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 ?
4001	(7*10^117930-79)/9	117930	Robert Price	01/2021
4002	27531^19168+19168^27531	117904	Hans Havermann	02/2021
4003	(46*10^117902+683)/9	117903	Robert Price	03/2019
4004	27670^18189+18189^27670	117869	Hans Havermann	02/2021
4005	(7*2^391521+1)/285	117858	Lelio R Paula	04/2014
4006	(56*10^117856+583)/9	117857	Robert Price	08/2021
4007	32169^4606+4606^32169	117846	Hans Havermann	02/2021
4008	(71*10^117803-143)/9	117804	Robert Price	10/2021
4009	2^391324+90901	117801	Yves Minet	02/2011
4010	2^391301-1859923	117794	Enzo Doria	03/2016
4011	2^391261-4131	117782	Yves Minet	02/2018
4012	(2^391211+554)/2	117766	Stefano Morozzi	09/2020
4013	38434^1157+1157^38434	117737	Hans Havermann	01/2021
4014	(2^391115-7)/11791	117734	Lelio R Paula	04/2014
4015	(85*10^117719+473)/9	117720	Robert Price	01/2020
4016	(2^391049+582)/2	117718	Stefano Morozzi	09/2020
4017	31083^6122+6122^31083	117709	Hans Havermann	02/2021
4018	2^390960+1880881	117691	Enzo Doria	11/2016
4019	2^390897-1860553	117672	Enzo Doria	11/2015
4020	2^390889-115003	117670	Enzo Doria	06/2015
4021	2^390779-30337	117637	Paul Bourdelais	02/2012
4022	(2^390735+378)/2	117623	Stefano Morozzi	02/2021
4023	11^112916-780	117590	Enzo Doria	12/2012
4024	27641^17916+17916^27641	117564	Hans Havermann	02/2021
4025	27906^16321+16321^27906	117561	Hans Havermann	02/2021
4026	27294^20275+20275^27294	117555	Hans Havermann	02/2021
4027	(2^390473+1002)/2	117544	Stefano Morozzi	09/2020
4028	35912^1875+1875^35912	117541	Hans Havermann	02/2021
4029	(16^97613-5^97613)/11	117537	Robert Price	07/2013
4030	(2^390438+1774)/2	117534	Stefano Morozzi	01/2021
4031	(2^390418+1722)/2	117528	Stefano Morozzi	09/2020
4032	(2^390403+654)/2	117523	Stefano Morozzi	09/2020
4033	(2^390343+2246)/2	117505	Stefano Morozzi	01/2021
4034	28043^15478+15478^28043	117493	Hans Havermann	02/2021
4035	(17*2^390272+1)/1983	117482	Lelio R Paula	04/2014
4036	37077^1474+1474^37077	117479	Hans Havermann	01/2021
4037	31^78759-30	117459	Theodore Burton	02/2007
4038	(2^390176+1222)/2	117455	Stefano Morozzi	09/2020
4039	(2^390133+1242)/2	117442	Stefano Morozzi	09/2020
4040	(2^390013+2634)/2	117406	Stefano Morozzi	09/2020
4041	3*10^117402+61	117403	Robert Price	09/2020
4042	2^389998+37	117402	Lelio R Paula	03/2013
4043	(2^389977+314)/2	117395	Stefano Morozzi	09/2020
4044	(2^389921+342)/2	117378	Stefano Morozzi	01/2021
4045	71830^43+43^71830	117333	Hans Havermann	01/2021
4046	(2^389768+1582)/2	117332	Stefano Morozzi	09/2020
4047	33802^2951+2951^33802	117292	Hans Havermann	02/2021
4048	26789^23866+23866^26789	117277	Hans Havermann	02/2021
4049	29^80192-1*80192^29	117273	Dylan Delgado	12/2019
4050	(13*10^117249+161)/3	117250	Robert Price	11/2018
4051	2^389478+43	117245	Lelio R Paula	03/2013
4052	(298*10^117229-7)/3	117231	Robert Price	06/2020
4053	(2^389416+342)/2	117226	Stefano Morozzi	01/2021
4054	(29*2^389351-1)/9	117207	Lelio R Paula	04/2014
4055	5*10^117205+23	117206	Robert Price	03/2019
4056	(2^389341-7)/3865	117200	Lelio R Paula	03/2014
4057	27272^19827+19827^27272	117195	Hans Havermann	01/2021
4058	(2^389276+2650)/2	117184	Stefano Morozzi	09/2020
4059	(844*10^117175-7)/9	117177	Robert Price	05/2021
4060	10^117142+209223	117143	Patrick De Geest	04/2018
4062	10^117142-1000000001	117142	Robert Price	03/2018
4061	10^117142-966057	117142	Patrick De Geest	04/2018
