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	2^775672+1866721	233501	Enzo Doria	03/2016
502	(11^223999+1)/12	233270	Paul Bourdelais	02/2010
503	2^774118+1885789	233033	Enzo Doria	04/2017
504	21^176191-20^176191	232964	Jean-Louis Charton	01/2015
505	2^773679-113425	232901	Enzo Doria	08/2014
506	10^232599+192489	232600	Patrick De Geest	12/2013
507	10^232599-3	232599	Markus Tervooren	10/2010
508	2^772552-458879	232562	Enzo Doria	04/2015
509	2^772214+1874899	232460	Enzo Doria	06/2016
510	2^771994-1862771	232394	Enzo Doria	12/2015
511	2^771889+1876037	232362	Enzo Doria	07/2016
512	2^771660+1866511	232293	Enzo Doria	02/2016
513	5^332150-18188	232163	Enzo Doria	06/2014
514	3^485977-2^485977	231870	Mike Oakes	09/2009
515	2^770082-114161	231818	Enzo Doria	01/2015
516	(20^177967+1)/21	231540	Paul Bourdelais	05/2013
517	2^767622-9221	231078	Lelio R Paula	01/2016
518	2^767344+1880311	230994	Enzo Doria	09/2016
519	(3^483611-1)/2	230741	Paul Bourdelais	02/2010
520	(10^230706+179)/9	230706	Serge Batalov	12/2014
521	2^766309+1875257	230682	Enzo Doria	06/2016
522	2^765635+1879883	230480	Enzo Doria	09/2016
523	2^764348-113697	230092	Enzo Doria	09/2014
524	2^764131+78863	230027	Enzo Doria	05/2016
525	2^763701+60197	229897	Enzo Doria	03/2016
526	2^762841-25905	229639	Enzo Doria	10/2013
527	2^761117-113569	229120	Enzo Doria	08/2014
528	2^757985-2790013	228177	Enzo Doria	12/2015
529	2^757038-1862081	227892	Enzo Doria	12/2015
530	2^756839+95849	227832	Makoto Morimoto	10/2013
531	(2^756839+6989)/756091	227826	Makoto Morimoto	09/2016
532	2^756773-112723	227812	Enzo Doria	07/2014
533	524309#+616367	227431	Makoto Morimoto	02/2016
534	2^755097-114193	227307	Enzo Doria	12/2014
535	2^754473-2791513	227120	Enzo Doria	01/2016
536	2^751426-764321	226202	Enzo Doria	12/2013
537	(18^180181-1)/17	226176	Andy Steward	04/2007
538	2^750740-3	225996	Paul Bourdelais	03/2012
539	2^750725+60227	225991	Enzo Doria	02/2016
540	2^750525-113743	225931	Enzo Doria	09/2014
541	(2^750151-1)/(4299340426317590093831289397764574647511836143783478715117383638888678527263)	225744	Dario Alpern	10/2014
542	2^749444-1861889	225606	Enzo Doria	12/2015
543	tau(311^16452)	225560	Nik Lygeros / Olivier Rozier / LR team	10/2013
544	2^749096+1876861	225501	Enzo Doria	07/2016
545	2^748657+79607	225369	Enzo Doria	06/2016
546	2^746653-291583	224765	Enzo Doria	07/2015
547	2^746461-114043	224708	Enzo Doria	11/2014
548	2^745098-350471	224297	Enzo Doria	06/2015
549	(154*10^224061-1)/9	224063	Serge Batalov	12/2014
550	2^744211-1845787	224030	Enzo Doria	07/2015
551	234178^9+9^234178	223463	Anatoly F. Selevich	07/2011
552	2^741651-461197	223260	Enzo Doria	07/2015
553	2^741362-1845251	223173	Enzo Doria	07/2015
554	2^740455-1863877	222900	Enzo Doria	12/2015
555	2^739636-2792219	222653	Enzo Doria	02/2016
556	11^213654-180	222498	Enzo Doria	01/2013
557	2^738957-1859743	222449	Enzo Doria	11/2015
558	(10^221654+179)/9	221654	Serge Batalov	12/2014
559	2^736281+79817	221643	Enzo Doria	06/2016
560	10^221631+247617	221632	Patrick De Geest	10/2013
561	10^221631-9	221631	Alexander Gramolin	02/2011
