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	26022^18191+18191^26022	110850	Hans Havermann	10/2020
7502	(2^368211+2250)/2	110843	Stefano Morozzi	01/2021
7503	(37*10^110813+251)/9	110814	Robert Price	09/2021
7504	2^368050-64875	110795	Lelio R Paula	05/2017
7505	2^368048+25	110794	Lelio R Paula	02/2013
7506	(2^368017+2262)/2	110784	Stefano Morozzi	02/2021
7507	69^60239-2	110771	Lelio R Paula	10/2013
7508	(23*2^367952+1)/15717	110762	Lelio R Paula	03/2014
7509	2^367924-69	110757	Lelio R Paula	02/2013
7510	(23*10^110738+61)/3	110739	Robert Price	01/2022
7511	(2^367779+3750)/2	110713	Stefano Morozzi	01/2021
7512	2^367709-109723	110692	Enzo Doria	04/2014
7513	2^367687+213413	110685	Enzo Doria	09/2023
7514	Phi(44407,-561)	110674	Henri Lifchitz	12/2025
7515	(3*2^367644-1)/107	110671	Lelio R Paula	03/2014
7516	(2^367626+3514)/2	110667	Stefano Morozzi	09/2020
7517	(1288676*34^72242-455)/33	110642	Eric Chen	03/2023
7518	379*10^110616+9	110619	Jason Yuen	01/2025
7519	(23*2^367398+1)/57963	110595	Lelio R Paula	03/2014
7520	140^51515-139	110558	Norbert Schneider	04/2019
7521	2^367215+1879223	110543	Enzo Doria	09/2016
7522	25782^19375+19375^25782	110534	Hans Havermann	10/2020
7523	26117^17058+17058^26117	110526	Hans Havermann	10/2020
7524	2^367141+41	110521	Lelio R Paula	02/2013
7525	2^367126+29835	110516	Lelio R Paula	05/2017
7526	(10^110503-1)/9+2(10^59183-1)/910^25660	110503	Makoto Morimoto	09/2020
7527	(10^110503-1)/9+2(10^65511-1)/910^22496	110503	Makoto Morimoto	09/2020
7528	(10^110503-1)/9+210^108327+210^2175	110503	Makoto Morimoto	09/2020
7529	(10^110503-1)/9+210^66251+210^44251	110503	Makoto Morimoto	09/2020
7530	(10^110503-1)/9+3(10^28813-1)/910^40845	110503	Makoto Morimoto	09/2020
7531	(10^110503-1)/9+3(10^82573-1)/910^13965	110503	Makoto Morimoto	09/2020
7532	(10^110503-1)/9+4(10^43305-1)/910^33599	110503	Makoto Morimoto	09/2020
7533	(10^110503-1)/9+510^70327+510^40175	110503	Makoto Morimoto	09/2020
7534	(10^110503-1)/9+510^99423+510^11079	110503	Makoto Morimoto	09/2020
7535	(10^110503-1)/9+7(10^23617-1)/910^43443	110503	Makoto Morimoto	09/2020
7536	(10^110503-1)/9+8(10^30251-1)/910^40126	110503	Makoto Morimoto	09/2020
7537	3(10^110503-1)/9+110^106036+1*10^4466	110503	Makoto Morimoto	09/2020
7538	3(10^110503-1)/9+110^58962+1*10^51540	110503	Makoto Morimoto	09/2020
7539	3(10^110503-1)/9+110^78213+1*10^32289	110503	Makoto Morimoto	09/2020
7540	3(10^110503-1)/9+210^76898+2*10^33604	110503	Makoto Morimoto	09/2020
7541	3(10^110503-1)/9-110^100802-1*10^9700	110503	Makoto Morimoto	09/2020
7542	3(10^110503-1)/9-110^76355-1*10^34147	110503	Makoto Morimoto	09/2020
7543	3(10^110503-1)/9-210^105704-2*10^4798	110503	Makoto Morimoto	09/2020
7544	7(10^110503-1)/9+1(10^27685-1)/9*10^41409	110503	Makoto Morimoto	09/2020
7545	7(10^110503-1)/9+1(10^91035-1)/9*10^9734	110503	Makoto Morimoto	09/2020
