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	5^332150-18188	232163	Enzo Doria	06/2014
502	3^485977-2^485977	231870	Mike Oakes	09/2009
503	2^770082-114161	231818	Enzo Doria	01/2015
504	(20^177967+1)/21	231540	Paul Bourdelais	05/2013
505	2^767622-9221	231078	Lelio R Paula	01/2016
506	2^767344+1880311	230994	Enzo Doria	09/2016
507	(3^483611-1)/2	230741	Paul Bourdelais	02/2010
508	(10^230706+179)/9	230706	Serge Batalov	12/2014
509	2^766309+1875257	230682	Enzo Doria	06/2016
510	2^765635+1879883	230480	Enzo Doria	09/2016
511	2^764348-113697	230092	Enzo Doria	09/2014
512	2^764131+78863	230027	Enzo Doria	05/2016
513	2^763701+60197	229897	Enzo Doria	03/2016
514	2^762841-25905	229639	Enzo Doria	10/2013
515	2^761117-113569	229120	Enzo Doria	08/2014
516	2^757985-2790013	228177	Enzo Doria	12/2015
517	2^757038-1862081	227892	Enzo Doria	12/2015
518	2^756839+95849	227832	Makoto Morimoto	10/2013
519	(2^756839+6989)/756091	227826	Makoto Morimoto	09/2016
520	2^756773-112723	227812	Enzo Doria	07/2014
521	524309#+616367	227431	Makoto Morimoto	02/2016
522	2^755097-114193	227307	Enzo Doria	12/2014
523	2^754473-2791513	227120	Enzo Doria	01/2016
524	2^751426-764321	226202	Enzo Doria	12/2013
525	(18^180181-1)/17	226176	Andy Steward	04/2007
526	2^750740-3	225996	Paul Bourdelais	03/2012
527	2^750725+60227	225991	Enzo Doria	02/2016
528	2^750525-113743	225931	Enzo Doria	09/2014
529	(2^750151-1)/(4299340426317590093831289397764574647511836143783478715117383638888678527263)	225744	Dario Alpern	10/2014
530	2^749444-1861889	225606	Enzo Doria	12/2015
531	tau(311^16452)	225560	Nik Lygeros / Olivier Rozier / LR team	10/2013
532	2^749096+1876861	225501	Enzo Doria	07/2016
533	2^748657+79607	225369	Enzo Doria	06/2016
534	2^746653-291583	224765	Enzo Doria	07/2015
535	2^746461-114043	224708	Enzo Doria	11/2014
536	2^745098-350471	224297	Enzo Doria	06/2015
537	(154*10^224061-1)/9	224063	Serge Batalov	12/2014
538	2^744211-1845787	224030	Enzo Doria	07/2015
539	234178^9+9^234178	223463	Anatoly F. Selevich	07/2011
540	2^741651-461197	223260	Enzo Doria	07/2015
541	2^741362-1845251	223173	Enzo Doria	07/2015
542	2^740455-1863877	222900	Enzo Doria	12/2015
543	2^739636-2792219	222653	Enzo Doria	02/2016
544	11^213654-180	222498	Enzo Doria	01/2013
545	2^738957-1859743	222449	Enzo Doria	11/2015
546	(10^221654+179)/9	221654	Serge Batalov	12/2014
547	2^736281+79817	221643	Enzo Doria	06/2016
548	10^221631+247617	221632	Patrick De Geest	10/2013
549	10^221631-9	221631	Alexander Gramolin	02/2011
550	2^735970-1839821	221550	Enzo Doria	06/2015
551	2^735367+60293	221368	Enzo Doria	03/2016
552	2^733264-2784089	220735	Enzo Doria	10/2015
553	2^733114-24555	220690	Enzo Doria	09/2013
554	2^731891-636259	220322	Enzo Doria	12/2013
555	2^731124-25539	220091	Enzo Doria	09/2013
556	2^730972-462029	220045	Enzo Doria	07/2015
557	2^730833+1868627	220003	Enzo Doria	04/2016
558	2^730645-2787133	219947	Enzo Doria	11/2015
559	2^730547-25581	219917	Enzo Doria	09/2013
560	2^730460+82291	219891	Enzo Doria	09/2016
561	L(1051849)	219824	Renaud Lifchitz	03/2009
562	11^210961-240	219694	Enzo Doria	01/2013
