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	26200^18097+18097^26200	111550	Hans Havermann	01/2021
7502	286^45405+45405^286	111532	Norbert Schneider	04/2015
7503	4*5^159563-9	111531	Lelio R Paula	11/2014
7504	5*10^111528-21	111529	Robert Price	12/2021
7505	(4^185225+23)/3	111517	Robert Price	10/2018
7506	2^370393-2797093	111500	Enzo Doria	03/2016
7507	(21*2^370382-1)/629	111495	Lelio R Paula	03/2014
7508	(2^370371+554)/2	111493	Stefano Morozzi	09/2020
7509	6^143273-5	111489	Paul Bourdelais	01/2021
7510	2^370292-2791979	111469	Enzo Doria	03/2016
7511	(14*10^111443-11)/3	111444	Robert Price	08/2022
7512	2^370177-461551	111435	Enzo Doria	07/2015
7513	(2^370169+1706)/2	111432	Stefano Morozzi	09/2020
7514	109^54683-108	111413	Norbert Schneider	02/2017
7516	(83*10^111406-173)/9	111407	Robert Price	04/2021
7515	959^37362-37362^959	111407	Henri Lifchitz	10/2024
7517	(2^370043+1010)/2	111394	Stefano Morozzi	09/2020
7518	32961^2396+2396^32961	111392	Hans Havermann	10/2020
7519	numbpart(10^10+76282)	111391	Serge Batalov	04/2015
7520	(19*10^111385+11)/3	111386	Robert Price	07/2023
7521	(23*10^111380-29)/3	111381	Robert Price	03/2022
7522	2^369974+733	111374	Lelio R Paula	05/2013
7523	121^53470+120	111367	Norbert Schneider	10/2018
7524	2^369915-286267	111356	Enzo Doria	07/2015
7525	(62*10^111347-629)/9	111348	Robert Price	07/2021
7526	2^369855-1615	111338	Lelio R Paula	05/2017
7527	(27^77783+5^77783)/32	111335	Robert Price	07/2026
7528	7*10^111325+3	111326	Robert Price	08/2015
7529	51^65176+2	111293	Lelio R Paula	08/2013
7530	Phi(43329,-43329)	111283	Henri Lifchitz	06/2025
7531	2^369643-1865767	111274	Enzo Doria	03/2016
7532	2^369603+885	111262	Lelio R Paula	05/2017
7533	25555^22564+22564^25555	111252	Hans Havermann	10/2020
7534	F(532391)/89441689/1425422598617	111243	Serge Batalov	07/2024
7535	L(532277)	111240	Renaud Lifchitz	03/2004
7536	105^55033-2	111233	Lelio R Paula	10/2017
7537	(35*10^111232-737)/9	111233	Robert Price	07/2018
7538	26970^13307+13307^26970	111227	Hans Havermann	10/2020
7539	25419^23716+23716^25419	111210	Hans Havermann	10/2020
7540	(26^78593-3^78593)/23	111206	Robert Price	02/2025
7541	9*10^111201-29	111202	Robert Price	09/2019
7542	2^369392+29835	111199	Lelio R Paula	05/2017
7543	3^233059+16	111198	Robert Price	03/2020
7544	2^369354-3413	111187	Yves Minet	12/2016
7545	2^369296-27	111170	Lelio R Paula	02/2013
7546	(2468^40960+1)/(2468^8192+1)	111161	Martin Hopf	08/2024
7547	2^369239-109837	111153	Enzo Doria	05/2014
7548	2^369224-291839	111148	Enzo Doria	07/2015
7549	2^369216+2798881	111146	Enzo Doria	04/2016
7550	26842^13817+13817^26842	111137	Hans Havermann	11/2020
7551	(5*10^111119-191)/3	111120	Robert Price	05/2021
7552	(29*10^111112-23)/3	111113	Robert Price	03/2022
7553	10^111111+163849	111112	Patrick De Geest	03/2017
7554	10^111111-312911	111111	Patrick De Geest	03/2017
