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 ?
7001	88^57416+87	111645	Norbert Schneider	11/2015
7002	2^370829-109693	111631	Enzo Doria	04/2014
7003	15^94906-2	111619	Lelio R Paula	11/2013
7004	25835^20904+20904^25835	111614	Hans Havermann	02/2021
7005	(2^370726+1198)/2	111600	Stefano Morozzi	09/2020
7006	27758^10479+10479^27758	111597	Hans Havermann	02/2021
7007	2^370695-4627	111591	Yves Minet	05/2019
7008	7*10^111579-87	111580	Robert Price	06/2020
7009	2^370643-37	111575	Yves Minet	01/2012
7010	(2^370655-5)/2439	111575	Lelio R Paula	03/2014
7011	2^370610-3911	111565	Yves Minet	04/2017
7012	(154*10^111549+17)/9	111551	Robert Price	06/2022
7013	26200^18097+18097^26200	111550	Hans Havermann	01/2021
7014	286^45405+45405^286	111532	Norbert Schneider	04/2015
7015	4*5^159563-9	111531	Lelio R Paula	11/2014
7016	5*10^111528-21	111529	Robert Price	12/2021
7017	(4^185225+23)/3	111517	Robert Price	10/2018
7018	2^370393-2797093	111500	Enzo Doria	03/2016
7019	(21*2^370382-1)/629	111495	Lelio R Paula	03/2014
7020	(2^370371+554)/2	111493	Stefano Morozzi	09/2020
7021	6^143273-5	111489	Paul Bourdelais	01/2021
7022	2^370292-2791979	111469	Enzo Doria	03/2016
7023	(14*10^111443-11)/3	111444	Robert Price	08/2022
7024	2^370177-461551	111435	Enzo Doria	07/2015
7025	(2^370169+1706)/2	111432	Stefano Morozzi	09/2020
7026	109^54683-108	111413	Norbert Schneider	02/2017
7027	(83*10^111406-173)/9	111407	Robert Price	04/2021
7028	959^37362-37362^959	111407	Henri Lifchitz	10/2024
7029	(2^370043+1010)/2	111394	Stefano Morozzi	09/2020
7030	32961^2396+2396^32961	111392	Hans Havermann	10/2020
7031	numbpart(10^10+76282)	111391	Serge Batalov	04/2015
7032	(19*10^111385+11)/3	111386	Robert Price	07/2023
7033	(23*10^111380-29)/3	111381	Robert Price	03/2022
7034	2^369974+733	111374	Lelio R Paula	05/2013
7035	121^53470+120	111367	Norbert Schneider	10/2018
7036	2^369915-286267	111356	Enzo Doria	07/2015
7037	(62*10^111347-629)/9	111348	Robert Price	07/2021
7038	2^369855-1615	111338	Lelio R Paula	05/2017
7039	7*10^111325+3	111326	Robert Price	08/2015
7040	51^65176+2	111293	Lelio R Paula	08/2013
7041	Phi(43329,-43329)	111283	Henri Lifchitz	06/2025
7042	2^369643-1865767	111274	Enzo Doria	03/2016
7043	2^369603+885	111262	Lelio R Paula	05/2017
7044	25555^22564+22564^25555	111252	Hans Havermann	10/2020
7045	F(532391)/89441689/1425422598617	111243	Serge Batalov	07/2024
7046	L(532277)	111240	Renaud Lifchitz	03/2004
7047	105^55033-2	111233	Lelio R Paula	10/2017
7048	(35*10^111232-737)/9	111233	Robert Price	07/2018
7049	26970^13307+13307^26970	111227	Hans Havermann	10/2020
7050	25419^23716+23716^25419	111210	Hans Havermann	10/2020
7051	(26^78593-3^78593)/23	111206	Robert Price	02/2025
7052	9*10^111201-29	111202	Robert Price	09/2019
7053	2^369392+29835	111199	Lelio R Paula	05/2017
7054	3^233059+16	111198	Robert Price	03/2020
