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	2^344196-465	103614	Lelio R Paula	11/2016
4002	2^344187-20001	103611	Enzo Doria	06/2013
4003	(117191#+(355573#)/(117191#))/(200233679)	103602	Makoto Morimoto	10/2017
4004	20^79621-19^79621	103590	Jean-Louis Charton	03/2011
4005	Phi(155391,10)/1243129	103586	Maksym Voznyy	09/2015
4006	2^344085-20365	103580	Enzo Doria	06/2013
4007	5^148169+54	103566	Lelio R Paula	11/2016
4008	2^344017-108795	103560	Enzo Doria	03/2014
4009	(2^343974+2670)/2	103547	Stefano Morozzi	09/2020
4010	2^343971-5077	103546	Lelio R Paula	09/2011
4011	(7*10^103531+71)/3	103532	Robert Price	05/2018
4012	2^343899+141	103524	Lelio R Paula	08/2011
4013	(2^343933+1)/(3*98294339989393)	103520	Gord Palameta	08/2018
4014	6^133029-67	103517	Lelio R Paula	11/2016
4015	(17*2^343877+1)/13625	103515	Lelio R Paula	12/2013
4016	66*10^103507+7	103509	Robert Price	07/2020
4017	26297^8614+8614^26297	103485	Hans Havermann	09/2020
4018	(2^343764+2658)/2	103483	Stefano Morozzi	09/2020
4019	26499^8036+8036^26499	103480	Hans Havermann	09/2020
4020	(136*10^103474-1)/9	103476	Serge Batalov	12/2014
4021	5^148014-24	103458	Lelio R Paula	11/2016
4022	28316^4503+4503^28316	103453	Hans Havermann	09/2020
4023	(22*10^103450+53)/3	103451	Robert Price	07/2019
4024	2^343604+9931	103436	Yves Minet	01/2011
4025	2^343601-21189	103435	Enzo Doria	06/2013
4026	2^343508-115229	103407	Enzo Doria	06/2015
4027	(509203*2^343491-1)/16147	103403	Lelio R Paula	05/2015
4028	3^216685-113056	103386	Enzo Doria	07/2014
4029	24829^14580+14580^24829	103382	Hans Havermann	08/2020
4030	91355!4+1024	103381	Robert Price	09/2019
4031	44^62903-43^62903	103379	Jean-Louis Charton	08/2012
4032	11^99262-20	103371	Lelio R Paula	12/2016
4033	(509203*2^343357-1)/5	103366	Lelio R Paula	05/2015
4034	(2^343363+3570)/2	103363	Stefano Morozzi	09/2020
4036	2^343356-2791889	103361	Enzo Doria	03/2016
4035	(25*10^103360-241)/9	103361	Robert Price	05/2018
4037	Phi(104989,10)/2939693	103350	Maksym Voznyy	09/2015
4038	24826^14511+14511^24826	103319	Hans Havermann	09/2020
4039	2^343182-171	103309	Lelio R Paula	08/2011
4040	(23619^23619+23620^23620)/7187	103294	David Broadhurst	09/2009
4041	2^343079-1835611	103278	Enzo Doria	05/2015
4042	2^343063-1147	103273	Yves Minet	06/2013
4043	24741^14930+14930^24741	103271	Hans Havermann	09/2020
4044	(16*10^103255-73)/3	103256	Robert Price	07/2020
4045	9*6^132689+7	103254	Lelio R Paula	11/2014
4046	2^342979-18085	103247	Enzo Doria	05/2013
4047	(16*10^103244-31)/3	103245	Robert Price	03/2019
4048	2^342966-16995	103244	Lelio R Paula	11/2016
4049	23797^21774+21774^23797	103230	Hans Havermann	09/2020
4050	25388^11637+11637^25388	103224	Hans Havermann	09/2020
4051	(2^342876+2086)/2	103216	Stefano Morozzi	09/2020
4052	(16*10^103214-31)/3	103215	Robert Price	03/2019
4054	(37*10^103211+611)/9	103212	Robert Price	11/2018
4053	(238*10^103210-1)/3	103212	Robert Price	04/2020
4055	5^147650+16	103203	Lelio R Paula	11/2016
4056	gcd(Phi(852060,10),(10^42603+1)^3(10^42603+1-10^21302)+(10^85206+10^42603)(10^21302+1)+10^127809)	103201	Serge Batalov	04/2015
4057	2^342817+2707067	103199	Enzo Doria	03/2016
4058	43^63177-42	103198	Theodore Burton	02/2007
4059	2^342805-21025	103195	Enzo Doria	06/2013
4060	2^342714+12285	103168	Lelio R Paula	11/2016