7555	2^369092-216923	111108	Enzo Doria	05/2014
7556	2^369081-55	111105	Lelio R Paula	02/2013
7557	(2^369047+3618)/2	111094	Stefano Morozzi	09/2020
7558	88^57124-87	111077	Norbert Schneider	11/2015
7559	2^368980+753	111075	Lelio R Paula	05/2013
7560	2^368946-3623	111064	Yves Minet	03/2017
7561	2^368929+29835	111059	Lelio R Paula	05/2017
7562	4^184463-3^184463	111058	Jean-Louis Charton	12/2004
7563	111^54298+110	111057	Norbert Schneider	04/2017
7564	(4*10^111032-7)/3	111033	Ray Chandler	04/2011
7565	(29*10^111020-41)/3	111021	Tyler Busby	03/2024
7566	35799^1262+1262^35799	111015	Hans Havermann	10/2020
7567	(298*10^111004+11)/3	111006	Robert Price	11/2020
7568	27648^10349+10349^27648	111004	Hans Havermann	11/2020
7569	28899^6932+6932^28899	110997	Hans Havermann	11/2020
7570	(749^38809+1)/(749^197+1)	110990	Martin Hopf	11/2023
7571	2^368641-460303	110972	Enzo Doria	06/2015
7572	2^368619-109087	110966	Enzo Doria	04/2014
7573	(74*10^110961+313)/9	110962	Robert Price	06/2019
7574	25258^24711+24711^25258	110956	Hans Havermann	11/2020
7575	2^368550+1125899906842623	110945	Alfred Reich	05/2026
7576	(2^368539+1290)/2	110941	Stefano Morozzi	01/2021
7577	3*2^368489+7	110927	Lelio R Paula	09/2014
7578	(14*10^110922+61)/3	110923	Robert Price	12/2018
7579	97411!4-2	110913	Robert Price	07/2017
7580	(301*10^110903+23)/9	110905	Robert Price	06/2021
7581	(9179*2^368330-1)/35	110881	Lelio R Paula	05/2015
7582	25830^19619+19619^25830	110880	Hans Havermann	10/2020
7583	(34*10^110882-7)/9/13/29/1019374319	110871	Makoto Morimoto	05/2016
7584	Phi(119761,10)/85476950837250449	110864	Anonymous	01/2026
7585	26022^18191+18191^26022	110850	Hans Havermann	10/2020
7586	(2^368211+2250)/2	110843	Stefano Morozzi	01/2021
7587	(37*10^110813+251)/9	110814	Robert Price	09/2021
7588	2^368050-64875	110795	Lelio R Paula	05/2017
7589	2^368048+25	110794	Lelio R Paula	02/2013
7590	(2^368017+2262)/2	110784	Stefano Morozzi	02/2021
7591	69^60239-2	110771	Lelio R Paula	10/2013
7592	(23*2^367952+1)/15717	110762	Lelio R Paula	03/2014
7593	2^367924-69	110757	Lelio R Paula	02/2013
7594	(23*10^110738+61)/3	110739	Robert Price	01/2022
7595	(2^367779+3750)/2	110713	Stefano Morozzi	01/2021
7596	2^367709-109723	110692	Enzo Doria	04/2014
7597	2^367687+213413	110685	Enzo Doria	09/2023
7598	Phi(44407,-561)	110674	Henri Lifchitz	12/2025
7599	(3*2^367644-1)/107	110671	Lelio R Paula	03/2014
7600	(2^367626+3514)/2	110667	Stefano Morozzi	09/2020
7601	(1288676*34^72242-455)/33	110642	Eric Chen	03/2023
7602	379*10^110616+9	110619	Jason Yuen	01/2025
7603	(23*2^367398+1)/57963	110595	Lelio R Paula	03/2014
7604	140^51515-139	110558	Norbert Schneider	04/2019
7605	2^367215+1879223	110543	Enzo Doria	09/2016
7606	25782^19375+19375^25782	110534	Hans Havermann	10/2020
7607	26117^17058+17058^26117	110526	Hans Havermann	10/2020
