220+1880611	236375	Enzo Doria	10/2016
592	19^184650-2	236122	Robert Price	10/2014
593	10^236059+216513	236060	Patrick De Geest	04/2016
594	10^236059-20909	236059	Robert Price	09/2015
595	(87^121487-1)/86	235625	Paul Bourdelais	12/2018
596	2^782634-113981	235597	Enzo Doria	11/2014
597	2^782423+1879733	235533	Enzo Doria	09/2016
598	2^781682-2789543	235310	Enzo Doria	12/2015
599	2^780408-113453	234927	Enzo Doria	08/2014
600	2^780368-1864829	234915	Enzo Doria	01/2016
601	2^779593-1836559	234681	Enzo Doria	05/2015
602	(8713#+(549391#)/(8713#))/360295171	234487	Makoto Morimoto	11/2017
603	(5^335429+1)/6	234455	Paul Bourdelais	08/2010
604	2^778395-113617	234321	Enzo Doria	08/2014
605	2^776245-2792353	233674	Enzo Doria	02/2016
606	2^776060-114029	233618	Enzo Doria	11/2014
607	2^775987-2789557	233596	Enzo Doria	12/2015
608	2^775672+1866721	233501	Enzo Doria	03/2016
609	(11^223999+1)/12	233270	Paul Bourdelais	02/2010
610	2^774118+1885789	233033	Enzo Doria	04/2017
611	21^176191-20^176191	232964	Jean-Louis Charton	01/2015
612	2^773679-113425	232901	Enzo Doria	08/2014
613	10^232599+192489	232600	Patrick De Geest	12/2013
614	10^232599-3	232599	Markus Tervooren	10/2010
615	2^772552-458879	232562	Enzo Doria	04/2015
616	2^772214+1874899	232460	Enzo Doria	06/2016
617	2^771994-1862771	232394	Enzo Doria	12/2015
618	2^771889+1876037	232362	Enzo Doria	07/2016
619	2^771660+1866511	232293	Enzo Doria	02/2016
620	5^332150-18188	232163	Enzo Doria	06/2014
621	3^485977-2^485977	231870	Mike Oakes	09/2009
622	2^770082-114161	231818	Enzo Doria	01/2015
623	(20^177967+1)/21	231540	Paul Bourdelais	05/2013
624	2^767622-9221	231078	Lelio R Paula	01/2016
625	2^767344+1880311	230994	Enzo Doria	09/2016
626	(3^483611-1)/2	230741	Paul Bourdelais	02/2010
627	(10^230706+179)/9	230706	Serge Batalov	12/2014
628	2^766309+1875257	230682	Enzo Doria	06/2016
629	2^765635+1879883	230480	Enzo Doria	09/2016
630	2^764348-113697	230092	Enzo Doria	09/2014
631	2^764131+78863	230027	Enzo Doria	05/2016
632	2^763701+60197	229897	Enzo Doria	03/2016
633	2^762841-25905	229639	Enzo Doria	10/2013
634	2^761117-113569	229120	Enzo Doria	08/2014
635	(98^114859+1)/99	228709	Paul Bourdelais	12/2018
636	(2^758231+1)/(32714694297653973236839266867)	228223	Gord Palameta	12/2018
637	2^757985-2790013	228177	Enzo Doria	12/2015
638	2^757038-1862081	227892	Enzo Doria	12/2015
639	2^756839+95849	227832	Makoto Morimoto	10/2013
640	(2^756839+6989)/756091	227826	Makoto Morimoto	09/2016
641	2^756773-112723	227812	Enzo Doria	07/2014
642	524309#+616367	227431	Makoto Morimoto	02/2016
643	2^755097-114193	227307	Enzo Doria	12/2014
644	2^754473-2791513	227120	Enzo Doria	01/2016
645	2^751426-764321	226202	Enzo Doria	12/2013
646	(18^180181-1)/17	226176	Andy Steward	04/2007
647	2^750740-3	225996	Paul Bourdelais	03/2012
648	2^750725+60227	225991	Enzo Doria	02/2016
649	2^750525-113743	225931	Enzo Doria	09/2014
650	(2^750151-1)/(4299340426317590093831289397764574647511836143783478715117383638888678527263)	225744	Dario Alpern	10/2014
651	2^749444-1861889	225606	Enzo Doria	12/2015
652	tau(311^16452)	225560	Nik Lygeros / Olivier Rozier / LR team	10/2013
653	2^749096+1876861	225501	Enzo Doria	07/2016
654	(519643#+43033)/(2318712706283)	225379	Makoto Morimoto	08/2019
655	2^748657+79607	225369	Enzo Doria	06/2016
656	2^746653-291583	224765	Enzo Doria	07/2015
657	2^746461-114043	224708	Enzo Doria	11/2014
658	2^745098-350471	224297	Enzo Doria	06/2015
659	(154*10^224061-1)/9	224063	Serge Batalov	12/2014
660	2^744211-1845787	224030	Enzo Doria	07/2015
661	2^743592-134579	223844	Hans Havermann	10/2018
662	2^742452+3	223501	Paul Bourdelais	06/2019
663	234178^9+9^234178	223463	Anatoly F. Selevich	07/2011
664	2^741651-461197	223260	Enzo Doria	07/2015
665	2^741362-1845251	223173	Enzo Doria	07/2015
666	2^740455-1863877	222900	Enzo Doria	12/2015
667	2^739636-2792219	222653	Enzo Doria	02/2016
668	11^213654-180	222498	Enzo Doria	01/2013
669	2^738957-1859743	222449	Enzo Doria	11/2015
670	(54^128189+1)/55	222073	Paul Bourdelais	11/2018
671	(10^221654+179)/9	221654	Serge Batalov	12/2014