7055	2^369354-3413	111187	Yves Minet	12/2016
7056	2^369296-27	111170	Lelio R Paula	02/2013
7057	(2468^40960+1)/(2468^8192+1)	111161	Martin Hopf	08/2024
7058	2^369239-109837	111153	Enzo Doria	05/2014
7059	2^369224-291839	111148	Enzo Doria	07/2015
7060	2^369216+2798881	111146	Enzo Doria	04/2016
7061	26842^13817+13817^26842	111137	Hans Havermann	11/2020
7062	(5*10^111119-191)/3	111120	Robert Price	05/2021
7063	(29*10^111112-23)/3	111113	Robert Price	03/2022
7064	10^111111+163849	111112	Patrick De Geest	03/2017
7065	10^111111-312911	111111	Patrick De Geest	03/2017
7066	2^369092-216923	111108	Enzo Doria	05/2014
7067	2^369081-55	111105	Lelio R Paula	02/2013
7068	(2^369047+3618)/2	111094	Stefano Morozzi	09/2020
7069	88^57124-87	111077	Norbert Schneider	11/2015
7070	2^368980+753	111075	Lelio R Paula	05/2013
7071	2^368946-3623	111064	Yves Minet	03/2017
7072	2^368929+29835	111059	Lelio R Paula	05/2017
7073	4^184463-3^184463	111058	Jean-Louis Charton	12/2004
7074	111^54298+110	111057	Norbert Schneider	04/2017
7075	(4*10^111032-7)/3	111033	Ray Chandler	04/2011
7076	(29*10^111020-41)/3	111021	Tyler Busby	03/2024
7077	35799^1262+1262^35799	111015	Hans Havermann	10/2020
7078	(298*10^111004+11)/3	111006	Robert Price	11/2020
7079	27648^10349+10349^27648	111004	Hans Havermann	11/2020
7080	28899^6932+6932^28899	110997	Hans Havermann	11/2020
7081	(749^38809+1)/(749^197+1)	110990	Martin Hopf	11/2023
7082	2^368641-460303	110972	Enzo Doria	06/2015
7083	2^368619-109087	110966	Enzo Doria	04/2014
7084	(74*10^110961+313)/9	110962	Robert Price	06/2019
7085	25258^24711+24711^25258	110956	Hans Havermann	11/2020
7086	(2^368539+1290)/2	110941	Stefano Morozzi	01/2021
7087	3*2^368489+7	110927	Lelio R Paula	09/2014
7088	(14*10^110922+61)/3	110923	Robert Price	12/2018
7089	97411!4-2	110913	Robert Price	07/2017
7090	(301*10^110903+23)/9	110905	Robert Price	06/2021
7091	(9179*2^368330-1)/35	110881	Lelio R Paula	05/2015
7092	25830^19619+19619^25830	110880	Hans Havermann	10/2020
7093	(34*10^110882-7)/9/13/29/1019374319	110871	Makoto Morimoto	05/2016
7094	26022^18191+18191^26022	110850	Hans Havermann	10/2020
7095	(2^368211+2250)/2	110843	Stefano Morozzi	01/2021
7096	(37*10^110813+251)/9	110814	Robert Price	09/2021
7097	2^368050-64875	110795	Lelio R Paula	05/2017
7098	2^368048+25	110794	Lelio R Paula	02/2013
7099	(2^368017+2262)/2	110784	Stefano Morozzi	02/2021
7100	69^60239-2	110771	Lelio R Paula	10/2013
7101	(23*2^367952+1)/15717	110762	Lelio R Paula	03/2014
7102	2^367924-69	110757	Lelio R Paula	02/2013
7103	(23*10^110738+61)/3	110739	Robert Price	01/2022
7104	(2^367779+3750)/2	110713	Stefano Morozzi	01/2021
7105	2^367709-109723	110692	Enzo Doria	04/2014
7106	2^367687+213413	110685	Enzo Doria	09/2023
7107	(3*2^367644-1)/107	110671	Lelio R Paula	03/2014
7108	(2^367626+3514)/2	110667	Stefano Morozzi	09/2020