563	2^729611-113437	219635	Enzo Doria	08/2014
564	F(1049897)	219416	Henri Lifchitz	10/2008
565	2^728604+1879321	219332	Enzo Doria	10/2016
566	33^144412+2	219292	Robert Price	04/2015
567	2^727998-1862711	219150	Enzo Doria	12/2015
568	2^727729-114073	219069	Enzo Doria	12/2014
569	2^727496-1851809	218999	Enzo Doria	08/2015
570	2^726591+2793143	218726	Enzo Doria	02/2016
571	2^725534-2791931	218408	Enzo Doria	02/2016
572	2^722184+1877821	217400	Enzo Doria	08/2016
573	(109*10^217360-1)/9	217362	Serge Batalov	12/2014
574	281*499979#/46410-2702372	216849	Robert Smith	08/2016
575	281*499979#/46410+2400766	216849	Robert Smith	08/2016
576	tau(311^15786)	216429	Nik Lygeros / Olivier Rozier / LR team	10/2013
577	2^718756-114107	216368	Enzo Doria	12/2014
578	2^717305+80327	215931	Enzo Doria	07/2016
579	2^717069-59773	215860	Enzo Doria	10/2015
580	277^88301-276^88301	215674	Jean-Louis Charton	06/2012
581	227^91413-40	215372	Enzo Doria	04/2015
582	2^714717+782897	215152	Enzo Doria	11/2016
583	tau(373^15186)	214796	Nik Lygeros / Olivier Rozier / LR team	10/2013
584	2^713241+1879157	214707	Enzo Doria	08/2016
585	11^206081-10^206081	214612	Jean-Louis Charton	10/2011
586	2^712801-69553	214575	Enzo Doria	01/2016
587	2^712603-25357	214515	Enzo Doria	09/2013
588	2^711721-1846723	214250	Enzo Doria	07/2015
589	2^710730-396765	213952	Enzo Doria	09/2013
590	2^708468-114329	213271	Enzo Doria	02/2015
591	(163*10^212779-1)/9	212781	Serge Batalov	12/2014
592	2^706838-69041	212780	Enzo Doria	11/2015
593	2^704577-113871	212099	Enzo Doria	10/2014
594	2^704110-2792441	211959	Enzo Doria	02/2016
595	2^703943-1862947	211908	Enzo Doria	12/2015
596	(10^211610-91)/9	211610	Serge Batalov	12/2014
597	227^89797+2	211565	Lelio R Paula	08/2012
598	2^702194-3	211382	Paul Bourdelais	03/2012
599	2^702064+1874911	211343	Enzo Doria	07/2016
600	2^701968-113873	211314	Enzo Doria	10/2014
601	2^701713-113779	211237	Enzo Doria	09/2014
602	2^701449-25201	211158	Enzo Doria	09/2013
603	2^701403-2786977	211144	Enzo Doria	11/2015
604	2^701189-25423	211079	Enzo Doria	09/2013
605	2^701162-459161	211071	Enzo Doria	05/2015
606	2^700400+9385	210842	Lelio R Paula	01/2014
607	2^700131+1874693	210761	Enzo Doria	06/2016
608	11^202357-1140	210734	Enzo Doria	12/2012
609	2^698929-2788423	210399	Enzo Doria	11/2015
610	(5^300893+4^300893)/9	210315	Jean-Louis Charton	11/2011
611	2^698316+1878601	210215	Enzo Doria	08/2016
612	2^697036+1878751	209829	Enzo Doria	08/2016
613	(2^696343-1)/11141489/36009913139329	209600	Tony Prest / Never Odd Or Even	02/2014
614	2^696254-115151	209594	Enzo Doria	06/2015
615	2^694633+1887257	209106	Enzo Doria	05/2017
616	2^693959+180923	208903	Enzo Doria	07/2016
617	2^693462-1847561	208753	Enzo Doria	07/2015
618	2^690890-59981	207979	Enzo Doria	11/2015
619	2^690163+1877063	207760	Enzo Doria	07/2016
620	2^689286-29381	207496	Enzo Doria	08/2015
621	2^689122-114521	207447	Enzo Doria	04/2015
622	2^688373+6077	207221	Enzo Doria	02/2016
623	2^688201+1875527	207170	Enzo Doria	07/2016
624	2^687619+81563	206994	Enzo Doria	08/2016