562	2^735970-1839821	221550	Enzo Doria	06/2015
563	2^735367+60293	221368	Enzo Doria	03/2016
564	2^733264-2784089	220735	Enzo Doria	10/2015
565	2^733114-24555	220690	Enzo Doria	09/2013
566	2^731891-636259	220322	Enzo Doria	12/2013
567	2^731124-25539	220091	Enzo Doria	09/2013
568	2^730972-462029	220045	Enzo Doria	07/2015
569	2^730833+1868627	220003	Enzo Doria	04/2016
570	2^730645-2787133	219947	Enzo Doria	11/2015
571	2^730547-25581	219917	Enzo Doria	09/2013
572	2^730460+82291	219891	Enzo Doria	09/2016
573	L(1051849)	219824	Renaud Lifchitz	03/2009
574	11^210961-240	219694	Enzo Doria	01/2013
575	2^729611-113437	219635	Enzo Doria	08/2014
576	F(1049897)	219416	Henri Lifchitz	10/2008
577	2^728604+1879321	219332	Enzo Doria	10/2016
578	33^144412+2	219292	Robert Price	04/2015
579	2^727998-1862711	219150	Enzo Doria	12/2015
580	2^727729-114073	219069	Enzo Doria	12/2014
581	2^727496-1851809	218999	Enzo Doria	08/2015
582	2^726591+2793143	218726	Enzo Doria	02/2016
583	2^725534-2791931	218408	Enzo Doria	02/2016
584	2^722184+1877821	217400	Enzo Doria	08/2016
585	(109*10^217360-1)/9	217362	Serge Batalov	12/2014
586	281*499979#/46410-2702372	216849	Robert Smith	08/2016
587	281*499979#/46410+2400766	216849	Robert Smith	08/2016
588	tau(311^15786)	216429	Nik Lygeros / Olivier Rozier / LR team	10/2013
589	2^718756-114107	216368	Enzo Doria	12/2014
590	2^717305+80327	215931	Enzo Doria	07/2016
591	2^717069-59773	215860	Enzo Doria	10/2015
592	277^88301-276^88301	215674	Jean-Louis Charton	06/2012
593	227^91413-40	215372	Enzo Doria	04/2015
594	2^714717+782897	215152	Enzo Doria	11/2016
595	tau(373^15186)	214796	Nik Lygeros / Olivier Rozier / LR team	10/2013
596	2^713241+1879157	214707	Enzo Doria	08/2016
597	11^206081-10^206081	214612	Jean-Louis Charton	10/2011
598	2^712801-69553	214575	Enzo Doria	01/2016
599	2^712603-25357	214515	Enzo Doria	09/2013
600	2^711721-1846723	214250	Enzo Doria	07/2015
601	2^710730-396765	213952	Enzo Doria	09/2013
602	2^708468-114329	213271	Enzo Doria	02/2015
603	(163*10^212779-1)/9	212781	Serge Batalov	12/2014
604	2^706838-69041	212780	Enzo Doria	11/2015
605	2^704577-113871	212099	Enzo Doria	10/2014
606	2^704110-2792441	211959	Enzo Doria	02/2016
607	2^703943-1862947	211908	Enzo Doria	12/2015
608	(10^211610-91)/9	211610	Serge Batalov	12/2014
609	227^89797+2	211565	Lelio R Paula	08/2012
610	2^702194-3	211382	Paul Bourdelais	03/2012
611	2^702064+1874911	211343	Enzo Doria	07/2016
612	2^701968-113873	211314	Enzo Doria	10/2014
613	2^701713-113779	211237	Enzo Doria	09/2014
614	2^701449-25201	211158	Enzo Doria	09/2013
615	2^701403-2786977	211144	Enzo Doria	11/2015
616	2^701189-25423	211079	Enzo Doria	09/2013
617	2^701162-459161	211071	Enzo Doria	05/2015
618	2^700400+9385	210842	Lelio R Paula	01/2014
619	2^700131+1874693	210761	Enzo Doria	06/2016
620	11^202357-1140	210734	Enzo Doria	12/2012
621	2^698929-2788423	210399	Enzo Doria	11/2015
622	(5^300893+4^300893)/9	210315	Jean-Louis Charton	11/2011
623	2^698316+1878601	210215	Enzo Doria	08/2016
624	2^697036+1878751	209829	Enzo Doria	08/2016