7109	(1288676*34^72242-455)/33	110642	Eric Chen	03/2023
7110	379*10^110616+9	110619	Jason Yuen	01/2025
7111	(23*2^367398+1)/57963	110595	Lelio R Paula	03/2014
7112	140^51515-139	110558	Norbert Schneider	04/2019
7113	2^367215+1879223	110543	Enzo Doria	09/2016
7114	25782^19375+19375^25782	110534	Hans Havermann	10/2020
7115	26117^17058+17058^26117	110526	Hans Havermann	10/2020
7116	2^367141+41	110521	Lelio R Paula	02/2013
7117	2^367126+29835	110516	Lelio R Paula	05/2017
7118	(10^110503-1)/9+2(10^59183-1)/910^25660	110503	Makoto Morimoto	09/2020
7119	(10^110503-1)/9+2(10^65511-1)/910^22496	110503	Makoto Morimoto	09/2020
7120	(10^110503-1)/9+210^108327+210^2175	110503	Makoto Morimoto	09/2020
7121	(10^110503-1)/9+210^66251+210^44251	110503	Makoto Morimoto	09/2020
7122	(10^110503-1)/9+3(10^28813-1)/910^40845	110503	Makoto Morimoto	09/2020
7123	(10^110503-1)/9+3(10^82573-1)/910^13965	110503	Makoto Morimoto	09/2020
7124	(10^110503-1)/9+4(10^43305-1)/910^33599	110503	Makoto Morimoto	09/2020
7125	(10^110503-1)/9+510^70327+510^40175	110503	Makoto Morimoto	09/2020
7126	(10^110503-1)/9+510^99423+510^11079	110503	Makoto Morimoto	09/2020
7127	(10^110503-1)/9+7(10^23617-1)/910^43443	110503	Makoto Morimoto	09/2020
7128	(10^110503-1)/9+8(10^30251-1)/910^40126	110503	Makoto Morimoto	09/2020
7129	3(10^110503-1)/9+110^106036+1*10^4466	110503	Makoto Morimoto	09/2020
7130	3(10^110503-1)/9+110^58962+1*10^51540	110503	Makoto Morimoto	09/2020
7131	3(10^110503-1)/9+110^78213+1*10^32289	110503	Makoto Morimoto	09/2020
7132	3(10^110503-1)/9+210^76898+2*10^33604	110503	Makoto Morimoto	09/2020
7133	3(10^110503-1)/9-110^100802-1*10^9700	110503	Makoto Morimoto	09/2020
7134	3(10^110503-1)/9-110^76355-1*10^34147	110503	Makoto Morimoto	09/2020
7135	3(10^110503-1)/9-210^105704-2*10^4798	110503	Makoto Morimoto	09/2020
7136	7(10^110503-1)/9+1(10^27685-1)/9*10^41409	110503	Makoto Morimoto	09/2020
7137	7(10^110503-1)/9+1(10^91035-1)/9*10^9734	110503	Makoto Morimoto	09/2020
7138	7(10^110503-1)/9-1(10^23717-1)/9*10^43393	110503	Makoto Morimoto	09/2020
7139	7(10^110503-1)/9-110^57906-1*10^52596	110503	Makoto Morimoto	09/2020
7140	7(10^110503-1)/9-110^72287-1*10^38215	110503	Makoto Morimoto	09/2020
7141	7(10^110503-1)/9-2(10^53823-1)/9*10^28340	110503	Makoto Morimoto	09/2020
7142	7(10^110503-1)/9-2(10^88659-1)/9*10^10922	110503	Makoto Morimoto	09/2020
7143	7(10^110503-1)/9-3(10^79921-1)/9*10^15291	110503	Makoto Morimoto	09/2020
7144	7(10^110503-1)/9-310^60024-3*10^50478	110503	Makoto Morimoto	09/2020
7145	7(10^110503-1)/9-4(10^103091-1)/9*10^3706	110503	Makoto Morimoto	09/2020
7146	7(10^110503-1)/9-410^103658-4*10^6844	110503	Makoto Morimoto	09/2020
7147	7(10^110503-1)/9-410^78188-4*10^32314	110503	Makoto Morimoto	09/2020
7148	7(10^110503-1)/9-5(10^35035-1)/9*10^37734	110503	Makoto Morimoto	09/2020
