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	2^1200021+149777	361243	Stefano Morozzi	10/2022
502	(64*10^360173-1)/243	360173	Serge Batalov	09/2014
503	(59^203309+1)/60	360029	Paul Bourdelais	09/2021
504	(2*10^359860-11)/9	359860	Rytis Slatkevicius	01/2023
505	2^1195093+1882577	359759	Enzo Doria	12/2016
506	3^753451+5*2^753451	359488	Jon Grantham	08/2023
507	(6^461108-11)/5	358812	Paul Bourdelais	04/2019
508	2^1191375+8543	358640	Phil Moore	06/2008
509	2^1190972+1880191	358519	Enzo Doria	11/2016
510	(45^216551-1)/44	358004	Paul Bourdelais	08/2020
511	(50^210319-1)/49	357324	Paul Bourdelais	08/2020
512	(531^131072+25^131072)/2	357184	Kellen Shenton	03/2021
513	2^1184565+21227	356590	Enzo Doria	08/2023
514	2^1179836+1885021	355167	Enzo Doria	02/2017
515	(19*10^353884-91)/9	353885	Alfred Reich	02/2023
516	20^271951+3	353817	Paul Bourdelais	01/2021
517	2^1173095+21	353137	Stefano Morozzi	10/2022
518	(63^195893-1)/62	352477	Paul Bourdelais	08/2020
519	2^1170326+7	352304	Stefano Morozzi	10/2022
520	numbpart(100000135540)	352269	Serge Batalov	04/2017
521	(10^352237-1)/9/10567111/950335427	352221	Maksym Voznyy	01/2015
522	5*3^737931-2^737931	352084	Jon Grantham	08/2023
523	2^1168554+783529	351770	Enzo Doria	01/2017
524	(2^1168183-1)/54763676838381762583	351639	Matthias Wurtinger	01/2011
525	2^1166152+1882411	351047	Enzo Doria	12/2016
526	2^1163972+20971	350391	Enzo Doria	08/2023
527	10^350071+7	350072	Alfred Reich	05/2021
528	2^1162154+1890207	349844	Enzo Doria	08/2017
529	(7*10^348724-61)/9	348724	Erik Branger	09/2016
530	(4*10^348453+41)/9	348453	Serge Batalov	11/2022
531	(127^165601-1)/126	348390	Alexander Zhirkov	09/2015
532	2^1155085+213377	347716	Enzo Doria	09/2023
533	2^1153083+1883693	347113	Enzo Doria	04/2017
534	(2^1148729+2^574365+1)/5	345802	Borys Jaworski	03/2007
535	2^1145882+80779	344945	Enzo Doria	09/2016
536	2^1136462+1887289	342110	Enzo Doria	05/2017
537	F(1636007)	341905	Henri Lifchitz	03/2009
538	(2^1135567+13)/3	341840	Stefano Morozzi	09/2022
539	2^1133678+782569	341272	Enzo Doria	11/2016
540	(11^327001+1)/12	340536	Paul Bourdelais	09/2013
541	(2^1127239+2^563620+1)/5	339333	Borys Jaworski	11/2006
542	Tau(907^20848)	339132	Nik Lygeros / Olivier Rozier	01/2016
543	2^1126380-3	339075	Paul Bourdelais	06/2019
544	2^1125446+1885099	338794	Enzo Doria	08/2017
545	(63^188147+1)/64	338539	Paul Bourdelais	12/2020
546	2^1124549+143807	338523	Enzo Doria	10/2016
547	(4*10^338476+23)/9	338476	Serge Batalov	11/2022
548	2^1121187+1886783	337511	Enzo Doria	04/2017
549	(48^200443-1)/47	336992	Paul Bourdelais	08/2020
550	(2*10^336405+43)/9	336405	Rytis Slatkevicius	01/2023
551	(94^170371-1)/93	336162	Paul Bourdelais	09/2020
552	2^1116184+1883521	336005	Enzo Doria	02/2017
553	2^1114517+1880087	335504	Enzo Doria	10/2016
554	(5*10^335480+31)/9	335480	Serge Batalov	11/2022
555	5*3^701688+2^701688	334791	Jon Grantham	08/2023
556	(101^166849+1)/102	334418	Paul Bourdelais	12/2020
557	(3^700897+1)/4	334413	Paul Bourdelais	04/2010
558	2^1104408-114539	332460	Enzo Doria	03/2015
559	2^1101921+82085	331712	Enzo Doria	10/2016
560	2^1100655+683513	331331	Enzo Doria	01/2017
561	(10^330906+71)/9	330906	Serge Batalov	07/2015
562	2^1098346+482899	330636	Enzo Doria	11/2016
563	(2^1096212+19)/5	329992	Stefano Morozzi	09/2022
564	2^1095679+1878713	329833	Enzo Doria	09/2016
