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	2^388469-43	116941	Lelio R Paula	03/2013
7002	27417^18416+18416^27417	116939	Hans Havermann	02/2021
7003	(2^388438+1842)/2	116932	Stefano Morozzi	02/2021
7004	(7*2^388372-1)/111	116911	Lelio R Paula	04/2014
7005	(7*2^388335-1)/25	116900	Lelio R Paula	04/2014
7006	2^388180+93	116854	Donovan Johnson	07/2008
7007	(2^388167+2510)/2	116850	Stefano Morozzi	09/2020
7008	(85*10^116842+293)/9	116843	Robert Price	12/2019
7009	35296^2043+2043^35296	116840	Hans Havermann	02/2021
7010	(2^388081+7)/1179	116821	Lelio R Paula	03/2014
7011	38633^1056+1056^38633	116814	Hans Havermann	02/2021
7012	2^387946-113261	116784	Enzo Doria	07/2014
7013	28*36^75009+305	116739	Eric Chen	12/2022
7014	28363^13056+13056^28363	116737	Hans Havermann	02/2021
7015	2^387745+75557	116723	Enzo Doria	04/2016
7016	(29*10^116719+313)/9	116720	Robert Price	04/2021
7017	29622^8699+8699^29622	116695	Hans Havermann	02/2021
7018	(206*10^116687-17)/9	116689	Robert Price	01/2020
7019	(7*10^116684+179)/3	116685	Robert Price	09/2018
7020	2^387554+71455	116666	Enzo Doria	04/2016
7021	(602*10^116647-71)/9	116649	Robert Price	12/2021
7022	3^244461-10	116638	Tyler NeSmith	09/2022
7023	(2^387447+78557)/365	116631	Lelio R Paula	12/2014
7024	(2*10^116620+43)/9	116620	Serge Batalov	11/2022
7025	(19*10^116617+287)/9/12893	116614	Alfred Reich	11/2022
7026	(145*10^116610-1)/9	116612	Serge Batalov	12/2014
7027	(25*10^116601-331)/9	116602	Robert Price	08/2018
7028	25791^26428-26428^25791	116587	Frank Doornink	03/2024
7030	(17*2^387284-1)/59	116584	Lelio R Paula	04/2014
7029	(2^387284+3726)/2	116584	Stefano Morozzi	09/2020
7031	2^387211+111546435	116563	Paul Bourdelais	10/2021
7032	10^116557+987654321	116558	Robert Price	12/2019
7033	10^116557+9141	116558	Patrick De Geest	02/2020
7034	10^116557-609431	116557	Patrick De Geest	02/2020
7035	209^50234-50234^209	116551	Norman Luhn	09/2024
7036	(28*10^116546+41)/3	116547	Robert Price	07/2021
7037	(2^387123+1814)/2	116536	Stefano Morozzi	02/2021
7038	(2^387076+2046)/2	116522	Stefano Morozzi	09/2020
7039	(2^387073+2570)/2	116521	Stefano Morozzi	09/2020
7040	(7*10^116514-1)/3	116515	Robert Price	08/2022
7041	(26*32^77406-390071011)/31	116508	Eric Chen	11/2023
7042	28846^10931+10931^28846	116500	Hans Havermann	02/2021
7043	10^116496+3593037	116497	Paul Bourdelais	10/2021
7044	272^47851-47851^272	116497	Norman Luhn	09/2024
7045	(31*2^386968+1)/7	116490	Lelio R Paula	03/2014
7046	(944^39157+1)/945	116489	Jinyuan Wang	12/2024
7047	998^38840+997	116487	Alfred Reich	03/2026
7048	2^386947+1869143	116483	Enzo Doria	05/2016
7050	(30^78857-1)/29	116480	Robert Price	12/2011
7049	Phi(78857,5#)	116480	Henri Lifchitz	12/2025
7051	(2^386903-3)/5	116469	Lelio R Paula	03/2014
7052	28107^13892+13892^28107	116441	Hans Havermann	02/2021
7053	29110^9957+9957^29110	116386	Hans Havermann	02/2021
7054	26469^24838+24838^26469	116335	Hans Havermann	01/2021
7055	2^386389-1864783	116315	Enzo Doria	03/2016
7056	993^38799+992	116279	Alfred Reich	03/2026
7057	(8*32^77250-163)/31	116273	Eric Chen	11/2023
7058	(31*2^386231-1)/1711	116266	Lelio R Paula	03/2014
7059	297^47012+47012^297	116250	Norbert Schneider	07/2018
7060	(35*10^116223-341)/9	116224	Robert Price	08/2021
7061	(2^386087-5)/40959	116220	Lelio R Paula	03/2014
7062	(2^386054+714)/2	116214	Stefano Morozzi	09/2020