7608	2^367141+41	110521	Lelio R Paula	02/2013
7609	2^367126+29835	110516	Lelio R Paula	05/2017
7610	(10^110503-1)/9+2(10^59183-1)/910^25660	110503	Makoto Morimoto	09/2020
7611	(10^110503-1)/9+2(10^65511-1)/910^22496	110503	Makoto Morimoto	09/2020
7612	(10^110503-1)/9+210^108327+210^2175	110503	Makoto Morimoto	09/2020
7613	(10^110503-1)/9+210^66251+210^44251	110503	Makoto Morimoto	09/2020
7614	(10^110503-1)/9+3(10^28813-1)/910^40845	110503	Makoto Morimoto	09/2020
7615	(10^110503-1)/9+3(10^82573-1)/910^13965	110503	Makoto Morimoto	09/2020
7616	(10^110503-1)/9+4(10^43305-1)/910^33599	110503	Makoto Morimoto	09/2020
7617	(10^110503-1)/9+510^70327+510^40175	110503	Makoto Morimoto	09/2020
7618	(10^110503-1)/9+510^99423+510^11079	110503	Makoto Morimoto	09/2020
7619	(10^110503-1)/9+7(10^23617-1)/910^43443	110503	Makoto Morimoto	09/2020
7620	(10^110503-1)/9+8(10^30251-1)/910^40126	110503	Makoto Morimoto	09/2020
7621	3(10^110503-1)/9+110^106036+1*10^4466	110503	Makoto Morimoto	09/2020
7622	3(10^110503-1)/9+110^58962+1*10^51540	110503	Makoto Morimoto	09/2020
7623	3(10^110503-1)/9+110^78213+1*10^32289	110503	Makoto Morimoto	09/2020
7624	3(10^110503-1)/9+210^76898+2*10^33604	110503	Makoto Morimoto	09/2020
7625	3(10^110503-1)/9-110^100802-1*10^9700	110503	Makoto Morimoto	09/2020
7626	3(10^110503-1)/9-110^76355-1*10^34147	110503	Makoto Morimoto	09/2020
7627	3(10^110503-1)/9-210^105704-2*10^4798	110503	Makoto Morimoto	09/2020
7628	7(10^110503-1)/9+1(10^27685-1)/9*10^41409	110503	Makoto Morimoto	09/2020
7629	7(10^110503-1)/9+1(10^91035-1)/9*10^9734	110503	Makoto Morimoto	09/2020
7630	7(10^110503-1)/9-1(10^23717-1)/9*10^43393	110503	Makoto Morimoto	09/2020
7631	7(10^110503-1)/9-110^57906-1*10^52596	110503	Makoto Morimoto	09/2020
7632	7(10^110503-1)/9-110^72287-1*10^38215	110503	Makoto Morimoto	09/2020
7633	7(10^110503-1)/9-2(10^53823-1)/9*10^28340	110503	Makoto Morimoto	09/2020
7634	7(10^110503-1)/9-2(10^88659-1)/9*10^10922	110503	Makoto Morimoto	09/2020
7635	7(10^110503-1)/9-3(10^79921-1)/9*10^15291	110503	Makoto Morimoto	09/2020
7636	7(10^110503-1)/9-310^60024-3*10^50478	110503	Makoto Morimoto	09/2020
7637	7(10^110503-1)/9-4(10^103091-1)/9*10^3706	110503	Makoto Morimoto	09/2020
7638	7(10^110503-1)/9-410^103658-4*10^6844	110503	Makoto Morimoto	09/2020
7639	7(10^110503-1)/9-410^78188-4*10^32314	110503	Makoto Morimoto	09/2020
7640	7(10^110503-1)/9-5(10^35035-1)/9*10^37734	110503	Makoto Morimoto	09/2020
7641	7(10^110503-1)/9-6(10^67347-1)/9*10^21578	110503	Makoto Morimoto	09/2020
7642	7(10^110503-1)/9-610^60391-6*10^50111	110503	Makoto Morimoto	09/2020
7643	(10^110503-1)-4(10^96247-1)/910^7128	110503	Makoto Morimoto	09/2020
7644	(10^110503-1)-410^74037-410^36465	110503	Makoto Morimoto	09/2020
7645	(10^110503-1)-410^77787-410^32715	110503	Makoto Morimoto	09/2020
7646	(10^110503-1)-410^91179-410^19323	110503	Makoto Morimoto	09/2020
