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	2^1075425+1880117	323736	Enzo Doria	10/2016
502	(28^223381+1)/29	323267	Paul Bourdelais	12/2020
503	10^322999+187071	323000	Stefano Morozzi	03/2019
504	10^322999-143151	322999	Patrick De Geest	05/2020
505	2^1072146+1886869	322749	Enzo Doria	04/2017
506	2^1072118-7321953	322740	Enzo Doria	02/2015
507	2^1071026+1886869	322411	Enzo Doria	04/2017
508	2^1070539+1880633	322265	Enzo Doria	10/2016
509	2^1069293-1147195	321890	Enzo Doria	05/2015
510	2^1065968+1880941	320889	Enzo Doria	10/2016
511	2^1065897-1147195	320867	Enzo Doria	05/2015
512	2^1063427+1882103	320124	Enzo Doria	12/2016
513	2^1061095-1061095	319422	Henri Lifchitz	10/2013
514	2^1060950+653119	319378	Enzo Doria	12/2016
515	2^1060363+782753	319202	Enzo Doria	11/2016
516	(71^172259-1)/70	318895	Paul Bourdelais	08/2020
517	2^1054736+483061	317508	Enzo Doria	12/2016
518	2^1053965+1879667	317276	Enzo Doria	10/2016
519	(43^194119-1)/42	317086	Paul Bourdelais	08/2020
520	2^1052186-458165	316740	Enzo Doria	03/2015
521	2^1046613-114685	315062	Enzo Doria	04/2015
522	2^1045625-459373	314765	Enzo Doria	06/2015
523	(7*10^314564-61)/9	314564	Erik Branger	09/2016
524	2^1044206+7	314338	Stefano Morozzi	10/2022
525	(7^371669-1)/6	314096	Paul Bourdelais	02/2010
526	(53^181981-1)/52	313784	Paul Bourdelais	08/2020
527	2^1041944+283051	313657	Enzo Doria	12/2016
528	2^1041153-114391	313419	Enzo Doria	02/2015
529	(2^1039700+9)/5	312981	Stefano Morozzi	09/2022
530	(74^167311+1)/75	312742	Paul Bourdelais	12/2020
531	2^1038871+1866983	312732	Enzo Doria	04/2016
532	(55^179573-1)/54	312521	Paul Bourdelais	08/2020
533	2^1037647+1881263	312363	Enzo Doria	11/2016
534	2^1037226+1879699	312237	Enzo Doria	10/2016
535	2^1036867+1865843	312129	Enzo Doria	02/2016
536	(76^165947+1)/77	312114	Paul Bourdelais	01/2021
537	2^1036020-114539	311874	Enzo Doria	02/2015
538	(90^159463-1)/89	311628	Paul Bourdelais	08/2020
539	2^1032240+1883431	310736	Enzo Doria	01/2017
540	2^1030352+1870021	310167	Enzo Doria	06/2016
541	2^1030046+1882843	310075	Enzo Doria	11/2016
542	3^648872+16	309591	Robert Price	04/2020
543	5^442281+2	309142	Paul Bourdelais	01/2021
544	2^1026190+15	308914	Stefano Morozzi	10/2022
545	A352736(16)	306985	Kellen Shenton	05/2022
546	(11^293831-1)/10	305993	Paul Bourdelais	03/2010
547	(67^167449-1)/66	305773	Paul Bourdelais	08/2020
548	(62^170539+1)/63	305671	Paul Bourdelais	12/2020
549	2^1015321-1015321	305643	Henri Lifchitz	08/2013
550	2^1014450+7	305380	Stefano Morozzi	10/2022
551	2^1014224-2791229	305312	Enzo Doria	01/2016
552	(10^304986+7)/673	304984	Alfred Reich	11/2021
553	65473^45250+45250^65473	304818	Hans Havermann	02/2022
554	66012^41423+41423^66012	304794	Hans Havermann	03/2022
555	65073^48202+48202^65073	304742	Hans Havermann	04/2022
556	238176^19+19^238176	304569	Hans Havermann	03/2022
557	73122^14615+14615^73122	304539	Hans Havermann	05/2022
558	64492^52639+52639^64492	304487	Hans Havermann	03/2022
559	65955^41288+41288^65955	304437	Hans Havermann	04/2022
560	71729^17530+17530^71729	304403	Hans Havermann	03/2022
561	70170^21733+21733^70170	304336	Hans Havermann	03/2022
562	2^1010751-107709	304267	Enzo Doria	03/2014
563	84473^3994+3994^84473	304222	Hans Havermann	03/2022
564	(2^1010623-1)/12602017578957977	304212	Tony Prest / Never Odd Or Even	02/2014
