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	(2^369047+3618)/2	111094	Stefano Morozzi	09/2020
7502	88^57124-87	111077	Norbert Schneider	11/2015
7503	2^368980+753	111075	Lelio R Paula	05/2013
7504	2^368946-3623	111064	Yves Minet	03/2017
7505	2^368929+29835	111059	Lelio R Paula	05/2017
7506	4^184463-3^184463	111058	Jean-Louis Charton	12/2004
7507	111^54298+110	111057	Norbert Schneider	04/2017
7508	(4*10^111032-7)/3	111033	Ray Chandler	04/2011
7509	(29*10^111020-41)/3	111021	Tyler Busby	03/2024
7510	35799^1262+1262^35799	111015	Hans Havermann	10/2020
7511	(298*10^111004+11)/3	111006	Robert Price	11/2020
7512	27648^10349+10349^27648	111004	Hans Havermann	11/2020
7513	28899^6932+6932^28899	110997	Hans Havermann	11/2020
7514	(749^38809+1)/(749^197+1)	110990	Martin Hopf	11/2023
7515	2^368641-460303	110972	Enzo Doria	06/2015
7516	2^368619-109087	110966	Enzo Doria	04/2014
7517	(74*10^110961+313)/9	110962	Robert Price	06/2019
7518	25258^24711+24711^25258	110956	Hans Havermann	11/2020
7519	2^368550+1125899906842623	110945	Alfred Reich	05/2026
7520	(2^368539+1290)/2	110941	Stefano Morozzi	01/2021
7521	3*2^368489+7	110927	Lelio R Paula	09/2014
7522	(14*10^110922+61)/3	110923	Robert Price	12/2018
7523	97411!4-2	110913	Robert Price	07/2017
7524	(301*10^110903+23)/9	110905	Robert Price	06/2021
7525	(9179*2^368330-1)/35	110881	Lelio R Paula	05/2015
7526	25830^19619+19619^25830	110880	Hans Havermann	10/2020
7527	(34*10^110882-7)/9/13/29/1019374319	110871	Makoto Morimoto	05/2016
7528	Phi(119761,10)/85476950837250449	110864	Anonymous	01/2026
7529	26022^18191+18191^26022	110850	Hans Havermann	10/2020
7530	(2^368211+2250)/2	110843	Stefano Morozzi	01/2021
7531	(37*10^110813+251)/9	110814	Robert Price	09/2021
7532	2^368050-64875	110795	Lelio R Paula	05/2017
7533	2^368048+25	110794	Lelio R Paula	02/2013
7534	(2^368017+2262)/2	110784	Stefano Morozzi	02/2021
7535	69^60239-2	110771	Lelio R Paula	10/2013
7536	(23*2^367952+1)/15717	110762	Lelio R Paula	03/2014
7537	2^367924-69	110757	Lelio R Paula	02/2013
7538	(23*10^110738+61)/3	110739	Robert Price	01/2022
7539	(2^367779+3750)/2	110713	Stefano Morozzi	01/2021
7540	2^367709-109723	110692	Enzo Doria	04/2014
7541	2^367687+213413	110685	Enzo Doria	09/2023
7542	Phi(44407,-561)	110674	Henri Lifchitz	12/2025
7543	(3*2^367644-1)/107	110671	Lelio R Paula	03/2014
7544	(2^367626+3514)/2	110667	Stefano Morozzi	09/2020
7545	(1288676*34^72242-455)/33	110642	Eric Chen	03/2023
7546	379*10^110616+9	110619	Jason Yuen	01/2025
7547	(23*2^367398+1)/57963	110595	Lelio R Paula	03/2014
7548	140^51515-139	110558	Norbert Schneider	04/2019
7549	2^367215+1879223	110543	Enzo Doria	09/2016
7550	25782^19375+19375^25782	110534	Hans Havermann	10/2020
7551	26117^17058+17058^26117	110526	Hans Havermann	10/2020
7552	2^367141+41	110521	Lelio R Paula	02/2013
7553	2^367126+29835	110516	Lelio R Paula	05/2017