7063	(10^116201+7)/39623	116197	Alfred Reich	06/2021
7064	2^385969-823	116189	Yves Minet	05/2012
7065	57^66162+2	116173	Lelio R Paula	08/2013
7066	2^385854+75049	116154	Enzo Doria	04/2016
7067	(2^385832+2590)/2	116147	Stefano Morozzi	09/2020
7068	2^385775-109587	116130	Enzo Doria	04/2014
7069	(14*10^116112-101)/3	116113	Robert Price	02/2019
7070	Phi(236354,10)/24817171	116109	Makoto Kamada	08/2019
7071	3*10^116107+23	116108	Robert Price	03/2022
7072	28729^10990+10990^28729	116094	Hans Havermann	02/2021
7073	2^385622+71839	116084	Enzo Doria	04/2016
7075	2^385564+781	116067	Lelio R Paula	01/2012
7074	(2^385565+1562)/2	116067	Stefano Morozzi	09/2020
7076	(2^385563+378)/2	116066	Stefano Morozzi	02/2021
7077	(2^385557+2214)/2	116064	Stefano Morozzi	09/2020
7078	29431^8776+8776^29431	116056	Hans Havermann	01/2021
7079	(266*10^116024-17)/3	116026	Robert Price	07/2020
7080	30263^6820+6820^30263	116022	Hans Havermann	02/2021
7081	2^385410+71893	116020	Enzo Doria	04/2016
7082	38225^1084+1084^38225	116014	Hans Havermann	02/2021
7083	26548^23433+23433^26548	116011	Hans Havermann	02/2021
7084	Phi(183801,-9)	115960	Henri Lifchitz	12/2025
7085	12^107422-11	115928	Riley Fisher	12/2023
7086	(25*2^385091+1)/27	115924	Lelio R Paula	04/2014
7087	(11*10^115910-131)/3	115911	Robert Price	09/2018
7088	2^384953-111943	115883	Paul Bourdelais	02/2012
7089	43^70942-2	115882	Lelio R Paula	04/2014
7090	(94*10^115879-7)/3	115881	Robert Price	03/2020
7091	7*10^115863+3	115864	Robert Price	08/2015
7092	2^384834+93	115847	Donovan Johnson	07/2008
7093	2^384809+71297	115840	Enzo Doria	04/2016
7094	(55*10^115829+323)/9	115830	Robert Price	10/2021
7095	(7*2^384759-1)/5	115825	Lelio R Paula	04/2014
7096	31348^4951+4951^31348	115822	Hans Havermann	02/2021
7097	(793*10^115810+53)/9	115812	Robert Price	01/2022
7098	(71*10^115810-17)/9	115811	Ray Chandler	08/2011
7099	(97*10^115794-1)/3	115796	Serge Batalov	12/2014
7100	31115^5266+5266^31115	115794	Hans Havermann	02/2021
7101	2*10^115784-27	115785	Robert Price	05/2018
7102	10^115773+126739	115774	Patrick De Geest	04/2018
7104	10^115773-1000000001	115773	Robert Price	03/2018
7103	10^115773-396221	115773	Patrick De Geest	04/2018
7105	(2^384582+778)/2	115771	Stefano Morozzi	09/2020
7106	30537^6178+6178^30537	115762	Hans Havermann	01/2021
7107	2^384530+1874305	115756	Enzo Doria	06/2016
7108	(3*2^384524-1)/7631	115750	Lelio R Paula	03/2014
7109	28275^12406+12406^28275	115748	Hans Havermann	01/2021
7110	(44*10^115697-413)/9	115698	Robert Price	03/2019
7111	31408^4825+4825^31408	115692	Hans Havermann	02/2021
7112	(2^384317+1026)/2	115691	Stefano Morozzi	09/2020
7113	2^384312+81091	115690	Yves Minet	02/2010
7114	(2^384265+2150)/2	115675	Stefano Morozzi	09/2020
7115	(2^384246+2182)/2	115670	Stefano Morozzi	09/2020
7116	(4*10^115668-79)/3	115669	Robert Price	02/2018
7117	(2^384193+242)/2	115654	Stefano Morozzi	09/2020
7118	994^38584+993	115652	Alfred Reich	03/2026
7119	(266947#+1267)/(7^2*181)	115647	Makoto Morimoto	06/2019
7120	(266947#+273808)/(2109157)	115646	Makoto Morimoto	10/2017
7121	18^92125-92125^18	115642	Dylan Delgado	08/2019
7122	(25^82723+3^82723)/28	115641	Robert Price	09/2025
7123	3^242337-4042	115625	Enzo Doria	05/2014
7124	(17699*31^77516-29)/30	115608	Eric Chen	05/2024
7125	(2^383931+674)/2	115575	Stefano Morozzi	09/2020
7126	7*10^115561+79	115562	Robert Price	07/2019