4063	10^117135+360577	117136	Patrick De Geest	07/2018
4064	10^117135-401	117135	Robert Price	01/2018
4065	26415^26488-26488^26415	117126	Norbert Schneider	05/2021
4066	4*10^117123+79	117124	Robert Price	08/2018
4067	2^389033-12797413	117111	Enzo Doria	04/2016
4068	(2^388987+2634)/2	117097	Stefano Morozzi	09/2020
4069	2^388960-109505	117089	Enzo Doria	04/2014
4070	7*10^117082-57	117083	Robert Price	06/2020
4071	(2^388928-5)/569	117077	Lelio R Paula	03/2014
4072	2^388888-1529	117067	Yves Minet	01/2013
4073	10^117059+28879	117060	Patrick De Geest	05/2016
4074	(10^117059-71)/1	117059	Serge Batalov	12/2014
4075	(2^388854+3630)/2	117057	Stefano Morozzi	09/2020
4076	(2^388842+2098)/2	117053	Stefano Morozzi	09/2020
4077	(2^388789+3150)/2	117037	Stefano Morozzi	09/2020
4078	(2^388748+378)/2	117025	Stefano Morozzi	02/2021
4079	(693^41189-1)/692	117005	Michael Stocker	05/2020
4080	(26*10^116999-503)/9	117000	Robert Price	07/2018
4081	(2^388609+1554)/2	116983	Stefano Morozzi	09/2020
4082	38496^1093+1093^38496	116975	Hans Havermann	02/2021
4083	3^245154-6256	116969	Enzo Doria	05/2014
4084	5*10^116966-43	116967	Robert Price	01/2019
4085	2^388536-113495	116961	Enzo Doria	08/2014
4086	(2^388512+382)/2	116954	Stefano Morozzi	02/2021
4087	2^388469-43	116941	Lelio R Paula	03/2013
4088	27417^18416+18416^27417	116939	Hans Havermann	02/2021
4089	(2^388438+1842)/2	116932	Stefano Morozzi	02/2021
4090	(7*2^388372-1)/111	116911	Lelio R Paula	04/2014
4091	(7*2^388335-1)/25	116900	Lelio R Paula	04/2014
4092	2^388180+93	116854	Donovan Johnson	07/2008
4093	(2^388167+2510)/2	116850	Stefano Morozzi	09/2020
4094	(85*10^116842+293)/9	116843	Robert Price	12/2019
4095	35296^2043+2043^35296	116840	Hans Havermann	02/2021
4096	(2^388081+7)/1179	116821	Lelio R Paula	03/2014
4097	38633^1056+1056^38633	116814	Hans Havermann	02/2021
4098	2^387946-113261	116784	Enzo Doria	07/2014
4099	28363^13056+13056^28363	116737	Hans Havermann	02/2021
4100	2^387745+75557	116723	Enzo Doria	04/2016
4101	(29*10^116719+313)/9	116720	Robert Price	04/2021
4102	29622^8699+8699^29622	116695	Hans Havermann	02/2021
4103	(206*10^116687-17)/9	116689	Robert Price	01/2020
4104	(7*10^116684+179)/3	116685	Robert Price	09/2018
4105	2^387554+71455	116666	Enzo Doria	04/2016
4106	(602*10^116647-71)/9	116649	Robert Price	12/2021
4107	(2^387447+78557)/365	116631	Lelio R Paula	12/2014
4108	(145*10^116610-1)/9	116612	Serge Batalov	12/2014
4109	(25*10^116601-331)/9	116602	Robert Price	08/2018
4110	(17*2^387284-1)/59	116584	Lelio R Paula	04/2014
4111	(2^387284+3726)/2	116584	Stefano Morozzi	09/2020
4112	2^387211+111546435	116563	Paul Bourdelais	10/2021
4113	10^116557+987654321	116558	Robert Price	12/2019
4114	10^116557+9141	116558	Patrick De Geest	02/2020
4115	10^116557-609431	116557	Patrick De Geest	02/2020
4116	(28*10^116546+41)/3	116547	Robert Price	07/2021
4117	(2^387123+1814)/2	116536	Stefano Morozzi	02/2021
4118	(2^387076+2046)/2	116522	Stefano Morozzi	09/2020
4119	(2^387073+2570)/2	116521	Stefano Morozzi	09/2020
4120	28846^10931+10931^28846	116500	Hans Havermann	02/2021
4121	10^116496+3593037	116497	Paul Bourdelais	10/2021
4122	(31*2^386968+1)/7	116490	Lelio R Paula	03/2014
4123	2^386947+1869143	116483	Enzo Doria	05/2016
4124	(30^78857-1)/29	116480	Robert Price	12/2011
4125	(2^386903-3)/5	116469	Lelio R Paula	03/2014
