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 ?
7501	2^366738-2985	110400	Yves Minet	09/2014
7502	(23*2^366739+1)/74575	110396	Lelio R Paula	03/2014
7503	(2^366722+1314)/2	110395	Stefano Morozzi	02/2021
7504	2^366716+1871791	110393	Enzo Doria	05/2016
7505	(239*23^81066-349)/22	110391	Eric Chen	08/2023
7506	2^366695+1334025	110387	Henri Lifchitz	10/2024
7507	(5^528189)%F(528189)	110385	Henri Lifchitz	06/2025
7508	2^366649+1871687	110373	Enzo Doria	05/2016
7509	2^366629-351205	110367	Enzo Doria	06/2015
7510	(31*10^110363+257)/9	110364	Robert Price	12/2021
7511	(5^183291)%(4^183291)	110353	Henri Lifchitz	06/2025
7512	(17*19^86292-215)/18	110347	Eric Chen	01/2023
7514	2^366558+1874479	110345	Enzo Doria	06/2016
7513	25132^24581+24581^25132	110345	Hans Havermann	10/2020
7515	(2^366539+770)/2	110339	Stefano Morozzi	09/2020
7516	26368^15285+15285^26368	110331	Hans Havermann	10/2020
7517	(23*10^110290+19)/3	110291	Robert Price	07/2019
7518	18^87853-4409	110280	Enzo Doria	03/2013
7519	28490^7419+7419^28490	110267	Hans Havermann	11/2020
7520	2^366218-23	110243	Lelio R Paula	02/2013
7521	(21*2^366193-1)/197	110235	Lelio R Paula	03/2014
7522	2^366178-343991	110231	Enzo Doria	07/2015
7523	12^102123-11	110210	Riley Fisher	09/2023
7524	(725*35^71368+16649)/34	110199	Eric Chen	05/2025
7525	25777^18798+18798^25777	110174	Hans Havermann	10/2020
7526	2^365944+1871341	110161	Enzo Doria	05/2016
7527	2^365838-461267	110129	Enzo Doria	07/2015
7528	30152^4491+4491^30152	110126	Hans Havermann	11/2020
7529	2^365802+23359	110118	Enzo Doria	10/2023
7530	10^110111+464019	110112	Patrick De Geest	05/2021
7531	10^110111-40001	110111	Robert Price	01/2021
7532	2^365763-6555	110106	Lelio R Paula	04/2017
7533	(2^365689+2^182845+1)/5	110083		11/2006
7534	(83^57367-1)/3536509644718	110080	Paul Vanderveen	05/2025
7535	2^365666-459161	110077	Enzo Doria	05/2015
7536	3*10^110076-7	110077	Robert Price	08/2015
7537	(102936^21961-1)/102935	110076	Anonymous	09/2025
7538	13^98785-72	110041	Lelio R Paula	03/2017
7540	(25^78707+1)/26	110027	Robert Price	06/2013
7539	(7*10^110027-277)/9	110027	Robert Price	02/2022
7541	(16*10^110014-73)/3	110015	Robert Price	07/2020
7542	Phi(8869,17!)	110007	Henri Lifchitz	12/2025
7543	(7*10^110006-151)/9	110006	Robert Price	02/2018
7544	6^141361-7	110001	Lelio R Paula	11/2014
7545	10^110000+8029681	110001	Hayden Chesnut	11/2024
7546	10^110000+2044477	110001	Hayden Chesnut	11/2024
7547	10^110000+76407	110001	Hayden Chesnut	11/2024
7548	10^110000+167311	110001	Hayden Chesnut	11/2024
7549	20^84536+81	109984	Lelio R Paula	03/2017
7550	5*2^365347-9	109982	Lelio R Paula	09/2014
7551	9*6^141303+7	109957	Lelio R Paula	11/2014
7552	27635^9522+9522^27635	109953	Hans Havermann	11/2020
7553	78^58099+77	109929	Norbert Schneider	02/2015
7554	2*10^109928-7	109929	Robert Price	10/2015
7555	30580^3933+3933^30580	109927	Hans Havermann	11/2020
7556	26380^14689+14689^26380	109926	Hans Havermann	11/2020
7557	(2^365161+1130)/2	109925	Stefano Morozzi	09/2020
7558	(27*2^365137-1)/2021	109916	Lelio R Paula	03/2014
7559	29^75157-30	109910	Anonymous	09/2024
7560	(4441*29^75152-24)/7	109905	Curtis Bright	05/2015
7561	(2^365087+7)/6015	109899	Lelio R Paula	01/2014
7562	(2^365069+3774)/2	109897	Stefano Morozzi	02/2021