7647	(10^110503-1)-5(10^99143-1)/910^5680	110503	Makoto Morimoto	09/2020
7648	(10^110503-1)-7(10^85075-1)/910^12714	110503	Makoto Morimoto	09/2020
7649	(10^110503-1)-710^100712-710^9790	110503	Makoto Morimoto	09/2020
7650	(10^110503-1)-710^76427-710^34075	110503	Makoto Morimoto	09/2020
7651	(10^110503-1)-710^90451-710^20051	110503	Makoto Morimoto	09/2020
7652	(10^110503-1)-810^106252-810^4250	110503	Makoto Morimoto	09/2020
7653	(11*10^110496+49)/3	110497	Robert Price	07/2018
7654	25447^21958+21958^25447	110481	Hans Havermann	11/2020
7655	(31*2^366976+1)/7	110472	Lelio R Paula	03/2014
7656	7*10^110468-23	110469	Robert Price	07/2019
7657	5*3^231464-2^231464	110438	Jon Grantham	08/2023
7658	2^366853+5711	110434	Lelio R Paula	05/2017
7659	(21181*2^366833+1)/3	110432	Lelio R Paula	07/2014
7660	(4^231439)%(3^231439)	110425	Henri Lifchitz	06/2025
7661	2^366816+315	110423	Lelio R Paula	05/2017
7662	(11^2667520)/(10^2667520)	110416	Henri Lifchitz	06/2025
7663	2^366775-2787037	110411	Enzo Doria	03/2016
7664	(112*10^110405-1)/3	110407	Serge Batalov	12/2014
7665	2^366751+2797553	110404	Enzo Doria	03/2016
7666	25276^23331+23331^25276	110404	Hans Havermann	10/2020
7667	2^366748+255	110403	Lelio R Paula	05/2017
7668	2^366738-2985	110400	Yves Minet	09/2014
7669	(23*2^366739+1)/74575	110396	Lelio R Paula	03/2014
7670	(2^366722+1314)/2	110395	Stefano Morozzi	02/2021
7671	2^366716+1871791	110393	Enzo Doria	05/2016
7672	(239*23^81066-349)/22	110391	Eric Chen	08/2023
7673	2^366695+1334025	110387	Henri Lifchitz	10/2024
7674	(5^528189)%F(528189)	110385	Henri Lifchitz	06/2025
7675	2^366649+1871687	110373	Enzo Doria	05/2016
7676	2^366629-351205	110367	Enzo Doria	06/2015
7677	(31*10^110363+257)/9	110364	Robert Price	12/2021
7678	(5^183291)%(4^183291)	110353	Henri Lifchitz	06/2025
7679	(17*19^86292-215)/18	110347	Eric Chen	01/2023
7681	2^366558+1874479	110345	Enzo Doria	06/2016
7680	25132^24581+24581^25132	110345	Hans Havermann	10/2020
7682	(2^366539+770)/2	110339	Stefano Morozzi	09/2020
7683	26368^15285+15285^26368	110331	Hans Havermann	10/2020
7684	(23*10^110290+19)/3	110291	Robert Price	07/2019
7685	18^87853-4409	110280	Enzo Doria	03/2013
7686	28490^7419+7419^28490	110267	Hans Havermann	11/2020
7687	2^366218-23	110243	Lelio R Paula	02/2013
7688	(21*2^366193-1)/197	110235	Lelio R Paula	03/2014
7689	2^366178-343991	110231	Enzo Doria	07/2015
7690	12^102123-11	110210	Riley Fisher	09/2023
7691	(725*35^71368+16649)/34	110199	Eric Chen	05/2025
7692	25777^18798+18798^25777	110174	Hans Havermann	10/2020
7693	2^365944+1871341	110161	Enzo Doria	05/2016
7694	2^365838-461267	110129	Enzo Doria	07/2015
7695	30152^4491+4491^30152	110126	Hans Havermann	11/2020
7696	2^365802+23359	110118	Enzo Doria	10/2023
7697	10^110111+464019	110112	Patrick De Geest	05/2021
7698	10^110111-40001	110111	Robert Price	01/2021