565	2^1094740-1851539	329550	Enzo Doria	08/2015
566	2^1092242+19	328798	Stefano Morozzi	10/2022
567	2^1091469-379369	328565	Enzo Doria	03/2014
568	(69^178093-1)/68	327485	Paul Bourdelais	08/2020
569	(10^326884+7)/421	326882	Alfred Reich	12/2021
570	2^1085750+582349	326844	Enzo Doria	11/2016
571	2^1083596+483061	326195	Enzo Doria	12/2016
572	(2^541456-1)*10^162995+2^541455-1	325990	paolo galliani	01/2019
573	2^1082908+583561	325988	Enzo Doria	05/2017
574	30^220411-29^220411	325574	Jean-Louis Charton	10/2018
575	2^1081308+7	325507	Stefano Morozzi	10/2022
576	2^1078242+1881649	324584	Enzo Doria	11/2016
577	2^1077737+1880117	324432	Enzo Doria	10/2016
578	3^679017-5*2^679017	323974	Jon Grantham	08/2023
579	2^1075425+1880117	323736	Enzo Doria	10/2016
580	(28^223381+1)/29	323267	Paul Bourdelais	12/2020
581	10^322999+187071	323000	Stefano Morozzi	03/2019
582	10^322999-143151	322999	Patrick De Geest	05/2020
583	2^1072146+1886869	322749	Enzo Doria	04/2017
584	2^1072118-7321953	322740	Enzo Doria	02/2015
585	2^1071026+1886869	322411	Enzo Doria	04/2017
586	2^1070539+1880633	322265	Enzo Doria	10/2016
587	2^1069293-1147195	321890	Enzo Doria	05/2015
588	2^1065968+1880941	320889	Enzo Doria	10/2016
589	2^1065897-1147195	320867	Enzo Doria	05/2015
590	2^1063427+1882103	320124	Enzo Doria	12/2016
591	2^1061095-1061095	319422	Henri Lifchitz	10/2013
592	2^1060950+653119	319378	Enzo Doria	12/2016
593	2^1060363+782753	319202	Enzo Doria	11/2016
594	(71^172259-1)/70	318895	Paul Bourdelais	08/2020
595	2^1054736+483061	317508	Enzo Doria	12/2016
596	2^1053965+1879667	317276	Enzo Doria	10/2016
597	(43^194119-1)/42	317086	Paul Bourdelais	08/2020
598	2^1052186-458165	316740	Enzo Doria	03/2015
599	11^303909+2	316489	Paul Bourdelais	08/2023
600	2^1046613-114685	315062	Enzo Doria	04/2015
601	2^1045625-459373	314765	Enzo Doria	06/2015
602	10^(2157363+1)-810^157363-1	314727	Robert Price	07/2023
603	(7*10^314564-61)/9	314564	Erik Branger	09/2016
604	2^1044206+7	314338	Stefano Morozzi	10/2022
605	(7^371669-1)/6	314096	Paul Bourdelais	02/2010
606	(53^181981-1)/52	313784	Paul Bourdelais	08/2020
607	(8^347437-5^347437)/3	313767	Jon Grantham	08/2023
608	2^1041944+283051	313657	Enzo Doria	12/2016
609	2^1041153-114391	313419	Enzo Doria	02/2015
610	(2^1039700+9)/5	312981	Stefano Morozzi	09/2022
611	(74^167311+1)/75	312742	Paul Bourdelais	12/2020
612	2^1038871+1866983	312732	Enzo Doria	04/2016
613	2^1038545+71657	312634	Enzo Doria	08/2023
614	(55^179573-1)/54	312521	Paul Bourdelais	08/2020
615	2^1037647+1881263	312363	Enzo Doria	11/2016
616	2^1037226+1879699	312237	Enzo Doria	10/2016
617	2^1036867+1865843	312129	Enzo Doria	02/2016
618	(76^165947+1)/77	312114	Paul Bourdelais	01/2021
619	2^1036020-114539	311874	Enzo Doria	02/2015
620	(90^159463-1)/89	311628	Paul Bourdelais	08/2020
621	2^1032240+1883431	310736	Enzo Doria	01/2017
622	2^1030352+1870021	310167	Enzo Doria	06/2016
623	2^1030046+1882843	310075	Enzo Doria	11/2016
624	3^648872+16	309591	Robert Price	04/2020
625	64221^64366+64366^64221	309451	Norbert Schneider	06/2023
626	2^1026999+20513	309158	Enzo Doria	07/2023
627	5^442281+2	309142	Paul Bourdelais	01/2021
628	2^1026204+22741	308919	Enzo Doria	09/2023
629	2^1026190+15	308914	Stefano Morozzi	10/2022
630	2^1025108+20851	308589	Enzo Doria	08/2023
631	A352736(16)	306985	Kellen Shenton	05/2022