7563	29652^5083+5083^29652	109894	Mark Rodenkirch	10/2020
7564	(2^365049+722)/2	109891	Stefano Morozzi	09/2020
7565	(35*10^109888-89)/9	109889	Robert Price	02/2022
7566	18^87533-11	109878	Lelio R Paula	04/2017
7567	2^364982-5	109871	Henri Lifchitz	04/2006
7568	3*10^109861+59	109862	Robert Price	08/2018
7569	5*10^109860-69	109861	Robert Price	02/2021
7570	2^364936-1867979	109857	Enzo Doria	04/2016
7571	27013^11652+11652^27013	109846	Hans Havermann	10/2020
7572	2^364867-112087	109836	Enzo Doria	06/2014
7573	4^182415-85061	109825	Mike Oakes	06/2011
7574	(2^364809+1034)/2	109819	Stefano Morozzi	09/2020
7575	24972^24972-8323^8323	109814	Henri Lifchitz	10/2024
7576	(53*10^109809-287)/9	109810	Robert Price	02/2022
7577	(52*10^109807-133)/9	109808	Robert Price	09/2021
7578	25708^18675+18675^25708	109806	Hans Havermann	10/2020
7579	(17^89227+16^89227)/33	109788	Robert Price	08/2013
7580	2^364687-187	109782	Lelio R Paula	01/2012
7581	2^364644+67	109769	Lelio R Paula	01/2012
7582	(9787*2^364625-1)/24947	109763	Lelio R Paula	05/2015
7583	(2^364616+5)/9	109760	Lelio R Paula	01/2014
7584	(55*10^109759+89)/9	109760	Robert Price	03/2019
7585	(14*32^72921+4171)/31	109757	Eric Chen	04/2023
7586	12^101694+73	109747	Lelio R Paula	03/2017
7587	13^98518-66	109744	Lelio R Paula	03/2017
7588	(35^71069+2^71069)/37	109734	Robert Price	01/2025
7589	(8*10^109721-269)/9	109721	Robert Price	09/2021
7590	2^364478-113261	109719	Enzo Doria	07/2014
7591	(2^364513+1)/(3*44290516579)	109719	Gord Palameta	08/2018
7592	(24737*2^364454+1)/3	109716	Lelio R Paula	07/2014
7593	27814^8777+8777^27814	109681	Hans Havermann	10/2020
7594	(62*10^109673+1)/9	109674	Serge Batalov	11/2010
7595	3^229824+340	109654	Lelio R Paula	03/2017
7596	(16623*33^72206-8095)/16	109649	Eric Chen	05/2023
7597	(2*10^109645-71)/3	109645	Robert Price	12/2017
7598	V(786978)	109644	Serge Batalov	07/2024
7599	2^364169-112813	109626	Enzo Doria	06/2014
7600	28822^6359+6359^28822	109622	Hans Havermann	11/2020
7601	10^109615+21	109616	Lelio R Paula	03/2017
7602	10^109615-456267	109615	Patrick De Geest	03/2017
7603	522^40331-40331^522	109607	Norman Luhn	09/2024
7604	2^364094-113	109604	Lelio R Paula	01/2012
7605	25251^21898+21898^25251	109600	Hans Havermann	11/2020
7606	(4^182026+11)/3	109591	Robert Price	02/2017
7607	2^364041-6883	109588	Lelio R Paula	09/2011
7608	12^101545+11	109586	Lelio R Paula	03/2017
7609	26536^13475+13475^26536	109582	Hans Havermann	11/2020
7610	2^363842-2787101	109528	Enzo Doria	03/2016
7611	(2^363812+3570)/2	109519	Stefano Morozzi	09/2020
7612	(996^36527+1)/997	109515	Jinyuan Wang	12/2024
7613	(22699*2^363782+1)/763	109511	Lelio R Paula	07/2014
7614	2^363769+5711	109506	Lelio R Paula	04/2017
7615	(31*2^363748+1)/49	109499	Lelio R Paula	03/2014
7616	26^77372+25	109480	Anonymous	09/2024
7617	(2^363670+100280245065)	109476	Paul Bourdelais	05/2022
7618	p(22245)#/2-8	109462	Robert Price	01/2017
7619	2^363556+55	109442	Lelio R Paula	01/2012
7620	(509*10^109414+31)/9	109416	Robert Price	08/2022
7621	(2^363437+1682)/2	109406	Stefano Morozzi	09/2020
7622	(55459*2^363411+1)/81	109401	Lelio R Paula	07/2014
7623	2^363406+1871569	109397	Enzo Doria	05/2016
7624	(129^51829-1)/128	109388	Anonymous	06/2024
7625	(2^363370+1338)/2	109385	Stefano Morozzi	02/2021