4061	18^82178-4481	103156	Enzo Doria	03/2013
4062	2^342665-17349	103153	Enzo Doria	05/2013
4063	30408^2467+2467^30408	103150	Hans Havermann	09/2020
4064	(2^342615+3090)/2	103138	Stefano Morozzi	09/2020
4065	2^342612+175	103137	Lelio R Paula	08/2011
4066	5*2^342585-3	103130	Lelio R Paula	09/2014
4067	(16*10^103127+77)/3	103128	Robert Price	03/2019
4068	2^342503-19209	103104	Enzo Doria	05/2013
4069	(2^342484+2586)/2	103098	Stefano Morozzi	09/2020
4070	2^342476+51	103096	Lelio R Paula	08/2011
4071	2^342460-18885	103091	Enzo Doria	05/2013
4072	(194*10^103074-17)/3	103076	Robert Price	09/2020
4073	7^121968+82	103075	Lelio R Paula	10/2016
4074	2^342392-108863	103071	Enzo Doria	03/2014
4075	3^216014+28	103065	Lelio R Paula	11/2016
4076	2^342353-108879	103059	Enzo Doria	03/2014
4077	10^103055+276081	103056	Patrick De Geest	12/2016
4078	10^103055-53	103055	Lelio R Paula	11/2016
4079	(58*10^103046+419)/9	103047	Robert Price	05/2019
4080	7^121933+4	103046	Lelio R Paula	11/2014
4081	(2^342235+3618)/2	103023	Stefano Morozzi	09/2020
4082	19^80560-68	103017	Lelio R Paula	10/2016
4083	2^342209+76607	103016	Enzo Doria	05/2016
4085	328^40945+40945^328	103013	Norbert Schneider	12/2014
4084	12^95454-91	103013	Lelio R Paula	10/2016
4086	25833^9716+9716^25833	103009	Hans Havermann	01/2019
4087	65^56809-64^56809	102990	Robert Price	08/2013
4088	5^147338-6	102985	Lelio R Paula	11/2014
4089	2^342084-112739	102978	Enzo Doria	06/2014
4090	9*6^132330+7	102974	Lelio R Paula	11/2014
4091	2^342034-16737	102963	Enzo Doria	05/2013
4092	(9787*2^342011-1)/25	102959	Lelio R Paula	05/2015
4093	(3^215802-5)/124343756	102956	Lelio R Paula	12/2013
4094	2^341991-17421	102950	Enzo Doria	05/2013
4095	2^341969-112225	102943	Enzo Doria	06/2014
4096	(9787*2^341864-1)/3	102915	Lelio R Paula	05/2015
4097	2^341859+1869413	102910	Enzo Doria	05/2016
4098	10^102909+61	102910	Lelio R Paula	11/2016
4099	10^102909-67049	102909	Patrick De Geest	12/2016
4100	23814^20935+20935^23814	102898	Hans Havermann	02/2019
4101	28345^4264+4264^28345	102888	Hans Havermann	02/2019
4102	25665^10204+10204^25665	102886	Hans Havermann	02/2019
4103	26288^8181+8181^26288	102860	Hans Havermann	02/2019
4104	2^341659+1836773	102850	Enzo Doria	03/2016
4105	2^341608-110639	102835	Enzo Doria	05/2014
4106	10^102824+49	102825	Lelio R Paula	11/2016
4107	10^102824-168011	102824	Patrick De Geest	12/2016
4108	11^98708-8	102794	Lelio R Paula	10/2016
4109	2^341466+4429	102792	Lelio R Paula	09/2011
4110	2^341460-107	102790	Lelio R Paula	08/2011
4111	(2^341388+47)/21014943	102761	Lelio R Paula	12/2013
4112	2^341355+21	102759	Lelio R Paula	08/2011
4113	2^341246+40755	102726	Lelio R Paula	11/2016
4114	(2^341256-5)/991699	102723	Lelio R Paula	12/2013
4115	7^121547+78	102720	Lelio R Paula	10/2016
4116	2^341223-461197	102719	Enzo Doria	06/2015
4117	27838^4893+4893^27838	102711	Hans Havermann	03/2019
4119	2^341190-20577	102709	Enzo Doria	06/2013
4118	(27*2^341212+1)/84674449	102709	Lelio R Paula	12/2013
4120	6^131976-65	102698	Lelio R Paula	10/2016
4121	2^341134+2533	102692	Henri Lifchitz	09/2005
4122	13^92184-54	102688	Lelio R Paula	10/2016
4123	2^341116-20873	102687	Enzo Doria	06/2013
4124	2^341094-19953	102680	Enzo Doria	06/2013
4125	23761^20950+20950^23761	102676	Hans Havermann	03/2019