7546	7(10^110503-1)/9-1(10^23717-1)/9*10^43393	110503	Makoto Morimoto	09/2020
7547	7(10^110503-1)/9-110^57906-1*10^52596	110503	Makoto Morimoto	09/2020
7548	7(10^110503-1)/9-110^72287-1*10^38215	110503	Makoto Morimoto	09/2020
7549	7(10^110503-1)/9-2(10^53823-1)/9*10^28340	110503	Makoto Morimoto	09/2020
7550	7(10^110503-1)/9-2(10^88659-1)/9*10^10922	110503	Makoto Morimoto	09/2020
7551	7(10^110503-1)/9-3(10^79921-1)/9*10^15291	110503	Makoto Morimoto	09/2020
7552	7(10^110503-1)/9-310^60024-3*10^50478	110503	Makoto Morimoto	09/2020
7553	7(10^110503-1)/9-4(10^103091-1)/9*10^3706	110503	Makoto Morimoto	09/2020
7554	7(10^110503-1)/9-410^103658-4*10^6844	110503	Makoto Morimoto	09/2020
7555	7(10^110503-1)/9-410^78188-4*10^32314	110503	Makoto Morimoto	09/2020
7556	7(10^110503-1)/9-5(10^35035-1)/9*10^37734	110503	Makoto Morimoto	09/2020
7557	7(10^110503-1)/9-6(10^67347-1)/9*10^21578	110503	Makoto Morimoto	09/2020
7558	7(10^110503-1)/9-610^60391-6*10^50111	110503	Makoto Morimoto	09/2020
7559	(10^110503-1)-4(10^96247-1)/910^7128	110503	Makoto Morimoto	09/2020
7560	(10^110503-1)-410^74037-410^36465	110503	Makoto Morimoto	09/2020
7561	(10^110503-1)-410^77787-410^32715	110503	Makoto Morimoto	09/2020
7562	(10^110503-1)-410^91179-410^19323	110503	Makoto Morimoto	09/2020
7563	(10^110503-1)-5(10^99143-1)/910^5680	110503	Makoto Morimoto	09/2020
7564	(10^110503-1)-7(10^85075-1)/910^12714	110503	Makoto Morimoto	09/2020
7565	(10^110503-1)-710^100712-710^9790	110503	Makoto Morimoto	09/2020
7566	(10^110503-1)-710^76427-710^34075	110503	Makoto Morimoto	09/2020
7567	(10^110503-1)-710^90451-710^20051	110503	Makoto Morimoto	09/2020
7568	(10^110503-1)-810^106252-810^4250	110503	Makoto Morimoto	09/2020
7569	(11*10^110496+49)/3	110497	Robert Price	07/2018
7570	25447^21958+21958^25447	110481	Hans Havermann	11/2020
7571	(31*2^366976+1)/7	110472	Lelio R Paula	03/2014
7572	7*10^110468-23	110469	Robert Price	07/2019
7573	5*3^231464-2^231464	110438	Jon Grantham	08/2023
7574	2^366853+5711	110434	Lelio R Paula	05/2017
7575	(21181*2^366833+1)/3	110432	Lelio R Paula	07/2014
7576	(4^231439)%(3^231439)	110425	Henri Lifchitz	06/2025
7577	2^366816+315	110423	Lelio R Paula	05/2017
7578	(11^2667520)/(10^2667520)	110416	Henri Lifchitz	06/2025
7579	2^366775-2787037	110411	Enzo Doria	03/2016
7580	(112*10^110405-1)/3	110407	Serge Batalov	12/2014
7581	2^366751+2797553	110404	Enzo Doria	03/2016
7582	25276^23331+23331^25276	110404	Hans Havermann	10/2020
7583	2^366748+255	110403	Lelio R Paula	05/2017
7584	2^366738-2985	110400	Yves Minet	09/2014
7585	(23*2^366739+1)/74575	110396	Lelio R Paula	03/2014
7586	(2^366722+1314)/2	110395	Stefano Morozzi	02/2021
7587	2^366716+1871791	110393	Enzo Doria	05/2016
7588	(239*23^81066-349)/22	110391	Eric Chen	08/2023
7589	2^366695+1334025	110387	Henri Lifchitz	10/2024