632	(11^293831-1)/10	305993	Paul Bourdelais	03/2010
633	(67^167449-1)/66	305773	Paul Bourdelais	08/2020
634	(62^170539+1)/63	305671	Paul Bourdelais	12/2020
635	2^1015321-1015321	305643	Henri Lifchitz	08/2013
636	2^1014450+7	305380	Stefano Morozzi	10/2022
637	2^1014224-2791229	305312	Enzo Doria	01/2016
638	(10^304986+7)/673	304984	Alfred Reich	11/2021
639	65473^45250+45250^65473	304818	Hans Havermann	02/2022
640	66012^41423+41423^66012	304794	Hans Havermann	03/2022
641	65073^48202+48202^65073	304742	Hans Havermann	04/2022
642	238176^19+19^238176	304569	Hans Havermann	03/2022
643	73122^14615+14615^73122	304539	Hans Havermann	05/2022
644	64492^52639+52639^64492	304487	Hans Havermann	03/2022
645	65955^41288+41288^65955	304437	Hans Havermann	04/2022
646	71729^17530+17530^71729	304403	Hans Havermann	03/2022
647	70170^21733+21733^70170	304336	Hans Havermann	03/2022
648	2^1010751-107709	304267	Enzo Doria	03/2014
649	84473^3994+3994^84473	304222	Hans Havermann	03/2022
650	(2^1010623-1)/12602017578957977	304212	Tony Prest / Never Odd Or Even	02/2014
651	74442^12125+12125^74442	303998	Hans Havermann	02/2022
652	77842^8039+8039^77842	303989	Hans Havermann	01/2022
653	64209^54140+54140^64209	303935	Hans Havermann	02/2022
654	2^1009577+1869587	303913	Enzo Doria	06/2016
655	67389^32338+32338^67389	303906	Hans Havermann	02/2022
656	8^336419-7^336419	303817	Jean-Louis Charton	01/2008
657	2^1009168+15	303790	Stefano Morozzi	10/2022
658	80766^5771+5771^80766	303782	Hans Havermann	01/2022
659	66094^39385+39385^66094	303724	Hans Havermann	01/2022
660	69147^24574+24574^69147	303589	Hans Havermann	02/2022
661	78390^7459+7459^78390	303580	Hans Havermann	01/2022
662	2^1008301+1869377	303529	Enzo Doria	06/2016
663	65008^46615+46615^65008	303492	Hans Havermann	02/2022
664	(2^1007838+5)/3	303389	Serge Batalov	08/2015
665	65018^46293+46293^65018	303343	Hans Havermann	01/2022
666	6^389756+5	303290	Paul Bourdelais	02/2021
667	71016^18649+18649^71016	303285	Hans Havermann	01/2022
668	80160^6047+6047^80160	303129	Hans Havermann	01/2022
669	67434^31237+31237^67434	303094	Hans Havermann	03/2022
670	65537^42102+42102^65537	303063	Hans Havermann	02/2022
671	71790^16553+16553^71790	302874	Hans Havermann	11/2021
672	65208^44129+44129^65208	302874	Hans Havermann	11/2021
673	84181^3960+3960^84181	302858	Hans Havermann	11/2021
674	71956^16087+16087^71956	302682	Hans Havermann	11/2021
675	2^1005326+383059	302634	Enzo Doria	12/2016
676	2^1004929+1877567	302514	Enzo Doria	08/2016
677	69341^22978+22978^69341	302418	Hans Havermann	12/2021
678	111443^516+516^111443	302306	Hans Havermann	12/2021
679	67638^29387+29387^67638	302218	Hans Havermann	11/2021
680	2^1003494+1874899	302082	Enzo Doria	06/2016
681	75189^10400+10400^75189	302037	Hans Havermann	12/2021
682	67237^31042+31042^67237	302026	Hans Havermann	12/2021
683	64540^47791+47791^64540	302005	Hans Havermann	11/2021
684	2^1003046+60529	301947	Enzo Doria	04/2016
685	83278^4209+4209^83278	301815	Hans Havermann	09/2021
686	64431^48250+48250^64431	301763	Hans Havermann	09/2021
687	67237^30714+30714^67237	301716	Hans Havermann	09/2021
688	64641^46288+46288^64641	301581	Hans Havermann	09/2021
689	71513^16482+16482^71513	301572	Hans Havermann	10/2021
690	72017^15396+15396^72017	301565	Hans Havermann	09/2021