625	2^686572-1845299	206679	Enzo Doria	07/2015
626	(21^156217-1)/20	206552	Paul Bourdelais	04/2010
627	2^685578+3	206380	Paul Bourdelais	04/2012
628	2^684836-49349	206157	Enzo Doria	10/2015
629	2^684163-2790967	205954	Enzo Doria	12/2015
630	326^81943-325^81943	205941	Jean-Louis Charton	07/2012
631	(2^684127-1)/23765203727	205933	Jens K. Andersen	04/2009
632	4^341233-3^341233	205443	Jean-Louis Charton	01/2006
633	2^681545+467	205166	Lelio R Paula	11/2013
634	2^681306+81049	205094	Enzo Doria	07/2016
635	2^680697+1877057	204911	Enzo Doria	07/2016
636	2^680415+71783	204826	Enzo Doria	04/2016
637	2^679860-459995	204659	Enzo Doria	06/2015
638	2^679593+1879547	204578	Enzo Doria	09/2016
639	2^678651+1875023	204295	Enzo Doria	07/2016
640	2^678561+678561	204268	Henri Lifchitz	05/2006
641	2^678101-114043	204129	Enzo Doria	11/2014
642	2^678028+1875631	204107	Enzo Doria	06/2016
643	2^676992-59783	203795	Enzo Doria	10/2015
644	2^676972+1866871	203789	Enzo Doria	03/2016
645	2^676761-9	203726	Robert Price	01/2017
646	2^676563-2792407	203666	Enzo Doria	02/2016
647	2^676306-114713	203589	Enzo Doria	04/2015
648	(2^675977-1)/(1686378749257*7171117283326998925471)	203456	Dario Alpern	07/2015
649	2^674627-25161	203083	Enzo Doria	09/2013
650	2^674603-69337	203076	Enzo Doria	12/2015
651	2^674459+74213	203033	Enzo Doria	04/2016
652	2^674116-458879	202930	Enzo Doria	04/2015
653	2^674076-114755	202918	Enzo Doria	04/2015
654	5^289937-4^289937	202658	Jean-Louis Charton	03/2013
655	2^672556-1835519	202460	Enzo Doria	04/2015
656	2^671446-351401	202126	Enzo Doria	07/2015
657	2^671373+77747	202104	Enzo Doria	05/2016
658	2^670726-114845	201909	Enzo Doria	05/2015
659	2^670539-25045	201853	Enzo Doria	09/2013
660	2^670213+282317	201755	Enzo Doria	09/2016
661	2^669854-113501	201647	Enzo Doria	08/2014
662	2^669718+81619	201606	Enzo Doria	08/2016
663	(145*10^201504-1)/9	201506	Serge Batalov	12/2014
664	2^668938-1839821	201371	Enzo Doria	06/2015
665	2^668492+1879303	201237	Enzo Doria	08/2016
666	6^258413-5^258413	201085	Jean-Louis Charton	03/2013
667	2^667894+1875589	201057	Enzo Doria	06/2016
668	2^667569-1836559	200959	Enzo Doria	05/2015
669	(172*10^200746-1)/9	200748	Serge Batalov	12/2014
670	2^666430+782569	200616	Enzo Doria	10/2016
671	103(10^100000+20110)^2-4707(10^100000+20110)+50383	200003	Robert Price	05/2017
672	numbpart(32235776596)	200002	Serge Batalov	04/2017
673	(10^200001+149)/3	200001	Serge Batalov	12/2014
674	2^662103-29287	199313	Enzo Doria	08/2015
675	2^660482-2891	198825	Yves Minet	05/2016
676	2^659583+1879223	198555	Enzo Doria	08/2016
677	(53*10^198529+1)/9	198530	Serge Batalov	07/2010
678	2^658828-29819	198327	Enzo Doria	08/2015
679	2^658776-2791229	198312	Enzo Doria	01/2016
680	2^658544-1854029	198242	Enzo Doria	09/2015
681	(157^90239-1)/156	198154	Alexander Zhirkov	06/2016
682	2^656462+1874419	197615	Enzo Doria	06/2016
683	2^655893-344563	197444	Enzo Doria	07/2015
684	2^655875+71333	197439	Enzo Doria	04/2016
685	2^655845-9	197430	Robert Price	01/2017
686	2^655682-1849121	197380	Enzo Doria	08/2015
687	2^655045-49603	197189	Enzo Doria	10/2015