7554	(10^110503-1)/9+2(10^59183-1)/910^25660	110503	Makoto Morimoto	09/2020
7555	(10^110503-1)/9+2(10^65511-1)/910^22496	110503	Makoto Morimoto	09/2020
7556	(10^110503-1)/9+210^108327+210^2175	110503	Makoto Morimoto	09/2020
7557	(10^110503-1)/9+210^66251+210^44251	110503	Makoto Morimoto	09/2020
7558	(10^110503-1)/9+3(10^28813-1)/910^40845	110503	Makoto Morimoto	09/2020
7559	(10^110503-1)/9+3(10^82573-1)/910^13965	110503	Makoto Morimoto	09/2020
7560	(10^110503-1)/9+4(10^43305-1)/910^33599	110503	Makoto Morimoto	09/2020
7561	(10^110503-1)/9+510^70327+510^40175	110503	Makoto Morimoto	09/2020
7562	(10^110503-1)/9+510^99423+510^11079	110503	Makoto Morimoto	09/2020
7563	(10^110503-1)/9+7(10^23617-1)/910^43443	110503	Makoto Morimoto	09/2020
7564	(10^110503-1)/9+8(10^30251-1)/910^40126	110503	Makoto Morimoto	09/2020
7565	3(10^110503-1)/9+110^106036+1*10^4466	110503	Makoto Morimoto	09/2020
7566	3(10^110503-1)/9+110^58962+1*10^51540	110503	Makoto Morimoto	09/2020
7567	3(10^110503-1)/9+110^78213+1*10^32289	110503	Makoto Morimoto	09/2020
7568	3(10^110503-1)/9+210^76898+2*10^33604	110503	Makoto Morimoto	09/2020
7569	3(10^110503-1)/9-110^100802-1*10^9700	110503	Makoto Morimoto	09/2020
7570	3(10^110503-1)/9-110^76355-1*10^34147	110503	Makoto Morimoto	09/2020
7571	3(10^110503-1)/9-210^105704-2*10^4798	110503	Makoto Morimoto	09/2020
7572	7(10^110503-1)/9+1(10^27685-1)/9*10^41409	110503	Makoto Morimoto	09/2020
7573	7(10^110503-1)/9+1(10^91035-1)/9*10^9734	110503	Makoto Morimoto	09/2020
7574	7(10^110503-1)/9-1(10^23717-1)/9*10^43393	110503	Makoto Morimoto	09/2020
7575	7(10^110503-1)/9-110^57906-1*10^52596	110503	Makoto Morimoto	09/2020
7576	7(10^110503-1)/9-110^72287-1*10^38215	110503	Makoto Morimoto	09/2020
7577	7(10^110503-1)/9-2(10^53823-1)/9*10^28340	110503	Makoto Morimoto	09/2020
7578	7(10^110503-1)/9-2(10^88659-1)/9*10^10922	110503	Makoto Morimoto	09/2020
7579	7(10^110503-1)/9-3(10^79921-1)/9*10^15291	110503	Makoto Morimoto	09/2020
7580	7(10^110503-1)/9-310^60024-3*10^50478	110503	Makoto Morimoto	09/2020
7581	7(10^110503-1)/9-4(10^103091-1)/9*10^3706	110503	Makoto Morimoto	09/2020
7582	7(10^110503-1)/9-410^103658-4*10^6844	110503	Makoto Morimoto	09/2020
7583	7(10^110503-1)/9-410^78188-4*10^32314	110503	Makoto Morimoto	09/2020
7584	7(10^110503-1)/9-5(10^35035-1)/9*10^37734	110503	Makoto Morimoto	09/2020
7585	7(10^110503-1)/9-6(10^67347-1)/9*10^21578	110503	Makoto Morimoto	09/2020
7586	7(10^110503-1)/9-610^60391-6*10^50111	110503	Makoto Morimoto	09/2020
7587	(10^110503-1)-4(10^96247-1)/910^7128	110503	Makoto Morimoto	09/2020
7588	(10^110503-1)-410^74037-410^36465	110503	Makoto Morimoto	09/2020
7589	(10^110503-1)-410^77787-410^32715	110503	Makoto Morimoto	09/2020
7590	(10^110503-1)-410^91179-410^19323	110503	Makoto Morimoto	09/2020
7591	(10^110503-1)-5(10^99143-1)/910^5680	110503	Makoto Morimoto	09/2020