4126	2^341053+129	102668	Lelio R Paula	08/2011
4128	(31*2^341006-1)/3	102655	Lelio R Paula	03/2014
4127	7^121471+94	102655	Lelio R Paula	10/2016
4130	2^341004-173	102653	Lelio R Paula	08/2011
4129	20^78901+3	102653	Lelio R Paula	10/2016
4131	(2^341001+1674)/2	102652	Stefano Morozzi	09/2020
4132	5^146853-52	102646	Lelio R Paula	10/2016
4133	2^340969-216931	102642	Enzo Doria	05/2014
4134	122^49196+121	102641	Norbert Schneider	10/2018
4135	2^340952+1870021	102637	Enzo Doria	05/2016
4136	5*2^340940-3	102634	Lelio R Paula	08/2014
4137	(6^131891+1)/7	102631	Paul Bourdelais	01/2010
4138	25876^9239+9239^25876	102615	Hans Havermann	02/2019
4139	(4*10^102612+83)/3	102613	Robert Price	02/2018
4140	75^54717+74	102598	Norbert Schneider	01/2015
4141	(17*10^102597+13)/3	102598	Robert Price	01/2019
4142	2^340806-20393	102593	Enzo Doria	06/2013
4143	(2^340790+5)/138267	102583	Lelio R Paula	12/2013
4144	6^131821+77	102577	Lelio R Paula	10/2016
4145	2^340688-29	102558	Henri Lifchitz	05/2005
4146	2^340685-109101	102557	Enzo Doria	04/2014
4147	65^56567-64	102552	Norbert Schneider	11/2014
4148	26230^8121+8121^26230	102550	Hans Havermann	03/2019
4149	(8*10^102541+49)/3	102542	Robert Price	05/2020
4150	(536*10^102533-23)/9	102535	Robert Price	02/2020
4151	2^340547-108897	102515	Enzo Doria	03/2014
4152	(2^340536+778)/2	102512	Stefano Morozzi	09/2020
4153	25592^10119+10119^25592	102500	Hans Havermann	02/2019
4154	7^121268+82	102484	Lelio R Paula	10/2016
4155	(6883*2^340443-1)/162401	102483	Lelio R Paula	05/2015
4156	2^340434-5955	102481	Lelio R Paula	11/2016
4157	(2^340381+47)/7	102465	Lelio R Paula	12/2013
4158	111^50095+110	102461	Norbert Schneider	04/2017
4159	2^340291-20301	102438	Enzo Doria	06/2013
4160	12^94915+89	102431	Lelio R Paula	10/2016
4161	24466^15349+15349^24466	102417	Hans Havermann	03/2019
4162	2^340208-20373	102413	Enzo Doria	06/2013
4163	6^131598-17273	102404	Enzo Doria	02/2013
4164	(2^340132+1182)/2	102390	Stefano Morozzi	09/2020
4165	(2^340133+1166)/2	102390	Stefano Morozzi	09/2020
4166	2^340115-21181	102385	Enzo Doria	06/2013
4167	(55459*2^340090+1)/1591	102379	Lelio R Paula	07/2014
4168	(2^340064+3630)/2	102370	Stefano Morozzi	09/2020
4169	89^52511-88^52511	102365	Robert Price	06/2015
4170	3^214539-112756	102362	Enzo Doria	07/2014
4171	23159^23450-23450^23159	102353	Norbert Schneider	12/2019
4172	2^340000-19877	102351	Enzo Doria	06/2013
4173	2^339990-114845	102348	Enzo Doria	05/2015
4174	(3^214516-2)/51383	102346	Lelio R Paula	12/2013
4175	20^78661-99	102341	Lelio R Paula	09/2016
4176	2^339951-19585	102336	Enzo Doria	05/2013
4177	(13*2^339943+1)/45	102333	Lelio R Paula	12/2013
4178	(236282#+121441)/(121441*25499429)	102332	Makoto Morimoto	08/2020
4180	2^339889+29327	102317	Yves Minet	06/2010
4179	(167*10^102315-17)/3	102317	Robert Price	03/2020
4181	26348^7641+7641^26348	102314	Hans Havermann	03/2019
4182	Phi(239414,10)/6333218543	102303	Makoto Kamada	08/2019
4183	2^339834-109493	102301	Enzo Doria	04/2014
4184	(16*10^102299-19)/3	102300	Robert Price	02/2019
4185	(11^98221-5^98221)/6	102286	Robert Price	01/2013
4186	3^214365+1820	102279	Lelio R Paula	10/2016
4187	31978^1579+1579^31978	102278	Hans Havermann	03/2019
4188	(11*2^339705-1)/183	102261	Lelio R Paula	03/2014