7127	(2^383872+3046)/2	115557	Stefano Morozzi	09/2020
7128	(11*2^383859-13)/15	115553	Renaud Lifchitz	03/2011
7129	2^383780-3149	115530	Yves Minet	10/2014
7130	(41*10^115523-383)/9	115524	Robert Price	11/2018
7131	27316^16923+16923^27316	115506	Hans Havermann	02/2021
7132	(2^383618+618)/2	115481	Stefano Morozzi	09/2020
7133	2^383560-455	115464	Yves Minet	03/2012
7134	(2^383544+5)/3	115458	Lelio R Paula	03/2014
7135	(22*10^115454+119)/3	115455	Robert Price	04/2021
7136	89^59221-88^59221	115445	Robert Price	06/2015
7137	(7^136559-5^136559)/2	115406	Jon Grantham	08/2023
7138	2^383347+1869413	115399	Enzo Doria	05/2016
7139	(103*10^115366+17)/3	115368	Robert Price	08/2020
7140	(2^383232+750)/2	115365	Stefano Morozzi	09/2020
7141	(2^383130-7)/131793	115329	Lelio R Paula	03/2014
7142	(12^106859+1)/13	115320	Paul Bourdelais	02/2010
7143	29961^7060+7060^29961	115315	Hans Havermann	01/2021
7145	2^383039+1869509	115307	Enzo Doria	05/2016
7144	32918^3183+3183^32918	115307	Hans Havermann	01/2021
7146	(109^56597-1)/90183471012	115302	Paul Vanderveen	06/2025
7147	36964^1315+1315^36964	115288	Hans Havermann	02/2021
7148	(13*2^382968+1)/7	115286	Lelio R Paula	04/2014
7149	(22*10^115282+29)/3	115283	Robert Price	02/2021
7150	(2^382945+2046)/2	115278	Stefano Morozzi	09/2020
7151	(2^382789+3182)/2	115231	Stefano Morozzi	09/2020
7152	30416^6141+6141^30416	115224	Hans Havermann	02/2021
7153	6*10^115211+79	115212	Robert Price	09/2020
7154	(2^382722+3598)/2	115211	Stefano Morozzi	09/2020
7155	27987^13078+13078^27987	115210	Hans Havermann	02/2021
7156	(2^382699+2090)/2	115204	Stefano Morozzi	09/2020
7157	(22*10^115188-193)/9	115189	Robert Price	07/2022
7158	2^382633+73697	115185	Enzo Doria	04/2016
7159	2^382509-113593	115147	Enzo Doria	08/2014
7160	2^382502-2791721	115145	Enzo Doria	03/2016
7161	(2^382495+1274)/2	115143	Stefano Morozzi	01/2021
7162	2^382464+22741	115134	Enzo Doria	09/2023
7163	26752^20065+20065^26752	115099	Hans Havermann	02/2021
7164	(41^71363+4^71363)/45	115092	Robert Price	09/2026
7165	26383^23008+23008^26383	115080	Hans Havermann	02/2021
7166	9^120590-120590	115073	Robert Price	03/2014
7167	28203^12016+12016^28203	115062	Hans Havermann	02/2021
7168	2^382198+9	115054	Lelio R Paula	03/2013
7169	18268*31^77131+22839	115035	Eric Chen	05/2024
7170	30101^6630+6630^30101	115032	Hans Havermann	01/2021
7171	(89*10^115030-179)/9	115031	Robert Price	12/2019
7172	25554^26089-26089^25554	114987	Frank Doornink	02/2024
7173	25142^26129-26129^25142	114979	Frank Doornink	12/2023
7174	(2^381935+2774)/2	114974	Stefano Morozzi	02/2021
7175	27300^16271+16271^27300	114972	Hans Havermann	02/2021
7176	(23*10^114962+7)/3	114963	Robert Price	05/2023
7177	2^381883-59197	114959	Enzo Doria	10/2015
7178	27423^15542+15542^27423	114944	Hans Havermann	02/2021
7179	(2^381820+1626)/2	114939	Stefano Morozzi	09/2020
7181	2^381806-4481	114936	Yves Minet	07/2011
7180	2^381808-1851507	114936	Enzo Doria	08/2015
7182	(2^381792+2502)/2	114931	Stefano Morozzi	09/2020
7183	2^381774-112373	114926	Enzo Doria	06/2014
7184	26341^22980+22980^26341	114883	Hans Havermann	01/2021
7185	(79^60539-1)/61747564999146	114867	Paul Vanderveen	05/2025
7186	2^381555-109051	114860	Enzo Doria	04/2014
7187	2^381551+213683	114859	Enzo Doria	09/2023
7188	2^381546-113501	114857	Enzo Doria	08/2014
7189	(7*10^114845-19)/3	114846	Robert Price	10/2020