565	74442^12125+12125^74442	303998	Hans Havermann	02/2022
566	77842^8039+8039^77842	303989	Hans Havermann	01/2022
567	64209^54140+54140^64209	303935	Hans Havermann	02/2022
568	2^1009577+1869587	303913	Enzo Doria	06/2016
569	67389^32338+32338^67389	303906	Hans Havermann	02/2022
570	8^336419-7^336419	303817	Jean-Louis Charton	01/2008
571	2^1009168+15	303790	Stefano Morozzi	10/2022
572	80766^5771+5771^80766	303782	Hans Havermann	01/2022
573	66094^39385+39385^66094	303724	Hans Havermann	01/2022
574	69147^24574+24574^69147	303589	Hans Havermann	02/2022
575	78390^7459+7459^78390	303580	Hans Havermann	01/2022
576	2^1008301+1869377	303529	Enzo Doria	06/2016
577	65008^46615+46615^65008	303492	Hans Havermann	02/2022
578	(2^1007838+5)/3	303389	Serge Batalov	08/2015
579	65018^46293+46293^65018	303343	Hans Havermann	01/2022
580	6^389756+5	303290	Paul Bourdelais	02/2021
581	71016^18649+18649^71016	303285	Hans Havermann	01/2022
582	80160^6047+6047^80160	303129	Hans Havermann	01/2022
583	67434^31237+31237^67434	303094	Hans Havermann	03/2022
584	65537^42102+42102^65537	303063	Hans Havermann	02/2022
585	71790^16553+16553^71790	302874	Hans Havermann	11/2021
586	65208^44129+44129^65208	302874	Hans Havermann	11/2021
587	84181^3960+3960^84181	302858	Hans Havermann	11/2021
588	71956^16087+16087^71956	302682	Hans Havermann	11/2021
589	2^1005326+383059	302634	Enzo Doria	12/2016
590	2^1004929+1877567	302514	Enzo Doria	08/2016
591	69341^22978+22978^69341	302418	Hans Havermann	12/2021
592	111443^516+516^111443	302306	Hans Havermann	12/2021
593	67638^29387+29387^67638	302218	Hans Havermann	11/2021
594	2^1003494+1874899	302082	Enzo Doria	06/2016
595	75189^10400+10400^75189	302037	Hans Havermann	12/2021
596	67237^31042+31042^67237	302026	Hans Havermann	12/2021
597	64540^47791+47791^64540	302005	Hans Havermann	11/2021
598	2^1003046+60529	301947	Enzo Doria	04/2016
599	83278^4209+4209^83278	301815	Hans Havermann	09/2021
600	64431^48250+48250^64431	301763	Hans Havermann	09/2021
601	67237^30714+30714^67237	301716	Hans Havermann	09/2021
602	64641^46288+46288^64641	301581	Hans Havermann	09/2021
603	71513^16482+16482^71513	301572	Hans Havermann	10/2021
604	72017^15396+15396^72017	301565	Hans Havermann	09/2021
605	65534^39927+39927^65534	301540	Hans Havermann	10/2021
606	(23^221411-1)/22	301501	Paul Bourdelais	08/2020
607	63169^59152+59152^63169	301441	Hans Havermann	09/2021
608	75055^10348+10348^75055	301336	Hans Havermann	09/2021
609	2^1000647+1881353	301225	Enzo Doria	11/2016
610	83686^3961+3961^83686	301086	Hans Havermann	10/2021
611	68529^24742+24742^68529	301078	Hans Havermann	09/2021
612	65207^41416+41416^65207	301072	Hans Havermann	10/2021
613	2^1000000+821751	301030	Tony Prest / Never Odd Or Even	10/2015
614	90762^2071+2071^90762	300984	Hans Havermann	06/2021
615	63909^51142+51142^63909	300934	Hans Havermann	08/2021
616	2^999646+1874029	300924	Enzo Doria	06/2016
617	66280^34607+34607^66280	300856	Hans Havermann	06/2021
618	65534^38925+38925^65534	300817	Hans Havermann	07/2021
619	63296^56517+56517^63296	300794	Hans Havermann	06/2021
620	110610^523+523^110610	300694	Hans Havermann	06/2021
621	66428^33609+33609^66428	300684	Hans Havermann	06/2021
622	74247^11210+11210^74247	300672	Hans Havermann	06/2021