7149	7(10^110503-1)/9-6(10^67347-1)/9*10^21578	110503	Makoto Morimoto	09/2020
7150	7(10^110503-1)/9-610^60391-6*10^50111	110503	Makoto Morimoto	09/2020
7151	(10^110503-1)-4(10^96247-1)/910^7128	110503	Makoto Morimoto	09/2020
7152	(10^110503-1)-410^74037-410^36465	110503	Makoto Morimoto	09/2020
7153	(10^110503-1)-410^77787-410^32715	110503	Makoto Morimoto	09/2020
7154	(10^110503-1)-410^91179-410^19323	110503	Makoto Morimoto	09/2020
7155	(10^110503-1)-5(10^99143-1)/910^5680	110503	Makoto Morimoto	09/2020
7156	(10^110503-1)-7(10^85075-1)/910^12714	110503	Makoto Morimoto	09/2020
7157	(10^110503-1)-710^100712-710^9790	110503	Makoto Morimoto	09/2020
7158	(10^110503-1)-710^76427-710^34075	110503	Makoto Morimoto	09/2020
7159	(10^110503-1)-710^90451-710^20051	110503	Makoto Morimoto	09/2020
7160	(10^110503-1)-810^106252-810^4250	110503	Makoto Morimoto	09/2020
7161	(11*10^110496+49)/3	110497	Robert Price	07/2018
7162	25447^21958+21958^25447	110481	Hans Havermann	11/2020
7163	(31*2^366976+1)/7	110472	Lelio R Paula	03/2014
7164	7*10^110468-23	110469	Robert Price	07/2019
7165	5*3^231464-2^231464	110438	Jon Grantham	08/2023
7166	2^366853+5711	110434	Lelio R Paula	05/2017
7167	(21181*2^366833+1)/3	110432	Lelio R Paula	07/2014
7168	(4^231439)%(3^231439)	110425	Henri Lifchitz	06/2025
7169	2^366816+315	110423	Lelio R Paula	05/2017
7170	(11^2667520)/(10^2667520)	110416	Henri Lifchitz	06/2025
7171	2^366775-2787037	110411	Enzo Doria	03/2016
7172	(112*10^110405-1)/3	110407	Serge Batalov	12/2014
7173	2^366751+2797553	110404	Enzo Doria	03/2016
7174	25276^23331+23331^25276	110404	Hans Havermann	10/2020
7175	2^366748+255	110403	Lelio R Paula	05/2017
7176	2^366738-2985	110400	Yves Minet	09/2014
7177	(23*2^366739+1)/74575	110396	Lelio R Paula	03/2014
7178	(2^366722+1314)/2	110395	Stefano Morozzi	02/2021
7179	2^366716+1871791	110393	Enzo Doria	05/2016
7180	(239*23^81066-349)/22	110391	Eric Chen	08/2023
7181	2^366695+1334025	110387	Henri Lifchitz	10/2024
7182	(5^528189)%F(528189)	110385	Henri Lifchitz	06/2025
7183	2^366649+1871687	110373	Enzo Doria	05/2016
7184	2^366629-351205	110367	Enzo Doria	06/2015
7185	(31*10^110363+257)/9	110364	Robert Price	12/2021
7186	(5^183291)%(4^183291)	110353	Henri Lifchitz	06/2025
7187	(17*19^86292-215)/18	110347	Eric Chen	01/2023
7189	2^366558+1874479	110345	Enzo Doria	06/2016
7188	25132^24581+24581^25132	110345	Hans Havermann	10/2020
7190	(2^366539+770)/2	110339	Stefano Morozzi	09/2020
7191	26368^15285+15285^26368	110331	Hans Havermann	10/2020
7192	(23*10^110290+19)/3	110291	Robert Price	07/2019
7193	18^87853-4409	110280	Enzo Doria	03/2013
7194	28490^7419+7419^28490	110267	Hans Havermann	11/2020
7195	2^366218-23	110243	Lelio R Paula	02/2013
7196	(21*2^366193-1)/197	110235	Lelio R Paula	03/2014
7197	2^366178-343991	110231	Enzo Doria	07/2015
7198	12^102123-11	110210	Riley Fisher	09/2023