7592	(10^110503-1)-7(10^85075-1)/910^12714	110503	Makoto Morimoto	09/2020
7593	(10^110503-1)-710^100712-710^9790	110503	Makoto Morimoto	09/2020
7594	(10^110503-1)-710^76427-710^34075	110503	Makoto Morimoto	09/2020
7595	(10^110503-1)-710^90451-710^20051	110503	Makoto Morimoto	09/2020
7596	(10^110503-1)-810^106252-810^4250	110503	Makoto Morimoto	09/2020
7597	(11*10^110496+49)/3	110497	Robert Price	07/2018
7598	25447^21958+21958^25447	110481	Hans Havermann	11/2020
7599	(31*2^366976+1)/7	110472	Lelio R Paula	03/2014
7600	7*10^110468-23	110469	Robert Price	07/2019
7601	5*3^231464-2^231464	110438	Jon Grantham	08/2023
7602	2^366853+5711	110434	Lelio R Paula	05/2017
7603	(21181*2^366833+1)/3	110432	Lelio R Paula	07/2014
7604	(4^231439)%(3^231439)	110425	Henri Lifchitz	06/2025
7605	2^366816+315	110423	Lelio R Paula	05/2017
7606	(11^2667520)/(10^2667520)	110416	Henri Lifchitz	06/2025
7607	2^366775-2787037	110411	Enzo Doria	03/2016
7608	(112*10^110405-1)/3	110407	Serge Batalov	12/2014
7609	2^366751+2797553	110404	Enzo Doria	03/2016
7610	25276^23331+23331^25276	110404	Hans Havermann	10/2020
7611	2^366748+255	110403	Lelio R Paula	05/2017
7612	2^366738-2985	110400	Yves Minet	09/2014
7613	(23*2^366739+1)/74575	110396	Lelio R Paula	03/2014
7614	(2^366722+1314)/2	110395	Stefano Morozzi	02/2021
7615	2^366716+1871791	110393	Enzo Doria	05/2016
7616	(239*23^81066-349)/22	110391	Eric Chen	08/2023
7617	2^366695+1334025	110387	Henri Lifchitz	10/2024
7618	(5^528189)%F(528189)	110385	Henri Lifchitz	06/2025
7619	2^366649+1871687	110373	Enzo Doria	05/2016
7620	2^366629-351205	110367	Enzo Doria	06/2015
7621	(31*10^110363+257)/9	110364	Robert Price	12/2021
7622	(5^183291)%(4^183291)	110353	Henri Lifchitz	06/2025
7623	(17*19^86292-215)/18	110347	Eric Chen	01/2023
7625	2^366558+1874479	110345	Enzo Doria	06/2016
7624	25132^24581+24581^25132	110345	Hans Havermann	10/2020
7626	(2^366539+770)/2	110339	Stefano Morozzi	09/2020
7627	26368^15285+15285^26368	110331	Hans Havermann	10/2020
7628	(23*10^110290+19)/3	110291	Robert Price	07/2019
7629	18^87853-4409	110280	Enzo Doria	03/2013
7630	28490^7419+7419^28490	110267	Hans Havermann	11/2020
7631	2^366218-23	110243	Lelio R Paula	02/2013
7632	(21*2^366193-1)/197	110235	Lelio R Paula	03/2014
7633	2^366178-343991	110231	Enzo Doria	07/2015
7634	12^102123-11	110210	Riley Fisher	09/2023
7635	(725*35^71368+16649)/34	110199	Eric Chen	05/2025
7636	25777^18798+18798^25777	110174	Hans Havermann	10/2020
7637	2^365944+1871341	110161	Enzo Doria	05/2016
7638	2^365838-461267	110129	Enzo Doria	07/2015
7639	30152^4491+4491^30152	110126	Hans Havermann	11/2020
7640	2^365802+23359	110118	Enzo Doria	10/2023
7641	10^110111+464019	110112	Patrick De Geest	05/2021
7642	10^110111-40001	110111	Robert Price	01/2021
7643	2^365763-6555	110106	Lelio R Paula	04/2017