625	(2^696343-1)/11141489/36009913139329	209600	Tony Prest / Never Odd Or Even	02/2014
626	2^696254-115151	209594	Enzo Doria	06/2015
627	2^694633+1887257	209106	Enzo Doria	05/2017
628	2^693959+180923	208903	Enzo Doria	07/2016
629	2^693462-1847561	208753	Enzo Doria	07/2015
630	2^690890-59981	207979	Enzo Doria	11/2015
631	2^690163+1877063	207760	Enzo Doria	07/2016
632	2^689286-29381	207496	Enzo Doria	08/2015
633	2^689122-114521	207447	Enzo Doria	04/2015
634	2^688373+6077	207221	Enzo Doria	02/2016
635	2^688201+1875527	207170	Enzo Doria	07/2016
636	2^687619+81563	206994	Enzo Doria	08/2016
637	2^686572-1845299	206679	Enzo Doria	07/2015
638	(21^156217-1)/20	206552	Paul Bourdelais	04/2010
639	2^685578+3	206380	Paul Bourdelais	04/2012
640	2^684836-49349	206157	Enzo Doria	10/2015
641	2^684163-2790967	205954	Enzo Doria	12/2015
642	326^81943-325^81943	205941	Jean-Louis Charton	07/2012
643	(2^684127-1)/23765203727	205933	Jens K. Andersen	04/2009
644	4^341233-3^341233	205443	Jean-Louis Charton	01/2006
645	2^681545+467	205166	Lelio R Paula	11/2013
646	2^681306+81049	205094	Enzo Doria	07/2016
647	2^680697+1877057	204911	Enzo Doria	07/2016
648	2^680415+71783	204826	Enzo Doria	04/2016
649	2^679860-459995	204659	Enzo Doria	06/2015
650	2^679593+1879547	204578	Enzo Doria	09/2016
651	2^678651+1875023	204295	Enzo Doria	07/2016
652	2^678561+678561	204268	Henri Lifchitz	05/2006
653	2^678101-114043	204129	Enzo Doria	11/2014
654	2^678028+1875631	204107	Enzo Doria	06/2016
655	2^676992-59783	203795	Enzo Doria	10/2015
656	2^676972+1866871	203789	Enzo Doria	03/2016
657	2^676761-9	203726	Robert Price	01/2017
658	2^676563-2792407	203666	Enzo Doria	02/2016
659	2^676306-114713	203589	Enzo Doria	04/2015
660	(2^675977-1)/(1686378749257*7171117283326998925471)	203456	Dario Alpern	07/2015
661	2^674627-25161	203083	Enzo Doria	09/2013
662	2^674603-69337	203076	Enzo Doria	12/2015
663	2^674459+74213	203033	Enzo Doria	04/2016
664	2^674116-458879	202930	Enzo Doria	04/2015
665	2^674076-114755	202918	Enzo Doria	04/2015
666	5^289937-4^289937	202658	Jean-Louis Charton	03/2013
667	2^672556-1835519	202460	Enzo Doria	04/2015
668	2^671446-351401	202126	Enzo Doria	07/2015
669	2^671373+77747	202104	Enzo Doria	05/2016
670	2^670726-114845	201909	Enzo Doria	05/2015
671	2^670539-25045	201853	Enzo Doria	09/2013
672	2^670213+282317	201755	Enzo Doria	09/2016
673	2^669854-113501	201647	Enzo Doria	08/2014
674	2^669718+81619	201606	Enzo Doria	08/2016
675	(145*10^201504-1)/9	201506	Serge Batalov	12/2014
676	2^668938-1839821	201371	Enzo Doria	06/2015
677	2^668492+1879303	201237	Enzo Doria	08/2016
678	6^258413-5^258413	201085	Jean-Louis Charton	03/2013
679	2^667894+1875589	201057	Enzo Doria	06/2016
680	2^667569-1836559	200959	Enzo Doria	05/2015
681	(172*10^200746-1)/9	200748	Serge Batalov	12/2014
682	2^666430+782569	200616	Enzo Doria	10/2016
683	103(10^100000+20110)^2-4707(10^100000+20110)+50383	200003	Robert Price	05/2017
684	numbpart(32235776596)	200002	Serge Batalov	04/2017
685	(10^200001+149)/3	200001	Serge Batalov	12/2014
686	2^662103-29287	199313	Enzo Doria	08/2015
687	2^660482-2891	198825	Yves Minet	05/2016