7199	(725*35^71368+16649)/34	110199	Eric Chen	05/2025
7200	25777^18798+18798^25777	110174	Hans Havermann	10/2020
7201	2^365944+1871341	110161	Enzo Doria	05/2016
7202	2^365838-461267	110129	Enzo Doria	07/2015
7203	30152^4491+4491^30152	110126	Hans Havermann	11/2020
7204	2^365802+23359	110118	Enzo Doria	10/2023
7205	10^110111+464019	110112	Patrick De Geest	05/2021
7206	10^110111-40001	110111	Robert Price	01/2021
7207	2^365763-6555	110106	Lelio R Paula	04/2017
7208	(2^365689+2^182845+1)/5	110083		11/2006
7209	(83^57367-1)/3536509644718	110080	Paul Vanderveen	05/2025
7210	2^365666-459161	110077	Enzo Doria	05/2015
7211	3*10^110076-7	110077	Robert Price	08/2015
7212	(102936^21961-1)/102935	110076	Anonymous	09/2025
7213	13^98785-72	110041	Lelio R Paula	03/2017
7215	(25^78707+1)/26	110027	Robert Price	06/2013
7214	(7*10^110027-277)/9	110027	Robert Price	02/2022
7216	(16*10^110014-73)/3	110015	Robert Price	07/2020
7217	(7*10^110006-151)/9	110006	Robert Price	02/2018
7218	6^141361-7	110001	Lelio R Paula	11/2014
7219	10^110000+8029681	110001	Hayden Chesnut	11/2024
7220	10^110000+2044477	110001	Hayden Chesnut	11/2024
7221	10^110000+76407	110001	Hayden Chesnut	11/2024
7222	10^110000+167311	110001	Hayden Chesnut	11/2024
7223	20^84536+81	109984	Lelio R Paula	03/2017
7224	5*2^365347-9	109982	Lelio R Paula	09/2014
7225	9*6^141303+7	109957	Lelio R Paula	11/2014
7226	27635^9522+9522^27635	109953	Hans Havermann	11/2020
7227	78^58099+77	109929	Norbert Schneider	02/2015
7228	2*10^109928-7	109929	Robert Price	10/2015
7229	30580^3933+3933^30580	109927	Hans Havermann	11/2020
7230	26380^14689+14689^26380	109926	Hans Havermann	11/2020
7231	(2^365161+1130)/2	109925	Stefano Morozzi	09/2020
7232	(27*2^365137-1)/2021	109916	Lelio R Paula	03/2014
7233	29^75157-30	109910	Anonymous	09/2024
7234	(4441*29^75152-24)/7	109905	Curtis Bright	05/2015
7235	(2^365087+7)/6015	109899	Lelio R Paula	01/2014
7236	(2^365069+3774)/2	109897	Stefano Morozzi	02/2021
7237	29652^5083+5083^29652	109894	Mark Rodenkirch	10/2020
7238	(2^365049+722)/2	109891	Stefano Morozzi	09/2020
7239	(35*10^109888-89)/9	109889	Robert Price	02/2022
7240	18^87533-11	109878	Lelio R Paula	04/2017
7241	2^364982-5	109871	Henri Lifchitz	04/2006
7242	3*10^109861+59	109862	Robert Price	08/2018
7243	5*10^109860-69	109861	Robert Price	02/2021
7244	2^364936-1867979	109857	Enzo Doria	04/2016
7245	27013^11652+11652^27013	109846	Hans Havermann	10/2020
7246	2^364867-112087	109836	Enzo Doria	06/2014
7247	4^182415-85061	109825	Mike Oakes	06/2011
7248	(2^364809+1034)/2	109819	Stefano Morozzi	09/2020
7249	24972^24972-8323^8323	109814	Henri Lifchitz	10/2024
7250	(53*10^109809-287)/9	109810	Robert Price	02/2022

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Probable Primes Top 10000

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