7644	(2^365689+2^182845+1)/5	110083		11/2006
7645	(83^57367-1)/3536509644718	110080	Paul Vanderveen	05/2025
7646	2^365666-459161	110077	Enzo Doria	05/2015
7647	3*10^110076-7	110077	Robert Price	08/2015
7648	(102936^21961-1)/102935	110076	Anonymous	09/2025
7649	13^98785-72	110041	Lelio R Paula	03/2017
7651	(25^78707+1)/26	110027	Robert Price	06/2013
7650	(7*10^110027-277)/9	110027	Robert Price	02/2022
7652	(16*10^110014-73)/3	110015	Robert Price	07/2020
7653	Phi(8869,17!)	110007	Henri Lifchitz	12/2025
7654	(7*10^110006-151)/9	110006	Robert Price	02/2018
7655	6^141361-7	110001	Lelio R Paula	11/2014
7656	10^110000+8029681	110001	Hayden Chesnut	11/2024
7657	10^110000+2044477	110001	Hayden Chesnut	11/2024
7658	10^110000+76407	110001	Hayden Chesnut	11/2024
7659	10^110000+167311	110001	Hayden Chesnut	11/2024
7660	20^84536+81	109984	Lelio R Paula	03/2017
7661	5*2^365347-9	109982	Lelio R Paula	09/2014
7662	9*6^141303+7	109957	Lelio R Paula	11/2014
7663	27635^9522+9522^27635	109953	Hans Havermann	11/2020
7664	78^58099+77	109929	Norbert Schneider	02/2015
7665	2*10^109928-7	109929	Robert Price	10/2015
7666	30580^3933+3933^30580	109927	Hans Havermann	11/2020
7667	26380^14689+14689^26380	109926	Hans Havermann	11/2020
7668	(2^365161+1130)/2	109925	Stefano Morozzi	09/2020
7669	(27*2^365137-1)/2021	109916	Lelio R Paula	03/2014
7670	29^75157-30	109910	Anonymous	09/2024
7671	(4441*29^75152-24)/7	109905	Curtis Bright	05/2015
7672	(2^365087+7)/6015	109899	Lelio R Paula	01/2014
7673	(2^365069+3774)/2	109897	Stefano Morozzi	02/2021
7674	29652^5083+5083^29652	109894	Mark Rodenkirch	10/2020
7675	(2^365049+722)/2	109891	Stefano Morozzi	09/2020
7676	(35*10^109888-89)/9	109889	Robert Price	02/2022
7677	18^87533-11	109878	Lelio R Paula	04/2017
7678	2^364982-5	109871	Henri Lifchitz	04/2006
7679	3*10^109861+59	109862	Robert Price	08/2018
7680	5*10^109860-69	109861	Robert Price	02/2021
7681	2^364936-1867979	109857	Enzo Doria	04/2016
7682	27013^11652+11652^27013	109846	Hans Havermann	10/2020
7683	2^364867-112087	109836	Enzo Doria	06/2014
7684	4^182415-85061	109825	Mike Oakes	06/2011
7685	(2^364809+1034)/2	109819	Stefano Morozzi	09/2020
7686	24972^24972-8323^8323	109814	Henri Lifchitz	10/2024
7687	(53*10^109809-287)/9	109810	Robert Price	02/2022
7688	(52*10^109807-133)/9	109808	Robert Price	09/2021
7689	25708^18675+18675^25708	109806	Hans Havermann	10/2020
7690	(17^89227+16^89227)/33	109788	Robert Price	08/2013
7691	2^364687-187	109782	Lelio R Paula	01/2012
7692	2^364644+67	109769	Lelio R Paula	01/2012
7693	(9787*2^364625-1)/24947	109763	Lelio R Paula	05/2015
7694	(2^364616+5)/9	109760	Lelio R Paula	01/2014
7695	(55*10^109759+89)/9	109760	Robert Price	03/2019
7696	(14*32^72921+4171)/31	109757	Eric Chen	04/2023
7697	12^101694+73	109747	Lelio R Paula	03/2017
7698	13^98518-66	109744	Lelio R Paula	03/2017