4189	2^339694-16995	102259	Lelio R Paula	09/2016
4190	(56*10^102255+691)/9	102256	Robert Price	05/2019
4191	122^49008+121	102249	Norbert Schneider	10/2018
4192	(2^339652+3178)/2	102246	Stefano Morozzi	09/2020
4194	7^120985-38	102245	Lelio R Paula	10/2016
4193	10^102244+122961	102245	Patrick De Geest	12/2016
4195	10^102244-27	102244	Lelio R Paula	09/2016
4196	7^120982-62	102242	Lelio R Paula	10/2016
4197	(2^339640+2670)/2	102242	Stefano Morozzi	09/2020
4198	4*6^131382-5	102236	Lelio R Paula	11/2014
4199	2^339586-1091	102226	Yves Minet	11/2012
4200	11^98161-3072000	102225	Enzo Doria	12/2012
4201	9*7^120961-4	102225	Lelio R Paula	11/2014
4202	5*3^214250+2	102224	Serge Batalov	10/2010
4203	12^94713-59	102213	Lelio R Paula	10/2016
4204	12^94705+89	102204	Lelio R Paula	10/2016
4205	2^339407-177	102172	Lelio R Paula	08/2011
4206	4*10^102163-57	102164	Robert Price	10/2018
4207	2^339355+65	102157	Lelio R Paula	07/2011
4208	(28*10^102142-31)/3	102143	Robert Price	12/2019
4209	(2^339323+47)/880715	102141	Lelio R Paula	12/2013
4210	(2^339268+1758)/2	102130	Stefano Morozzi	09/2020
4211	s(178551)	102122	Robert Price	05/2020
4214	2^339168+21	102100	Lelio R Paula	07/2011
4213	2^339167-108807	102100	Enzo Doria	03/2014
4212	(2^339169+42)/2	102100	Stefano Morozzi	09/2020
4215	2^339156+163	102097	Lelio R Paula	08/2011
4216	(2^339149+746)/2	102094	Stefano Morozzi	09/2020
4217	(25*10^102076-67)/3	102077	Robert Price	06/2019
4218	2^339081-4543	102074	Yves Minet	03/2019
4219	2*10^102062+77	102063	Robert Price	08/2020
4220	24327^15668+15668^24327	102053	Hans Havermann	02/2019
4221	25080^11711+11711^25080	102041	Hans Havermann	02/2019
4222	(2^338982-7)/1754517	102038	Lelio R Paula	12/2013
4223	2^338891-18885	102017	Enzo Doria	05/2013
4224	8*10^102000+51	102001	Robert Price	08/2019
4225	(2^338832+642)/2	101999	Stefano Morozzi	09/2020
4226	2^338829-113239	101998	Enzo Doria	07/2014
4227	2^338828-113297	101998	Enzo Doria	07/2014
4228	2^338796+93	101988	Donovan Johnson	06/2008
4229	lucasU(1373,1,32502)-lucasU(1373,1,32501)	101978	Mike Oakes	05/2009
4230	25295^10744+10744^25295	101969	Hans Havermann	01/2019
4231	25712^9243+9243^25712	101969	Hans Havermann	01/2019
4232	(71^55079-1)/70	101964	Paul Bourdelais	08/2017
4233	2^338682-19865	101954	Enzo Doria	06/2013
4234	(2^(112895*3+1)+243)/7	101954	Kevin Acres	12/2013
4235	(2^338666+3154)/2	101949	Stefano Morozzi	09/2020
4236	28594^3673+3673^28594	101939	Hans Havermann	02/2019
4237	2^338568+37	101920	Lelio R Paula	07/2011
4238	2^338559-1858777	101917	Enzo Doria	04/2016
4239	(9*2^338520+1)/365	101904	Lelio R Paula	12/2013
4240	24502^14419+14419^24502	101903	Hans Havermann	01/2019
4241	2^338497-17041	101898	Enzo Doria	05/2013
4242	2^338475+54615	101892	Lelio R Paula	10/2016
4243	2^338426-19797	101877	Enzo Doria	06/2013
4244	2^338368-20369	101859	Enzo Doria	06/2013
4245	2^338366+74179	101859	Enzo Doria	04/2016
4246	27088^5755+5755^27088	101853	Hans Havermann	01/2019
4247	2^338280-19745	101833	Enzo Doria	06/2013
4248	(3*2^338236-1)/347	101818	Lelio R Paula	03/2014
4249	6^130841+103	101815	Lelio R Paula	10/2016
4250	2^338122-20117	101785	Enzo Doria	06/2013

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Probable Primes Top 10000

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