7590	(5^528189)%F(528189)	110385	Henri Lifchitz	06/2025
7591	2^366649+1871687	110373	Enzo Doria	05/2016
7592	2^366629-351205	110367	Enzo Doria	06/2015
7593	(31*10^110363+257)/9	110364	Robert Price	12/2021
7594	(5^183291)%(4^183291)	110353	Henri Lifchitz	06/2025
7595	(17*19^86292-215)/18	110347	Eric Chen	01/2023
7597	2^366558+1874479	110345	Enzo Doria	06/2016
7596	25132^24581+24581^25132	110345	Hans Havermann	10/2020
7598	(2^366539+770)/2	110339	Stefano Morozzi	09/2020
7599	26368^15285+15285^26368	110331	Hans Havermann	10/2020
7600	(23*10^110290+19)/3	110291	Robert Price	07/2019
7601	18^87853-4409	110280	Enzo Doria	03/2013
7602	28490^7419+7419^28490	110267	Hans Havermann	11/2020
7603	2^366218-23	110243	Lelio R Paula	02/2013
7604	(21*2^366193-1)/197	110235	Lelio R Paula	03/2014
7605	2^366178-343991	110231	Enzo Doria	07/2015
7606	12^102123-11	110210	Riley Fisher	09/2023
7607	(725*35^71368+16649)/34	110199	Eric Chen	05/2025
7608	25777^18798+18798^25777	110174	Hans Havermann	10/2020
7609	2^365944+1871341	110161	Enzo Doria	05/2016
7610	2^365838-461267	110129	Enzo Doria	07/2015
7611	30152^4491+4491^30152	110126	Hans Havermann	11/2020
7612	2^365802+23359	110118	Enzo Doria	10/2023
7613	10^110111+464019	110112	Patrick De Geest	05/2021
7614	10^110111-40001	110111	Robert Price	01/2021
7615	2^365763-6555	110106	Lelio R Paula	04/2017
7616	(2^365689+2^182845+1)/5	110083		11/2006
7617	(83^57367-1)/3536509644718	110080	Paul Vanderveen	05/2025
7618	2^365666-459161	110077	Enzo Doria	05/2015
7619	3*10^110076-7	110077	Robert Price	08/2015
7620	(102936^21961-1)/102935	110076	Anonymous	09/2025
7621	13^98785-72	110041	Lelio R Paula	03/2017
7623	(25^78707+1)/26	110027	Robert Price	06/2013
7622	(7*10^110027-277)/9	110027	Robert Price	02/2022
7624	(16*10^110014-73)/3	110015	Robert Price	07/2020
7625	Phi(8869,17!)	110007	Henri Lifchitz	12/2025
7626	(7*10^110006-151)/9	110006	Robert Price	02/2018
7627	6^141361-7	110001	Lelio R Paula	11/2014
7628	10^110000+8029681	110001	Hayden Chesnut	11/2024
7629	10^110000+2044477	110001	Hayden Chesnut	11/2024
7630	10^110000+76407	110001	Hayden Chesnut	11/2024
7631	10^110000+167311	110001	Hayden Chesnut	11/2024
7632	20^84536+81	109984	Lelio R Paula	03/2017
7633	5*2^365347-9	109982	Lelio R Paula	09/2014
7634	9*6^141303+7	109957	Lelio R Paula	11/2014
7635	27635^9522+9522^27635	109953	Hans Havermann	11/2020
7636	78^58099+77	109929	Norbert Schneider	02/2015
7637	2*10^109928-7	109929	Robert Price	10/2015
7638	30580^3933+3933^30580	109927	Hans Havermann	11/2020
7639	26380^14689+14689^26380	109926	Hans Havermann	11/2020
7640	(2^365161+1130)/2	109925	Stefano Morozzi	09/2020
7641	(27*2^365137-1)/2021	109916	Lelio R Paula	03/2014
7642	29^75157-30	109910	Anonymous	09/2024
7643	(4441*29^75152-24)/7	109905	Curtis Bright	05/2015