688	2^655000-2784089	197175	Enzo Doria	10/2015
689	(18^157051-1)/17	197141	Paul Bourdelais	03/2010
690	2^654400-39719	196995	Enzo Doria	09/2015
691	2^654216-459995	196939	Enzo Doria	06/2015
692	2^653851+82295	196829	Enzo Doria	09/2016
693	2^653636-29429	196765	Enzo Doria	08/2015
694	2^653601-69673	196754	Enzo Doria	02/2016
695	(44*10^196684+1)/9	196685	Serge Batalov	07/2010
696	2^652786-1852571	196509	Enzo Doria	08/2015
697	2^652752-1325	196498	Yves Minet	07/2015
698	2^652470-1859141	196414	Enzo Doria	10/2015
699	2^652307+1877483	196364	Enzo Doria	08/2016
700	2^652293-115273	196360	Enzo Doria	06/2015
701	2^651218-1868201	196037	Enzo Doria	04/2016
702	2^651047-49687	195985	Enzo Doria	10/2015
703	2^650285-2785333	195756	Enzo Doria	10/2015
704	2^649811+1877573	195613	Enzo Doria	08/2016
705	2^649586+182839	195545	Enzo Doria	11/2016
706	2^649537-1867363	195531	Enzo Doria	04/2016
707	2^649536-1861499	195530	Enzo Doria	12/2015
708	(103*10^195478-1)/3	195480	Serge Batalov	12/2014
709	2^649102-59351	195400	Enzo Doria	10/2015
710	2^648988+1178971	195365	Enzo Doria	06/2016
711	2^648975-114319	195361	Enzo Doria	02/2015
712	2^648619-24835	195254	Enzo Doria	09/2013
713	2^648190-24737	195125	Enzo Doria	09/2013
714	11^187185-90	194934	Enzo Doria	09/2012
715	2^647068+77281	194787	Enzo Doria	05/2016
716	15^165559-14^165559	194713	Jean-Louis Charton	03/2011
717	F(931517)	194676	Henri Lifchitz	09/2008
718	2^646589+1179407	194643	Enzo Doria	06/2016
719	2^646289-114621	194553	Enzo Doria	05/2015
720	2^646236-39659	194537	Enzo Doria	09/2015
721	2^646161-59833	194514	Enzo Doria	11/2015
722	2*10^194413+3	194414	Robert Price	07/2015
723	2^645360-1848599	194273	Enzo Doria	08/2015
724	(112*10^194150-1)/3	194152	Serge Batalov	12/2014
725	2^644382+75169	193979	Enzo Doria	04/2016
726	2^644304-1861409	193955	Enzo Doria	11/2015
727	5*10^193907-9	193908	Robert Price	05/2015
728	2^644043+1876703	193877	Enzo Doria	07/2016
729	2^643735+1879733	193784	Enzo Doria	09/2016
730	(5^277183+1)/6	193742	Paul Bourdelais	07/2010
731	2^643216-286565	193628	Enzo Doria	07/2015
732	2^642888-24965	193529	Enzo Doria	09/2013
733	2^642448-114825	193397	Enzo Doria	05/2015
734	2^642437-1856623	193393	Enzo Doria	10/2015
735	2^642039-59797	193273	Enzo Doria	11/2015
736	2^641692-286349	193169	Enzo Doria	07/2015
737	2^641690-24737	193168	Enzo Doria	09/2013
738	2^641514+1876549	193115	Enzo Doria	07/2016
739	2^640888-2785619	192927	Enzo Doria	10/2015
740	2^640874-2783741	192923	Enzo Doria	09/2015
741	2^640181+467	192714	Lelio R Paula	08/2013
742	2^639536-1850249	192520	Enzo Doria	08/2015
743	2^639110-2792441	192392	Enzo Doria	02/2016
744	2^638955-29827	192345	Enzo Doria	08/2015
745	2^638713-2784223	192272	Enzo Doria	10/2015
746	2^638490-113507	192205	Enzo Doria	08/2014
747	2^638189-39943	192115	Enzo Doria	09/2015
748	2^638110+1877119	192091	Enzo Doria	07/2016
749	2^638066-2785211	192078	Enzo Doria	10/2015
750	2^637475-115309	191900	Enzo Doria	07/2015

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PRP Records

Probable Primes Top 10000

(174961 PRPs in the top)