672	2^736281+79817	221643	Enzo Doria	06/2016
673	10^221631+247617	221632	Patrick De Geest	10/2013
674	10^221631-9	221631	Alexander Gramolin	02/2011
675	2^735970-1839821	221550	Enzo Doria	06/2015
676	2^735367+60293	221368	Enzo Doria	03/2016
677	(29^151153+1)/30	221045	Paul Bourdelais	09/2017
678	2^733264-2784089	220735	Enzo Doria	10/2015
679	2^733114-24555	220690	Enzo Doria	09/2013
680	2^731891-636259	220322	Enzo Doria	12/2013
681	2^731124-25539	220091	Enzo Doria	09/2013
682	2^730972-462029	220045	Enzo Doria	07/2015
683	2^730833+1868627	220003	Enzo Doria	04/2016
684	2^730645-2787133	219947	Enzo Doria	11/2015
685	2^730547-25581	219917	Enzo Doria	09/2013
686	2^730460+82291	219891	Enzo Doria	09/2016
687	(2^730339+1)/(3278390620037943469324347)	219831	Gord Palameta	12/2018
688	L(1051849)	219824	Renaud Lifchitz	03/2009
689	11^210961-240	219694	Enzo Doria	01/2013
690	2^729611-113437	219635	Enzo Doria	08/2014
691	F(1049897)	219416	Henri Lifchitz	10/2008
692	2^728604+1879321	219332	Enzo Doria	10/2016
693	33^144412+2	219292	Robert Price	04/2015
694	2^728277-183313	219234	Hans Havermann	10/2018
695	2^727998-1862711	219150	Enzo Doria	12/2015
696	2^727729-114073	219069	Enzo Doria	12/2014
697	2^727496-1851809	218999	Enzo Doria	08/2015
698	2^726591+2793143	218726	Enzo Doria	02/2016
699	2^725534-2791931	218408	Enzo Doria	02/2016
700	2^722184+1877821	217400	Enzo Doria	08/2016
701	(109*10^217360-1)/9	217362	Serge Batalov	12/2014
702	281*499979#/46410-2702372	216849	Robert Smith	08/2016
703	281*499979#/46410+2400766	216849	Robert Smith	08/2016
704	tau(311^15786)	216429	Nik Lygeros / Olivier Rozier / LR team	10/2013
705	2^718756-114107	216368	Enzo Doria	12/2014
706	2^717305+80327	215931	Enzo Doria	07/2016
707	2^717069-59773	215860	Enzo Doria	10/2015
708	30^146021-29^146021	215691	Jean-Louis Charton	09/2018
709	277^88301-276^88301	215674	Jean-Louis Charton	06/2012
710	227^91413-40	215372	Enzo Doria	04/2015
711	2^714717+782897	215152	Enzo Doria	11/2016
712	tau(373^15186)	214796	Nik Lygeros / Olivier Rozier / LR team	10/2013
713	2^713241+1879157	214707	Enzo Doria	08/2016
714	11^206081-10^206081	214612	Jean-Louis Charton	10/2011
715	2^712801-69553	214575	Enzo Doria	01/2016
716	2^712603-25357	214515	Enzo Doria	09/2013
717	2^711721-1846723	214250	Enzo Doria	07/2015
718	2^710730-396765	213952	Enzo Doria	09/2013
719	2^708468-114329	213271	Enzo Doria	02/2015
720	(163*10^212779-1)/9	212781	Serge Batalov	12/2014
721	2^706838-69041	212780	Enzo Doria	11/2015
722	2^704577-113871	212099	Enzo Doria	10/2014
723	2^704110-2792441	211959	Enzo Doria	02/2016
724	2^703943-1862947	211908	Enzo Doria	12/2015
725	(60^119083+1)/61	211746	Paul Bourdelais	10/2018
726	(10^211610-91)/9	211610	Serge Batalov	12/2014
727	227^89797+2	211565	Lelio R Paula	08/2012
728	2^702194-3	211382	Paul Bourdelais	03/2012
729	2^702064+1874911	211343	Enzo Doria	07/2016
730	2^701968-113873	211314	Enzo Doria	10/2014
731	2^701713-113779	211237	Enzo Doria	09/2014
732	2^701449-25201	211158	Enzo Doria	09/2013
733	2^701403-2786977	211144	Enzo Doria	11/2015
734	2^701189-25423	211079	Enzo Doria	09/2013
735	2^701162-459161	211071	Enzo Doria	05/2015
736	(24^152783-1)/23	210872	Paul Bourdelais	04/2018
737	2^700400+9385	210842	Lelio R Paula	01/2014
738	2^700131+1874693	210761	Enzo Doria	06/2016
739	11^202357-1140	210734	Enzo Doria	12/2012
740	2^698929-2788423	210399	Enzo Doria	11/2015
741	(5^300893+4^300893)/9	210315	Jean-Louis Charton	11/2011
742	2^698316+1878601	210215	Enzo Doria	08/2016
743	2^697036+1878751	209829	Enzo Doria	08/2016
744	(2^696343-1)/11141489/36009913139329	209600	Tony Prest / Never Odd Or Even	02/2014
745	2^696254-115151	209594	Enzo Doria	06/2015
746	(35^135623+1)/36	209410	Paul Bourdelais	07/2018
747	2^694633+1887257	209106	Enzo Doria	05/2017
748	2^693959+180923	208903	Enzo Doria	07/2016
749	2^693462-1847561	208753	Enzo Doria	07/2015
750	2^690890-59981	207979	Enzo Doria	11/2015

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PRP Records

Probable Primes Top 10000

(253466 PRPs in the top)