7644	(2^365087+7)/6015	109899	Lelio R Paula	01/2014
7645	(2^365069+3774)/2	109897	Stefano Morozzi	02/2021
7646	29652^5083+5083^29652	109894	Mark Rodenkirch	10/2020
7647	(2^365049+722)/2	109891	Stefano Morozzi	09/2020
7648	(35*10^109888-89)/9	109889	Robert Price	02/2022
7649	18^87533-11	109878	Lelio R Paula	04/2017
7650	2^364982-5	109871	Henri Lifchitz	04/2006
7651	3*10^109861+59	109862	Robert Price	08/2018
7652	5*10^109860-69	109861	Robert Price	02/2021
7653	2^364936-1867979	109857	Enzo Doria	04/2016
7654	27013^11652+11652^27013	109846	Hans Havermann	10/2020
7655	2^364867-112087	109836	Enzo Doria	06/2014
7656	4^182415-85061	109825	Mike Oakes	06/2011
7657	(2^364809+1034)/2	109819	Stefano Morozzi	09/2020
7658	24972^24972-8323^8323	109814	Henri Lifchitz	10/2024
7659	(53*10^109809-287)/9	109810	Robert Price	02/2022
7660	(52*10^109807-133)/9	109808	Robert Price	09/2021
7661	25708^18675+18675^25708	109806	Hans Havermann	10/2020
7662	(17^89227+16^89227)/33	109788	Robert Price	08/2013
7663	2^364687-187	109782	Lelio R Paula	01/2012
7664	2^364644+67	109769	Lelio R Paula	01/2012
7665	(9787*2^364625-1)/24947	109763	Lelio R Paula	05/2015
7666	(2^364616+5)/9	109760	Lelio R Paula	01/2014
7667	(55*10^109759+89)/9	109760	Robert Price	03/2019
7668	(14*32^72921+4171)/31	109757	Eric Chen	04/2023
7669	12^101694+73	109747	Lelio R Paula	03/2017
7670	13^98518-66	109744	Lelio R Paula	03/2017
7671	(35^71069+2^71069)/37	109734	Robert Price	01/2025
7672	(8*10^109721-269)/9	109721	Robert Price	09/2021
7673	2^364478-113261	109719	Enzo Doria	07/2014
7674	(2^364513+1)/(3*44290516579)	109719	Gord Palameta	08/2018
7675	(24737*2^364454+1)/3	109716	Lelio R Paula	07/2014
7676	27814^8777+8777^27814	109681	Hans Havermann	10/2020
7677	(62*10^109673+1)/9	109674	Serge Batalov	11/2010
7678	3^229824+340	109654	Lelio R Paula	03/2017
7679	(16623*33^72206-8095)/16	109649	Eric Chen	05/2023
7680	(2*10^109645-71)/3	109645	Robert Price	12/2017
7681	V(786978)	109644	Serge Batalov	07/2024
7682	2^364169-112813	109626	Enzo Doria	06/2014
7683	28822^6359+6359^28822	109622	Hans Havermann	11/2020
7684	10^109615+21	109616	Lelio R Paula	03/2017
7685	10^109615-456267	109615	Patrick De Geest	03/2017
7686	522^40331-40331^522	109607	Norman Luhn	09/2024
7687	2^364094-113	109604	Lelio R Paula	01/2012
7688	25251^21898+21898^25251	109600	Hans Havermann	11/2020
7689	(4^182026+11)/3	109591	Robert Price	02/2017
7690	2^364041-6883	109588	Lelio R Paula	09/2011
7691	12^101545+11	109586	Lelio R Paula	03/2017
7692	26536^13475+13475^26536	109582	Hans Havermann	11/2020
7693	2^363842-2787101	109528	Enzo Doria	03/2016
7694	(2^363812+3570)/2	109519	Stefano Morozzi	09/2020
7695	(996^36527+1)/997	109515	Jinyuan Wang	12/2024
7696	(22699*2^363782+1)/763	109511	Lelio R Paula	07/2014
7697	2^363769+5711	109506	Lelio R Paula	04/2017
7698	(31*2^363748+1)/49	109499	Lelio R Paula	03/2014