688	2^659583+1879223	198555	Enzo Doria	08/2016
689	(53*10^198529+1)/9	198530	Serge Batalov	07/2010
690	2^658828-29819	198327	Enzo Doria	08/2015
691	2^658776-2791229	198312	Enzo Doria	01/2016
692	2^658544-1854029	198242	Enzo Doria	09/2015
693	(157^90239-1)/156	198154	Alexander Zhirkov	06/2016
694	2^656462+1874419	197615	Enzo Doria	06/2016
695	2^655893-344563	197444	Enzo Doria	07/2015
696	2^655875+71333	197439	Enzo Doria	04/2016
697	2^655845-9	197430	Robert Price	01/2017
698	2^655682-1849121	197380	Enzo Doria	08/2015
699	2^655045-49603	197189	Enzo Doria	10/2015
700	2^655000-2784089	197175	Enzo Doria	10/2015
701	(18^157051-1)/17	197141	Paul Bourdelais	03/2010
702	2^654400-39719	196995	Enzo Doria	09/2015
703	2^654216-459995	196939	Enzo Doria	06/2015
704	2^653851+82295	196829	Enzo Doria	09/2016
705	2^653636-29429	196765	Enzo Doria	08/2015
706	2^653601-69673	196754	Enzo Doria	02/2016
707	(44*10^196684+1)/9	196685	Serge Batalov	07/2010
708	2^652786-1852571	196509	Enzo Doria	08/2015
709	2^652752-1325	196498	Yves Minet	07/2015
710	2^652470-1859141	196414	Enzo Doria	10/2015
711	2^652307+1877483	196364	Enzo Doria	08/2016
712	2^652293-115273	196360	Enzo Doria	06/2015
713	2^651218-1868201	196037	Enzo Doria	04/2016
714	2^651047-49687	195985	Enzo Doria	10/2015
715	2^650285-2785333	195756	Enzo Doria	10/2015
716	2^649811+1877573	195613	Enzo Doria	08/2016
717	2^649586+182839	195545	Enzo Doria	11/2016
718	2^649537-1867363	195531	Enzo Doria	04/2016
719	2^649536-1861499	195530	Enzo Doria	12/2015
720	(103*10^195478-1)/3	195480	Serge Batalov	12/2014
721	2^649102-59351	195400	Enzo Doria	10/2015
722	2^648988+1178971	195365	Enzo Doria	06/2016
723	2^648975-114319	195361	Enzo Doria	02/2015
724	2^648619-24835	195254	Enzo Doria	09/2013
725	2^648190-24737	195125	Enzo Doria	09/2013
726	11^187185-90	194934	Enzo Doria	09/2012
727	2^647068+77281	194787	Enzo Doria	05/2016
728	15^165559-14^165559	194713	Jean-Louis Charton	03/2011
729	F(931517)	194676	Henri Lifchitz	09/2008
730	2^646589+1179407	194643	Enzo Doria	06/2016
731	2^646289-114621	194553	Enzo Doria	05/2015
732	2^646236-39659	194537	Enzo Doria	09/2015
733	2^646161-59833	194514	Enzo Doria	11/2015
734	2*10^194413+3	194414	Robert Price	07/2015
735	2^645360-1848599	194273	Enzo Doria	08/2015
736	(112*10^194150-1)/3	194152	Serge Batalov	12/2014
737	2^644382+75169	193979	Enzo Doria	04/2016
738	2^644304-1861409	193955	Enzo Doria	11/2015
739	5*10^193907-9	193908	Robert Price	05/2015
740	2^644043+1876703	193877	Enzo Doria	07/2016
741	2^643735+1879733	193784	Enzo Doria	09/2016
742	(5^277183+1)/6	193742	Paul Bourdelais	07/2010
743	2^643216-286565	193628	Enzo Doria	07/2015
744	2^642888-24965	193529	Enzo Doria	09/2013
745	2^642448-114825	193397	Enzo Doria	05/2015
746	2^642437-1856623	193393	Enzo Doria	10/2015
747	2^642039-59797	193273	Enzo Doria	11/2015
748	2^641692-286349	193169	Enzo Doria	07/2015
749	2^641690-24737	193168	Enzo Doria	09/2013
750	2^641514+1876549	193115	Enzo Doria	07/2016

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PRP Records

Probable Primes Top 10000

(180278 PRPs in the top)