4126	28107^13892+13892^28107	116441	Hans Havermann	02/2021
4127	29110^9957+9957^29110	116386	Hans Havermann	02/2021
4128	26469^24838+24838^26469	116335	Hans Havermann	01/2021
4129	2^386389-1864783	116315	Enzo Doria	03/2016
4130	(31*2^386231-1)/1711	116266	Lelio R Paula	03/2014
4131	297^47012+47012^297	116250	Norbert Schneider	07/2018
4132	(35*10^116223-341)/9	116224	Robert Price	08/2021
4133	(2^386087-5)/40959	116220	Lelio R Paula	03/2014
4134	(2^386054+714)/2	116214	Stefano Morozzi	09/2020
4135	(10^116201+7)/39623	116197	Alfred Reich	06/2021
4136	2^385969-823	116189	Yves Minet	05/2012
4137	57^66162+2	116173	Lelio R Paula	08/2013
4138	2^385854+75049	116154	Enzo Doria	04/2016
4139	(2^385832+2590)/2	116147	Stefano Morozzi	09/2020
4140	2^385775-109587	116130	Enzo Doria	04/2014
4141	(14*10^116112-101)/3	116113	Robert Price	02/2019
4142	Phi(236354,10)/24817171	116109	Makoto Kamada	08/2019
4143	28729^10990+10990^28729	116094	Hans Havermann	02/2021
4144	2^385622+71839	116084	Enzo Doria	04/2016
4145	2^385564+781	116067	Lelio R Paula	01/2012
4146	(2^385565+1562)/2	116067	Stefano Morozzi	09/2020
4147	(2^385563+378)/2	116066	Stefano Morozzi	02/2021
4148	(2^385557+2214)/2	116064	Stefano Morozzi	09/2020
4149	29431^8776+8776^29431	116056	Hans Havermann	01/2021
4150	(266*10^116024-17)/3	116026	Robert Price	07/2020
4151	30263^6820+6820^30263	116022	Hans Havermann	02/2021
4152	2^385410+71893	116020	Enzo Doria	04/2016
4153	38225^1084+1084^38225	116014	Hans Havermann	02/2021
4154	26548^23433+23433^26548	116011	Hans Havermann	02/2021
4155	(25*2^385091+1)/27	115924	Lelio R Paula	04/2014
4156	(11*10^115910-131)/3	115911	Robert Price	09/2018
4157	2^384953-111943	115883	Paul Bourdelais	02/2012
4158	43^70942-2	115882	Lelio R Paula	04/2014
4159	(94*10^115879-7)/3	115881	Robert Price	03/2020
4160	7*10^115863+3	115864	Robert Price	08/2015
4161	2^384834+93	115847	Donovan Johnson	07/2008
4162	2^384809+71297	115840	Enzo Doria	04/2016
4163	(55*10^115829+323)/9	115830	Robert Price	10/2021
4164	(7*2^384759-1)/5	115825	Lelio R Paula	04/2014
4165	31348^4951+4951^31348	115822	Hans Havermann	02/2021
4166	(71*10^115810-17)/9	115811	Ray Chandler	08/2011
4167	(97*10^115794-1)/3	115796	Serge Batalov	12/2014
4168	31115^5266+5266^31115	115794	Hans Havermann	02/2021
4169	2*10^115784-27	115785	Robert Price	05/2018
4170	10^115773+126739	115774	Patrick De Geest	04/2018
4172	10^115773-1000000001	115773	Robert Price	03/2018
4171	10^115773-396221	115773	Patrick De Geest	04/2018
4173	(2^384582+778)/2	115771	Stefano Morozzi	09/2020
4174	30537^6178+6178^30537	115762	Hans Havermann	01/2021
4175	2^384530+1874305	115756	Enzo Doria	06/2016
4176	(3*2^384524-1)/7631	115750	Lelio R Paula	03/2014
4177	28275^12406+12406^28275	115748	Hans Havermann	01/2021
4178	(44*10^115697-413)/9	115698	Robert Price	03/2019
4179	31408^4825+4825^31408	115692	Hans Havermann	02/2021
4180	(2^384317+1026)/2	115691	Stefano Morozzi	09/2020
4181	2^384312+81091	115690	Yves Minet	02/2010
4182	(2^384265+2150)/2	115675	Stefano Morozzi	09/2020
4183	(2^384246+2182)/2	115670	Stefano Morozzi	09/2020
4184	(4*10^115668-79)/3	115669	Robert Price	02/2018
4185	(2^384193+242)/2	115654	Stefano Morozzi	09/2020
4186	(266947#+1267)/(7^2*181)	115647	Makoto Morimoto	06/2019
4187	(266947#+273808)/(2109157)	115646	Makoto Morimoto	10/2017
4188	18^92125-92125^18	115642	Dylan Delgado	08/2019