7699	2^365763-6555	110106	Lelio R Paula	04/2017
7700	(2^365689+2^182845+1)/5	110083		11/2006
7701	(83^57367-1)/3536509644718	110080	Paul Vanderveen	05/2025
7702	2^365666-459161	110077	Enzo Doria	05/2015
7703	3*10^110076-7	110077	Robert Price	08/2015
7704	(102936^21961-1)/102935	110076	Anonymous	09/2025
7705	13^98785-72	110041	Lelio R Paula	03/2017
7707	(25^78707+1)/26	110027	Robert Price	06/2013
7706	(7*10^110027-277)/9	110027	Robert Price	02/2022
7708	(16*10^110014-73)/3	110015	Robert Price	07/2020
7709	Phi(8869,17!)	110007	Henri Lifchitz	12/2025
7710	(7*10^110006-151)/9	110006	Robert Price	02/2018
7711	6^141361-7	110001	Lelio R Paula	11/2014
7712	10^110000+8029681	110001	Hayden Chesnut	11/2024
7713	10^110000+2044477	110001	Hayden Chesnut	11/2024
7714	10^110000+76407	110001	Hayden Chesnut	11/2024
7715	10^110000+167311	110001	Hayden Chesnut	11/2024
7716	20^84536+81	109984	Lelio R Paula	03/2017
7717	5*2^365347-9	109982	Lelio R Paula	09/2014
7718	9*6^141303+7	109957	Lelio R Paula	11/2014
7719	27635^9522+9522^27635	109953	Hans Havermann	11/2020
7720	78^58099+77	109929	Norbert Schneider	02/2015
7721	2*10^109928-7	109929	Robert Price	10/2015
7722	30580^3933+3933^30580	109927	Hans Havermann	11/2020
7723	26380^14689+14689^26380	109926	Hans Havermann	11/2020
7724	(2^365161+1130)/2	109925	Stefano Morozzi	09/2020
7725	(27*2^365137-1)/2021	109916	Lelio R Paula	03/2014
7726	29^75157-30	109910	Anonymous	09/2024
7727	(4441*29^75152-24)/7	109905	Curtis Bright	05/2015
7728	(2^365087+7)/6015	109899	Lelio R Paula	01/2014
7729	(2^365069+3774)/2	109897	Stefano Morozzi	02/2021
7730	29652^5083+5083^29652	109894	Mark Rodenkirch	10/2020
7731	(2^365049+722)/2	109891	Stefano Morozzi	09/2020
7732	(35*10^109888-89)/9	109889	Robert Price	02/2022
7733	18^87533-11	109878	Lelio R Paula	04/2017
7734	2^364982-5	109871	Henri Lifchitz	04/2006
7735	3*10^109861+59	109862	Robert Price	08/2018
7736	5*10^109860-69	109861	Robert Price	02/2021
7737	2^364936-1867979	109857	Enzo Doria	04/2016
7738	27013^11652+11652^27013	109846	Hans Havermann	10/2020
7739	2^364867-112087	109836	Enzo Doria	06/2014
7740	4^182415-85061	109825	Mike Oakes	06/2011
7741	(2^364809+1034)/2	109819	Stefano Morozzi	09/2020
7742	24972^24972-8323^8323	109814	Henri Lifchitz	10/2024
7743	(53*10^109809-287)/9	109810	Robert Price	02/2022
7744	(52*10^109807-133)/9	109808	Robert Price	09/2021
7745	25708^18675+18675^25708	109806	Hans Havermann	10/2020
7746	(17^89227+16^89227)/33	109788	Robert Price	08/2013
7747	2^364687-187	109782	Lelio R Paula	01/2012
7748	2^364644+67	109769	Lelio R Paula	01/2012
7749	(9787*2^364625-1)/24947	109763	Lelio R Paula	05/2015
7750	(2^364616+5)/9	109760	Lelio R Paula	01/2014

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Probable Primes Top 10000

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