7190	26675^20178+20178^26675	114833	Hans Havermann	02/2021
7191	(2^381436+1182)/2	114824	Stefano Morozzi	09/2020
7192	3^240644+16	114817	Robert Price	04/2020
7193	(13^114814)%(10^114814)	114814	Henri Lifchitz	05/2025
7194	2^381360-110429	114801	Enzo Doria	05/2014
7195	(17*10^114795+79)/3	114796	Robert Price	04/2019
7196	(66^63079+1)/67	114774	Paul Bourdelais	09/2017
7197	2^381252-115079	114769	Enzo Doria	06/2015
7198	(2^381251+3186)/2	114768	Stefano Morozzi	09/2020
7199	2^381209-29323	114756	Enzo Doria	07/2015
7200	2^381207-111546435	114755	Paul Bourdelais	10/2021
7201	569^41651-568^41651	114754	Jean-Louis Charton	11/2009
7202	2^381201+1873205	114753	Enzo Doria	06/2016
7204	(85*10^114737+293)/9	114738	Robert Price	12/2019
7205	(265*10^114736+17)/3	114738	Robert Price	03/2020
7203	379*10^114735+9	114738	Jason Yuen	01/2025
7206	(2^381062+2170)/2	114711	Stefano Morozzi	09/2020
7207	2^380974-112991	114685	Enzo Doria	07/2014
7208	37097^1234+1234^37097	114679	Hans Havermann	02/2021
7209	(26*10^114658-119)/3	114659	Robert Price	07/2023
7210	88^58949-87	114626	Norbert Schneider	11/2015
7211	(2^380773+662)/2	114624	Stefano Morozzi	09/2020
7212	Phi(155285,10)/242674820198201	114610	Makoto Kamada	02/2024
7213	(10^155285-1)(10^2389-1)(10^13-1)*11111/(10^31057-1)/(10^11945-1)/(10^65-1)/242674820198201	114610	Anonymous	04/2025
7214	29913^6782+6782^29913	114608	Hans Havermann	02/2021
7215	(331*10^114605-7)/9	114607	Robert Price	04/2022
7216	2^380700+91	114603	Lelio R Paula	03/2013
7217	394^44151+393	114594	Alfred Reich	03/2026
7218	(2^380632+2578)/2	114582	Stefano Morozzi	09/2020
7219	7*10^114577+27	114578	Robert Price	11/2020
7221	10^114575+3^114576	114576	Mike Oakes	09/2010
7220	10^114575+66561	114576	Patrick De Geest	02/2017
7222	10^114575-581081	114575	Patrick De Geest	02/2017
7223	2^380587-115315	114569	Enzo Doria	06/2015
7224	31874^3927+3927^31874	114558	Hans Havermann	02/2021
7225	2^380513-216925	114546	Enzo Doria	05/2014
7226	2^380451-1840087	114528	Enzo Doria	06/2015
7227	(2^380426+1510)/2	114520	Stefano Morozzi	09/2020
7228	(15*2^380388-1)/539	114507	Lelio R Paula	04/2014
7229	2^380279-461347	114476	Enzo Doria	07/2015
7230	(331*10^114454-7)/9	114456	Robert Price	04/2022
7231	27121^16590+16590^27121	114447	Hans Havermann	01/2021
7232	25966^25555+25555^25966	114445	Hans Havermann	01/2021
7233	(611*32^76029-53)/31	114437	Eric Chen	11/2023
7234	(11*10^114400+529)/9	114401	Robert Price	09/2021
7235	2^380021+1871147	114398	Enzo Doria	05/2016
7236	2^380005+1869707	114393	Enzo Doria	05/2016
7237	2^379958-113297	114379	Enzo Doria	07/2014
7238	(2^379897+1274)/2	114361	Stefano Morozzi	01/2021
7239	2^379881-109105	114356	Enzo Doria	04/2014
7240	(21*2^379857-1)/13	114349	Lelio R Paula	03/2014
7241	(4*10^114340+83)/3	114341	Robert Price	02/2018
7242	(26*10^114317-77)/3	114318	Robert Price	11/2019
7243	(4*10^114296+149)/9	114296	Robert Price	04/2018
7244	88^58773-87	114284	Norbert Schneider	11/2015
7245	27764^13065+13065^27764	114280	Hans Havermann	01/2021
7246	(132^53891-1)/131	114278	Anonymous	06/2024
7247	2^379529-2790283	114250	Enzo Doria	03/2016
7248	2^379522+1869115	114248	Enzo Doria	05/2016
7249	(145*10^114226-1)/9	114228	Serge Batalov	12/2014
7250	2^379317-115033	114186	Enzo Doria	06/2015

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Probable Primes Top 10000

(303416 PRPs in the top)