623	(59^169777-1)/58	300649	Paul Bourdelais	08/2020
624	10^300476+3	300477	Ed Trice	10/2012
625	10^300476-530913	300476	Patrick De Geest	03/2016
626	66703^31960+31960^66703	300471	Hans Havermann	06/2021
627	63722^51915+51915^63722	300468	Hans Havermann	06/2021
628	2^998053+1879667	300444	Enzo Doria	09/2016
629	77018^7959+7959^77018	300437	Hans Havermann	07/2021
630	314738^9+9^314738	300337	Anatoly F. Selevich	02/2011
631	69478^20987+20987^69478	300281	Hans Havermann	07/2021
632	64088^48393+48393^64088	300239	Hans Havermann	07/2021
633	64605^44146+44146^64605	300084	Hans Havermann	08/2021
634	7^355039-6^355039	300043	Jean-Louis Charton	05/2011
635	67594^27465+27465^67594	300035	Hans Havermann	06/2021
636	10^300000+287389	300001	Patrick De Geest	10/2019
637	10^300000-83657	300000	Patrick De Geest	10/2019
638	70599^17756+17756^70599	300000	Hans Havermann	06/2021
639	numbpart(72526161452)	299999	Serge Batalov	04/2017
640	2^996182-114431	299881	Enzo Doria	02/2015
641	2^996034-17	299837	Stefano Morozzi	07/2022
642	(19*10^299640+77)/3	299641	Robert Price	03/2023
643	2^995214-2788361	299590	Enzo Doria	12/2015
644	2^994791-114319	299462	Enzo Doria	01/2015
645	2^994490-1863791	299372	Enzo Doria	01/2016
646	2^993322+1885729	299020	Enzo Doria	03/2017
647	(36395^65536+36393^65536)/2	298913	Kellen Shenton	04/2022
648	2^992711-2788807	298836	Enzo Doria	12/2015
649	2^992525-114199	298780	Enzo Doria	12/2014
650	2^992329+1884707	298721	Enzo Doria	02/2017
651	2^991968-23	298613	Stefano Morozzi	07/2022
652	2^991715-19	298536	Stefano Morozzi	07/2022
653	(10^298414+7)/191/823/56921/1334467	298398	Alfred Reich	10/2021
654	2^989562+25	297888	Stefano Morozzi	05/2021
655	(19*10^297497+77)/3	297498	Robert Price	03/2023
656	(2*10^297488-23)/3	297488	Robert Price	10/2022
657	(2^986191+1)/3	296873	Vincent Diepeveen	06/2008
658	2^985217-114553	296580	Enzo Doria	03/2015
659	(76^157649-1)/75	296507	Paul Bourdelais	07/2019
660	2^984131-1828009	296253	Enzo Doria	01/2015
661	2^983620+60451	296100	Phil Moore	03/2008
662	2^982721-2683	295829	Yves Minet	02/2016
663	2^981298-2788421	295401	Enzo Doria	12/2015
664	2^981163-2790967	295360	Enzo Doria	12/2015
665	2^981016-15	295316	Stefano Morozzi	07/2022
666	2^979594+1865839	294888	Enzo Doria	02/2016
667	2*10^294527-91	294528	Robert Price	02/2023
668	10^294475+49	294476	Robert Price	02/2023
669	2^976760+1885021	294035	Enzo Doria	02/2017
670	2^974441+1878407	293336	Enzo Doria	08/2016
671	2^974180+1876831	293258	Enzo Doria	07/2016
672	2^974170+453319	293255	Enzo Doria	01/2017
673	2^972744-114419	292826	Enzo Doria	03/2015
674	11^281143+6	292781	Paul Bourdelais	03/2021
675	(4*10^292619-91)/3	292620	Robert Price	12/2022
676	CopelandErdos(292447)	292447	Mark Rodenkirch	12/2015
677	3*10^292344-97	292345	Robert Price	01/2023
678	2^970911+1873373	292274	Enzo Doria	07/2016
679	2^970670+383059	292201	Enzo Doria	12/2016
680	2^970141-100363	292042	Enzo Doria	02/2014
681	2^969945+1874717	291983	Enzo Doria	06/2016
682	2^969384+1880701	291814	Enzo Doria	10/2016
683	(3^611333-2^611333)/(99035947*87109884549431)	291659	Mike Oakes	02/2017
684	2^962194+60139	289650	Enzo Doria	02/2016
685	2^959307-1861507	288781	Enzo Doria	11/2015
686	14^251797-3	288592	Paul Bourdelais	12/2020
687	(2*10^288371-23)/3	288371	Robert Price	10/2022