7699	26^77372+25	109480	Anonymous	09/2024
7700	(2^363670+100280245065)	109476	Paul Bourdelais	05/2022
7701	p(22245)#/2-8	109462	Robert Price	01/2017
7702	2^363556+55	109442	Lelio R Paula	01/2012
7703	(509*10^109414+31)/9	109416	Robert Price	08/2022
7704	(2^363437+1682)/2	109406	Stefano Morozzi	09/2020
7705	(55459*2^363411+1)/81	109401	Lelio R Paula	07/2014
7706	2^363406+1871569	109397	Enzo Doria	05/2016
7707	(129^51829-1)/128	109388	Anonymous	06/2024
7708	(2^363370+1338)/2	109385	Stefano Morozzi	02/2021
7709	(2^363349+7)/9	109378	Lelio R Paula	01/2014
7710	(13869^26569-1)/(13869^163-1)	109375	Ryan Propper	11/2023
7711	3^229236+100	109374	Lelio R Paula	03/2017
7712	(2^363315+3258)/2	109369	Stefano Morozzi	02/2021
7713	2^363268-58695	109355	Lelio R Paula	04/2017
7714	2^363191-112321	109332	Enzo Doria	06/2014
7715	26231^14718+14718^26231	109327	Hans Havermann	10/2020
7716	25461^19672+19672^25461	109326	Hans Havermann	10/2020
7717	4*10^109316-63	109317	Robert Price	10/2018
7718	2^363120+3	109311	Donovan Johnson	04/2006
7719	(10^109297-1)/9	109297	Paul Bourdelais, Harvey Dubner	04/2007
7720	2^363042-114641	109287	Enzo Doria	04/2015
7721	2^363020-112793	109280	Enzo Doria	06/2014
7722	(8732^27889-1)/(8732^167-1)	109256	Ryan Propper	11/2023
7723	(85*10^109253+203)/9	109254	Robert Price	09/2020
7724	24990^23431+23431^24990	109202	Hans Havermann	10/2020
7725	Phi(369781,-2)	109200	Henri Lifchitz	12/2025
7726	(2^362746+3738)/2	109198	Stefano Morozzi	09/2020
7727	(2^362716+1282)/2	109189	Stefano Morozzi	01/2021
7728	(67607*2^362695+1)/70499	109183	Lelio R Paula	07/2014
7729	25060^22737+22737^25060	109180	Hans Havermann	10/2020
7730	(9*2^362644+1)/5	109167	Lelio R Paula	03/2014
7731	5^156181+38	109166	Lelio R Paula	02/2017
7732	(2^362623+3618)/2	109161	Stefano Morozzi	09/2020
7733	25138^21993+21993^25138	109157	Hans Havermann	10/2020
7734	4*10^109142+91	109143	Robert Price	08/2018
7735	3^228750+68	109142	Lelio R Paula	03/2017
7736	(2^362561+786)/2	109142	Stefano Morozzi	09/2020
7737	578*29^74623+7	109132	Eric Chen	06/2025
7738	(23*10^109113+61)/3	109114	Robert Price	01/2022
7739	2*10^109100-49	109101	Robert Price	09/2020
7740	(10223*2^362376+1)/9	109090	Lelio R Paula	07/2014
7741	65^60167-64^60167	109078	Robert Price	08/2013
7742	Phi(63393,-1105)	109075	Henri Lifchitz	12/2025
7743	7*3^228589-2	109066	Lelio R Paula	09/2014
7744	24874^24243+24243^24874	109063	Hans Havermann	11/2020
7745	(17*10^109059-161)/9	109060	Robert Price	02/2021
7746	29158^5495+5495^29158	109050	Hans Havermann	11/2020
7747	(78557*2^362188+1)/189	109033	Lelio R Paula	07/2014
7748	2*7^129008+9	109025	Lelio R Paula	11/2014
7749	88*10^109022+7	109024	Robert Price	03/2020
7750	28194^7337+7337^28194	108985	Hans Havermann	10/2020

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