7699	(35^71069+2^71069)/37	109734	Robert Price	01/2025
7700	(8*10^109721-269)/9	109721	Robert Price	09/2021
7701	2^364478-113261	109719	Enzo Doria	07/2014
7702	(2^364513+1)/(3*44290516579)	109719	Gord Palameta	08/2018
7703	(24737*2^364454+1)/3	109716	Lelio R Paula	07/2014
7704	27814^8777+8777^27814	109681	Hans Havermann	10/2020
7705	(62*10^109673+1)/9	109674	Serge Batalov	11/2010
7706	3^229824+340	109654	Lelio R Paula	03/2017
7707	(16623*33^72206-8095)/16	109649	Eric Chen	05/2023
7708	(2*10^109645-71)/3	109645	Robert Price	12/2017
7709	V(786978)	109644	Serge Batalov	07/2024
7710	2^364169-112813	109626	Enzo Doria	06/2014
7711	28822^6359+6359^28822	109622	Hans Havermann	11/2020
7712	10^109615+21	109616	Lelio R Paula	03/2017
7713	10^109615-456267	109615	Patrick De Geest	03/2017
7714	522^40331-40331^522	109607	Norman Luhn	09/2024
7715	2^364094-113	109604	Lelio R Paula	01/2012
7716	25251^21898+21898^25251	109600	Hans Havermann	11/2020
7717	(4^182026+11)/3	109591	Robert Price	02/2017
7718	2^364041-6883	109588	Lelio R Paula	09/2011
7719	12^101545+11	109586	Lelio R Paula	03/2017
7720	26536^13475+13475^26536	109582	Hans Havermann	11/2020
7721	2^363842-2787101	109528	Enzo Doria	03/2016
7722	(2^363812+3570)/2	109519	Stefano Morozzi	09/2020
7723	(996^36527+1)/997	109515	Jinyuan Wang	12/2024
7724	(22699*2^363782+1)/763	109511	Lelio R Paula	07/2014
7725	2^363769+5711	109506	Lelio R Paula	04/2017
7726	(31*2^363748+1)/49	109499	Lelio R Paula	03/2014
7727	26^77372+25	109480	Anonymous	09/2024
7728	(2^363670+100280245065)	109476	Paul Bourdelais	05/2022
7729	p(22245)#/2-8	109462	Robert Price	01/2017
7730	2^363556+55	109442	Lelio R Paula	01/2012
7731	(509*10^109414+31)/9	109416	Robert Price	08/2022
7732	(2^363437+1682)/2	109406	Stefano Morozzi	09/2020
7733	(55459*2^363411+1)/81	109401	Lelio R Paula	07/2014
7734	2^363406+1871569	109397	Enzo Doria	05/2016
7735	(129^51829-1)/128	109388	Anonymous	06/2024
7736	(2^363370+1338)/2	109385	Stefano Morozzi	02/2021
7737	(2^363349+7)/9	109378	Lelio R Paula	01/2014
7738	(13869^26569-1)/(13869^163-1)	109375	Ryan Propper	11/2023
7739	3^229236+100	109374	Lelio R Paula	03/2017
7740	(2^363315+3258)/2	109369	Stefano Morozzi	02/2021
7741	2^363268-58695	109355	Lelio R Paula	04/2017
7742	2^363191-112321	109332	Enzo Doria	06/2014
7743	26231^14718+14718^26231	109327	Hans Havermann	10/2020
7744	25461^19672+19672^25461	109326	Hans Havermann	10/2020
7745	4*10^109316-63	109317	Robert Price	10/2018
7746	2^363120+3	109311	Donovan Johnson	04/2006
7747	(10^109297-1)/9	109297	Paul Bourdelais, Harvey Dubner	04/2007
7748	2^363042-114641	109287	Enzo Doria	04/2015
7749	2^363020-112793	109280	Enzo Doria	06/2014
7750	(8732^27889-1)/(8732^167-1)	109256	Ryan Propper	11/2023

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Probable Primes Top 10000

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