691	65534^39927+39927^65534	301540	Hans Havermann	10/2021
692	(23^221411-1)/22	301501	Paul Bourdelais	08/2020
693	63169^59152+59152^63169	301441	Hans Havermann	09/2021
694	75055^10348+10348^75055	301336	Hans Havermann	09/2021
695	2^1000647+1881353	301225	Enzo Doria	11/2016
696	83686^3961+3961^83686	301086	Hans Havermann	10/2021
697	68529^24742+24742^68529	301078	Hans Havermann	09/2021
698	65207^41416+41416^65207	301072	Hans Havermann	10/2021
700	2^1000000+821751	301030	Tony Prest / Never Odd Or Even	10/2015
699	2^999999+77151	301030	Norman Luhn	09/2023
701	90762^2071+2071^90762	300984	Hans Havermann	06/2021
702	63909^51142+51142^63909	300934	Hans Havermann	08/2021
703	2^999646+1874029	300924	Enzo Doria	06/2016
704	66280^34607+34607^66280	300856	Hans Havermann	06/2021
705	65534^38925+38925^65534	300817	Hans Havermann	07/2021
706	63296^56517+56517^63296	300794	Hans Havermann	06/2021
707	110610^523+523^110610	300694	Hans Havermann	06/2021
708	66428^33609+33609^66428	300684	Hans Havermann	06/2021
709	74247^11210+11210^74247	300672	Hans Havermann	06/2021
710	(59^169777-1)/58	300649	Paul Bourdelais	08/2020
711	10^300476+3	300477	Ed Trice	10/2012
712	10^300476-530913	300476	Patrick De Geest	03/2016
713	66703^31960+31960^66703	300471	Hans Havermann	06/2021
714	63722^51915+51915^63722	300468	Hans Havermann	06/2021
715	2^998053+1879667	300444	Enzo Doria	09/2016
716	77018^7959+7959^77018	300437	Hans Havermann	07/2021
717	314738^9+9^314738	300337	Anatoly F. Selevich	02/2011
718	69478^20987+20987^69478	300281	Hans Havermann	07/2021
719	64088^48393+48393^64088	300239	Hans Havermann	07/2021
720	64605^44146+44146^64605	300084	Hans Havermann	08/2021
721	7^355039-6^355039	300043	Jean-Louis Charton	05/2011
722	67594^27465+27465^67594	300035	Hans Havermann	06/2021
723	10^300000+287389	300001	Patrick De Geest	10/2019
724	10^300000-83657	300000	Patrick De Geest	10/2019
725	70599^17756+17756^70599	300000	Hans Havermann	06/2021
726	numbpart(72526161452)	299999	Serge Batalov	04/2017
727	2^996182-114431	299881	Enzo Doria	02/2015
728	3*2^996126+5	299865	Jon Grantham	07/2023
729	2^996034-17	299837	Stefano Morozzi	07/2022
730	(19*10^299640+77)/3	299641	Robert Price	03/2023
731	2^995214-2788361	299590	Enzo Doria	12/2015
732	2^994791-114319	299462	Enzo Doria	01/2015
733	2^994490-1863791	299372	Enzo Doria	01/2016
734	2^993322+1885729	299020	Enzo Doria	03/2017
735	(36395^65536+36393^65536)/2	298913	Kellen Shenton	04/2022
736	2^992711-2788807	298836	Enzo Doria	12/2015
737	2^992525-114199	298780	Enzo Doria	12/2014
738	(7^353501-3^353501)/4	298743	Jon Grantham	08/2023
739	2^992329+1884707	298721	Enzo Doria	02/2017
740	2^991968-23	298613	Stefano Morozzi	07/2022
741	2^991715-19	298536	Stefano Morozzi	07/2022
742	(10^298414+7)/191/823/56921/1334467	298398	Alfred Reich	10/2021
743	2^989562+25	297888	Stefano Morozzi	05/2021
744	(19*10^297497+77)/3	297498	Robert Price	03/2023
745	(2*10^297488-23)/3	297488	Robert Price	10/2022
746	(2^986191+1)/3	296873	Vincent Diepeveen	06/2008
747	2^985217-114553	296580	Enzo Doria	03/2015
748	(76^157649-1)/75	296507	Paul Bourdelais	07/2019
749	2^984650+21529	296410	Enzo Doria	08/2023
750	2^984131-1828009	296253	Enzo Doria	01/2015

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Probable Primes Top 10000

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