7626	(2^363349+7)/9	109378	Lelio R Paula	01/2014
7627	(13869^26569-1)/(13869^163-1)	109375	Ryan Propper	11/2023
7628	3^229236+100	109374	Lelio R Paula	03/2017
7629	(2^363315+3258)/2	109369	Stefano Morozzi	02/2021
7630	2^363268-58695	109355	Lelio R Paula	04/2017
7631	2^363191-112321	109332	Enzo Doria	06/2014
7632	26231^14718+14718^26231	109327	Hans Havermann	10/2020
7633	25461^19672+19672^25461	109326	Hans Havermann	10/2020
7634	4*10^109316-63	109317	Robert Price	10/2018
7635	2^363120+3	109311	Donovan Johnson	04/2006
7636	(10^109297-1)/9	109297	Paul Bourdelais, Harvey Dubner	04/2007
7637	2^363042-114641	109287	Enzo Doria	04/2015
7638	2^363020-112793	109280	Enzo Doria	06/2014
7639	(8732^27889-1)/(8732^167-1)	109256	Ryan Propper	11/2023
7640	(85*10^109253+203)/9	109254	Robert Price	09/2020
7641	24990^23431+23431^24990	109202	Hans Havermann	10/2020
7642	Phi(369781,-2)	109200	Henri Lifchitz	12/2025
7643	(2^362746+3738)/2	109198	Stefano Morozzi	09/2020
7644	(2^362716+1282)/2	109189	Stefano Morozzi	01/2021
7645	(67607*2^362695+1)/70499	109183	Lelio R Paula	07/2014
7646	25060^22737+22737^25060	109180	Hans Havermann	10/2020
7647	(9*2^362644+1)/5	109167	Lelio R Paula	03/2014
7648	5^156181+38	109166	Lelio R Paula	02/2017
7649	(2^362623+3618)/2	109161	Stefano Morozzi	09/2020
7650	25138^21993+21993^25138	109157	Hans Havermann	10/2020
7651	4*10^109142+91	109143	Robert Price	08/2018
7652	3^228750+68	109142	Lelio R Paula	03/2017
7653	(2^362561+786)/2	109142	Stefano Morozzi	09/2020
7654	578*29^74623+7	109132	Eric Chen	06/2025
7655	(23*10^109113+61)/3	109114	Robert Price	01/2022
7656	2*10^109100-49	109101	Robert Price	09/2020
7657	(10223*2^362376+1)/9	109090	Lelio R Paula	07/2014
7658	65^60167-64^60167	109078	Robert Price	08/2013
7659	Phi(63393,-1105)	109075	Henri Lifchitz	12/2025
7660	7*3^228589-2	109066	Lelio R Paula	09/2014
7661	24874^24243+24243^24874	109063	Hans Havermann	11/2020
7662	(17*10^109059-161)/9	109060	Robert Price	02/2021
7663	29158^5495+5495^29158	109050	Hans Havermann	11/2020
7664	(78557*2^362188+1)/189	109033	Lelio R Paula	07/2014
7665	2*7^129008+9	109025	Lelio R Paula	11/2014
7666	88*10^109022+7	109024	Robert Price	03/2020
7667	28194^7337+7337^28194	108985	Hans Havermann	10/2020
7668	(5*10^108960+91)/3	108961	Robert Price	04/2018
7669	2^361957+76367	108960	Enzo Doria	05/2016
7670	(11*29^74504-245655)/28	108955	Eric Chen	06/2025
7671	2^361873-1411	108935	Yves Minet	01/2013
7672	(24737*2^361857+1)/35	108933	Lelio R Paula	07/2014
7673	216^216^216+91^91^91	108917	Henri Lifchitz	03/2025
7674	47^65132-65132^47	108908	Norman Luhn	09/2024
7675	115^52842-114	108892	Norbert Schneider	07/2018
7676	13^97745-24	108883	Lelio R Paula	03/2017
7677	(2^361696+2562)/2	108882	Stefano Morozzi	09/2020
7678	17^88475+8	108864	Lelio R Paula	04/2017
7679	2^361567+51	108843	Lelio R Paula	01/2012
7680	2^361563-109501	108842	Enzo Doria	04/2014
7681	12^100852+83	108838	Lelio R Paula	03/2017
7682	2^361497+767	108822	Lelio R Paula	01/2012
7683	L(520691)/78103651/1057002731/42794551909	108791	Serge Batalov	07/2024
7684	28019^7630+7630^28019	108785	Hans Havermann	10/2020
7685	24723^24758-24758^24723	108765	Norbert Schneider	11/2020
7686	2^361280-112349	108757	Enzo Doria	06/2014
7687	2^361271-5955	108754	Lelio R Paula	04/2017