688	(31*10^288238-1)/3	288240	Robert Price	02/2023
689	2^957372+283531	288198	Enzo Doria	02/2017
690	2^957192-1864049	288144	Enzo Doria	01/2016
691	2^956446+1875199	287919	Enzo Doria	06/2016
692	7*10^287854+39	287855	Robert Price	01/2023
693	(17^233689+1)/18	287542	Paul Bourdelais	09/2013
694	2^955178+1883587	287538	Enzo Doria	12/2016
695	2^954127-954127^2	287221	Henri Lifchitz	01/2021
696	2^954001+1875257	287183	Enzo Doria	07/2016
697	(23891^65536+1)/2	286932	Serge Batalov	03/2018
698	2^952268+1878601	286662	Enzo Doria	09/2016
699	2^950801+81557	286220	Enzo Doria	08/2016
700	22845^65536+22844^65536	285658	Kellen Shenton	03/2021
701	(11*2^948635-13)/15	285568	Renaud Lifchitz	11/2011
702	(54^164839+1)/55	285565	Paul Bourdelais	07/2019
703	2^948510+782569	285530	Enzo Doria	10/2016
704	2^948374-114137	285490	Enzo Doria	01/2015
705	2^947739+1872923	285298	Enzo Doria	06/2016
706	2^944561-21	284342	Stefano Morozzi	07/2022
707	(4*10^284330-31)/9	284330	Serge Batalov	11/2022
708	(32*10^283826-23)/9	283827	Serge Batalov	01/2023
709	2^942533+82067	283731	Enzo Doria	09/2016
710	(10^283342-31)/3	283342	Robert Price	03/2023
711	2^940950+1874989	283255	Enzo Doria	06/2016
712	2^940426-2786141	283097	Enzo Doria	11/2015
713	(2*10^282948-11)/9	282948	Serge Batalov	11/2022
714	2^939881-114115	282933	Enzo Doria	12/2014
715	10^282493+632551	282494	Patrick De Geest	02/2017
717	10^282493-9^282493	282493	Jean-Louis Charton	03/2007
716	10^282493-132327	282493	Patrick De Geest	02/2017
718	3^591827-2^591827	282374	Mike Oakes	08/2009
719	Tau(509^18946)	282048	Nik Lygeros / Olivier Rozier	05/2015
720	2^936716-1835519	281980	Enzo Doria	04/2015
721	2^936588+79411	281942	Enzo Doria	06/2016
722	2^936047+1877423	281779	Enzo Doria	08/2016
723	2^935713+1869377	281678	Enzo Doria	05/2016
724	2^933082+1877059	280886	Enzo Doria	08/2016
725	(5*10^280710+1)/3	280711	Serge Batalov	10/2014
726	2^931976+25	280553	Stefano Morozzi	05/2021
727	(42^172663+1)/43	280274	Paul Bourdelais	07/2019
728	(10^279978+11)/3	279978	Serge Batalov	07/2015
729	2^929524-1864829	279815	Enzo Doria	01/2016
730	2^929152+60181	279703	Enzo Doria	02/2016
731	2^928621-2787883	279543	Enzo Doria	11/2015
732	(2^927763+lucasV(-1,2,927763)+1)/2	279285	Mike Oakes	04/2017
733	2^927429+1882277	279184	Enzo Doria	12/2016
734	2^926766-11	278985	Stefano Morozzi	07/2022
735	(71^150697-1)/70	278978	Paul Bourdelais	07/2019
736	(33^183661-1)/32	278891	Paul Bourdelais	12/2018
737	(166*10^278633-7)/3	278635	Robert Price	02/2023
738	(2^925391+lucasV(-1,2,925391)+1)/2	278571	Mike Oakes	03/2017
739	2^925330-1301	278553	Yves Minet	06/2015
740	(299*10^278546+1)/3	278548	Robert Price	01/2023
741	(21^210599+1)/22	278457	Paul Bourdelais	08/2013
742	(266*10^278325+1)/3	278327	Robert Price	01/2023
743	2^923261-69175	277930	Enzo Doria	11/2015
744	757^96487-756^96487	277796	Jean-Louis Charton	12/2012
745	2^922301+57	277641	Stefano Morozzi	05/2021
746	((((((((((((((291487327^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2	277369	Serge Batalov	07/2016
747	(5^396413-1)/4	277081	Paul Bourdelais	06/2010
748	2^920318+2792299	277044	Enzo Doria	02/2016
749	2^918596-2786939	276525	Enzo Doria	11/2015
750	2^916639+60563	275936	Enzo Doria	04/2016

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