4189	3^242337-4042	115625	Enzo Doria	05/2014
4190	(2^383931+674)/2	115575	Stefano Morozzi	09/2020
4191	7*10^115561+79	115562	Robert Price	07/2019
4192	(2^383872+3046)/2	115557	Stefano Morozzi	09/2020
4193	(11*2^383859-13)/15	115553	Renaud Lifchitz	03/2011
4194	2^383780-3149	115530	Yves Minet	10/2014
4195	(41*10^115523-383)/9	115524	Robert Price	11/2018
4196	27316^16923+16923^27316	115506	Hans Havermann	02/2021
4197	(2^383618+618)/2	115481	Stefano Morozzi	09/2020
4198	2^383560-455	115464	Yves Minet	03/2012
4199	(2^383544+5)/3	115458	Lelio R Paula	03/2014
4200	(22*10^115454+119)/3	115455	Robert Price	04/2021
4201	89^59221-88^59221	115445	Robert Price	06/2015
4202	2^383347+1869413	115399	Enzo Doria	05/2016
4203	(103*10^115366+17)/3	115368	Robert Price	08/2020
4204	(2^383232+750)/2	115365	Stefano Morozzi	09/2020
4205	(2^383130-7)/131793	115329	Lelio R Paula	03/2014
4206	(12^106859+1)/13	115320	Paul Bourdelais	02/2010
4207	29961^7060+7060^29961	115315	Hans Havermann	01/2021
4209	2^383039+1869509	115307	Enzo Doria	05/2016
4208	32918^3183+3183^32918	115307	Hans Havermann	01/2021
4210	36964^1315+1315^36964	115288	Hans Havermann	02/2021
4211	(13*2^382968+1)/7	115286	Lelio R Paula	04/2014
4212	(22*10^115282+29)/3	115283	Robert Price	02/2021
4213	(2^382945+2046)/2	115278	Stefano Morozzi	09/2020
4214	(2^382789+3182)/2	115231	Stefano Morozzi	09/2020
4215	30416^6141+6141^30416	115224	Hans Havermann	02/2021
4216	6*10^115211+79	115212	Robert Price	09/2020
4217	(2^382722+3598)/2	115211	Stefano Morozzi	09/2020
4218	27987^13078+13078^27987	115210	Hans Havermann	02/2021
4219	(2^382699+2090)/2	115204	Stefano Morozzi	09/2020
4220	2^382633+73697	115185	Enzo Doria	04/2016
4221	2^382509-113593	115147	Enzo Doria	08/2014
4222	2^382502-2791721	115145	Enzo Doria	03/2016
4223	(2^382495+1274)/2	115143	Stefano Morozzi	01/2021
4224	26752^20065+20065^26752	115099	Hans Havermann	02/2021
4225	26383^23008+23008^26383	115080	Hans Havermann	02/2021
4226	9^120590-120590	115073	Robert Price	03/2014
4227	28203^12016+12016^28203	115062	Hans Havermann	02/2021
4228	2^382198+9	115054	Lelio R Paula	03/2013
4229	30101^6630+6630^30101	115032	Hans Havermann	01/2021
4230	(89*10^115030-179)/9	115031	Robert Price	12/2019
4231	(2^381935+2774)/2	114974	Stefano Morozzi	02/2021
4232	27300^16271+16271^27300	114972	Hans Havermann	02/2021
4233	2^381883-59197	114959	Enzo Doria	10/2015
4234	27423^15542+15542^27423	114944	Hans Havermann	02/2021
4235	(2^381820+1626)/2	114939	Stefano Morozzi	09/2020
4237	2^381806-4481	114936	Yves Minet	07/2011
4236	2^381808-1851507	114936	Enzo Doria	08/2015
4238	(2^381792+2502)/2	114931	Stefano Morozzi	09/2020
4239	2^381774-112373	114926	Enzo Doria	06/2014
4240	26341^22980+22980^26341	114883	Hans Havermann	01/2021
4241	2^381555-109051	114860	Enzo Doria	04/2014
4242	2^381546-113501	114857	Enzo Doria	08/2014
4243	(7*10^114845-19)/3	114846	Robert Price	10/2020
4244	26675^20178+20178^26675	114833	Hans Havermann	02/2021
4245	(2^381436+1182)/2	114824	Stefano Morozzi	09/2020
4246	3^240644+16	114817	Robert Price	04/2020
4247	2^381360-110429	114801	Enzo Doria	05/2014
4248	(17*10^114795+79)/3	114796	Robert Price	04/2019
4249	(66^63079+1)/67	114774	Paul Bourdelais	09/2017
4250	2^381252-115079	114769	Enzo Doria	06/2015

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Probable Primes Top 10000

(288949 PRPs in the top)