7688	12^100757+19	108736	Lelio R Paula	03/2017
7689	25368^19333+19333^25368	108735	Hans Havermann	11/2020
7690	(2^361195+3618)/2	108731	Stefano Morozzi	09/2020
7691	2^361153-111546435	108718	Paul Bourdelais	10/2021
7692	14^94849-61	108710	Lelio R Paula	05/2017
7693	27267^9700+9700^27267	108708	Hans Havermann	11/2020
7694	(19^85009-5^85009)/14	108705	Robert Price	07/2013
7695	24832^23853+23853^24832	108704	Hans Havermann	11/2020
7696	27502^8963+8963^27502	108701	Hans Havermann	11/2020
7697	(130^51419-1)/129	108695	Anonymous	06/2024
7698	25807^16278+16278^25807	108689	Hans Havermann	11/2020
7699	39^68306+38	108680	Alfred Reich	03/2026
7700	(11*2^361027+1)/40463	108677	Lelio R Paula	03/2014
7701	2^360973+1299	108664	Lelio R Paula	04/2017
7702	24^78728+23	108662	Anonymous	09/2024
7703	2^360959-109101	108660	Enzo Doria	04/2014
7704	6*5^155454+7	108659	Lelio R Paula	11/2014
7705	10^108656+79	108657	Lelio R Paula	02/2017
7706	10^108656-50001	108656	Patrick De Geest	03/2017
7707	2^360918-35	108648	Lelio R Paula	01/2012
7708	4*10^108646-47	108647	Robert Price	10/2021
7709	(11*2^360886-1)/7	108638	Lelio R Paula	03/2014
7710	3*10^108624-49	108625	Robert Price	07/2018
7711	(2^360831+666)/2	108621	Stefano Morozzi	09/2020
7712	(134*10^108610+7)/3	108612	Robert Price	02/2020
7713	2*10^108609+29	108610	Robert Price	02/2021
7714	(10^108604+7)/71/191	108600	Alfred Reich	06/2021
7715	(2^360742+3222)/2	108594	Stefano Morozzi	09/2020
7716	2^360706-458903	108584	Enzo Doria	04/2015
7717	31112^3087+3087^31112	108567	Hans Havermann	11/2020
7718	2^360641-113185	108564	Enzo Doria	07/2014
7719	(29*10^108559-71)/3	108560	Robert Price	07/2021
7721	2^360618+75019	108557	Enzo Doria	04/2016
7720	2^360618+2025	108557	Henri Lifchitz	01/2025
7722	2^360607-216367	108554	Harrison Mesh	06/2022
7723	29^74228+556	108551	Eric Chen	06/2025
7724	(14*10^108545-221)/9	108546	Robert Price	04/2018
7725	(44*10^108544-233)/9	108545	Robert Price	01/2019
7726	3*5^155286+2	108541	Lelio R Paula	11/2014
7727	7^128422+4	108530	Lelio R Paula	11/2014
7728	7^128421-80	108529	Lelio R Paula	03/2017
7729	2^360497+53807	108521	Yves Minet	07/2010
7730	2^360468-4559	108512	Yves Minet	03/2019
7731	(2^360451+578)/2	108507	Stefano Morozzi	09/2020
7732	2^360366+1459	108481	Lelio R Paula	09/2011
7733	2^360364-1499	108481	Yves Minet	05/2013
7734	25662^16871+16871^25662	108477	Hans Havermann	10/2020
7735	25009^21748+21748^25009	108475	Hans Havermann	10/2020
7736	14^94642-23	108472	Lelio R Paula	05/2017
7737	(197*10^108446-11)/3	108448	Robert Price	03/2020
7738	(2^360229+1290)/2	108440	Stefano Morozzi	01/2021
7739	4*10^108412+9	108413	Robert Price	05/2015
7740	(259*10^108409-1)/3	108411	Robert Price	12/2020
7741	(2^360122+1194)/2	108408	Stefano Morozzi	09/2020
7742	133^51042-132	108406	Norbert Schneider	02/2019
7743	2^360093-351103	108399	Enzo Doria	06/2015
7744	2^360042+723	108384	Lelio R Paula	01/2012
7745	85^56164-2	108364	Lelio R Paula	10/2013
7746	2^359937-29323	108352	Enzo Doria	07/2015
7747	22^80712-23	108350	Anonymous	09/2024
7748	(2^359922+1762)/2	108348	Stefano Morozzi	09/2020
7749	(2^359903+758)/2	108342	Stefano Morozzi	09/2020
7750	2^359898-19997	108341	Enzo Doria	06/2013

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