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	2^328497-216933	98888	Enzo Doria	05/2014
4002	2^328487+32769	98885	Lelio R Paula	08/2016
4003	3^207250-112358	98884	Enzo Doria	06/2014
4004	13^88754-90	98867	Lelio R Paula	08/2016
4005	2^328406+709	98861	Lelio R Paula	02/2013
4006	(17*2^328413-1)/16173	98860	Lelio R Paula	03/2014
4007	7^116976+76	98857	Lelio R Paula	08/2016
4008	2^328335+1155	98839	Lelio R Paula	08/2016
4010	(3*2^328311+1)/5	98832	Lelio R Paula	11/2013
4009	287^40210+40210^287	98832	Norbert Schneider	11/2014
4011	(2^328284+9)/1325	98821	Lelio R Paula	10/2013
4012	(21*2^328258+1)/2125	98814	Lelio R Paula	11/2013
4013	65^54491+48	98788	Lelio R Paula	04/2016
4014	3^207042+98	98785	Lelio R Paula	08/2016
4015	3^206977-112756	98754	Enzo Doria	07/2014
4016	7^116846-50	98747	Lelio R Paula	08/2016
4017	2^327967-28635	98728	Lelio R Paula	08/2016
4018	707^34642+34642^707	98710	Norbert Schneider	12/2017
4019	6^126850-47	98709	Lelio R Paula	08/2016
4020	8*6^126830-7	98694	Lelio R Paula	11/2014
4021	11^94770-270	98693	Enzo Doria	08/2012
4022	2^327832+43	98688	Lelio R Paula	12/2012
4023	2^327795+761	98677	Lelio R Paula	02/2013
4024	10^98669+147411	98670	Patrick De Geest	11/2016
4026	10^98669-9^(98669-1)	98669	Robert Price	05/2016
4025	10^98669-105249	98669	Patrick De Geest	11/2016
4027	2^327671-109801	98639	Enzo Doria	04/2014
4028	5^141090-14	98618	Lelio R Paula	08/2016
4029	20^75799+47	98617	Lelio R Paula	08/2016
4030	2^327515-1017	98592	Lelio R Paula	08/2016
4031	6^126692+97681	98586	Mike Oakes	04/2011
4032	2^327467-741	98578	Lelio R Paula	08/2016
4033	(2^327329+9)/19	98535	Lelio R Paula	10/2013
4034	7^116577-66	98519	Lelio R Paula	08/2016
4035	(3*2^327250+1)/7	98512	Lelio R Paula	11/2013
4036	(19*2^327192+1)/275	98494	Lelio R Paula	11/2013
4037	2^327162-66945	98486	Lelio R Paula	08/2016
4038	4*10^98472-3	98473	Erik Branger	11/2013
4039	(6883*2^327047-1)/77	98453	Lelio R Paula	05/2015
4040	(71*10^98446+1)/9	98447	Serge Batalov	11/2010
4041	13^88363+94	98432	Lelio R Paula	08/2016
4042	48^58543-47^58543	98425	Jean-Louis Charton	11/2005
4043	6^126481+41	98422	Lelio R Paula	08/2016
4044	78*10^98413-7	98415	Robert Price	05/2017
4045	7^116416+46	98383	Lelio R Paula	08/2016
4046	7^116407-24	98376	Lelio R Paula	07/2016
4047	439^37228+37228^439	98374	Norbert Schneider	08/2018
4049	2^326782-1860671	98372	Enzo Doria	03/2016
4048	17^79948+58	98372	Lelio R Paula	08/2016
4050	3^206143-98	98356	Lelio R Paula	08/2016
4051	8*5^140705+7	98350	Lelio R Paula	11/2014
4052	2^326585+11	98312	Lelio R Paula	12/2012
4053	2^326582-459161	98311	Enzo Doria	05/2015
4054	(2^326548+9)/5	98301	Lelio R Paula	10/2013
4055	2^326538+71659	98298	Enzo Doria	04/2016
4056	15^83575-58	98292	Lelio R Paula	08/2016
4057	10^98288+3	98289	Robert Price	03/2011
4058	10^98288-117017	98288	Patrick De Geest	11/2011
4059	(44*10^98284-719)/9	98285	Robert Price	12/2017
4060	2^326421-2797573	98263	Enzo Doria	04/2016
4061	2^326401+16095	98257	Lelio R Paula	07/2016
4062	7^116240-116240^7	98235	Norbert Schneider	05/2017
4063	17^79826-78	98222	Lelio R Paula	08/2016
4064	2^326268-809	98217	Yves Minet	04/2011
4065	(418*10^98199+23)/9	98201	Robert Price	08/2017
4066	12*10^98198-7	98200	Robert Price	11/2017
4067	15^83496-76	98199	Lelio R Paula	08/2016
4068	(10223*2^326179+1)/6125	98190	Lelio R Paula	07/2014
4069	9*5^140471-4	98186	Lelio R Paula	11/2014
4070	2^326069-2383	98157	Yves Minet	10/2013
4071	2^325973+1185	98128	Lelio R Paula	07/2016
4072	(25*2^325949-1)/17	98121	Lelio R Paula	02/2014
4073	2^325945-1847269	98120	Enzo Doria	07/2015
4074	8*10^98111-67	98112	Robert Price	10/2017
4075	2^325866+15	98096	Lelio R Paula	12/2012
4076	2^325765+1974305	98066	Enzo Doria	06/2016
4077	2^325733-58695	98056	Lelio R Paula	07/2016
4078	2^325717-3645	98051	Lelio R Paula	07/2016
4079	(23*2^325583-1)/21	98011	Lelio R Paula	02/2014
4080	(7*10^98007-13)/3	98008	Robert Price	06/2016
4081	2^325512-459959	97989	Enzo Doria	05/2015
4082	(3^205354-8)/17	97978	Lelio R Paula	09/2013
4083	2^325433+76817	97966	Enzo Doria	05/2016
4084	5*10^97963+81	97964	Robert Price	08/2017
4085	2^325390-109061	97953	Enzo Doria	04/2014
4086	13^87921+24	97940	Lelio R Paula	08/2016
4087	961^32831-960^32831	97926	Jean-Louis Charton	02/2011
4088	2^325215+12909	97900	Lelio R Paula	07/2016
4089	7*10^97874-69	97875	Robert Price	01/2017
4091	(17^79537+5^79537)/22	97865	Robert Price	06/2013
4090	15^83212+22	97865	Lelio R Paula	08/2016
4092	2^325087-109057	97861	Enzo Doria	04/2014
4093	2^325074+1870657	97858	Enzo Doria	05/2016
4095	2^325066-2111	97855	Yves Minet	08/2013
4094	CopelandErdos(97855)	97855	Eric W. Weisstein	10/2015
4096	18^77944-89	97841	Lelio R Paula	07/2016
4097	119^47136+118	97833	Norbert Schneider	09/2018
4098	6^125720-17663	97830	Enzo Doria	02/2013
4099	2^324972-2069	97827	Yves Minet	05/2013
4100	2^324958-4691	97823	Yves Minet	05/2019
4101	2^324944-2788319	97818	Enzo Doria	03/2016
4103	4*10^97799-9	97800	Erik Branger	11/2013
4102	2^324882+577294575	97800	Lelio R Paula	09/2016
4104	2^324863-1867921	97794	Enzo Doria	04/2016
4105	6^125662-18473	97785	Enzo Doria	03/2013
4106	12^90604+11	97779	Lelio R Paula	07/2016
4107	5^139830+24	97737	Lelio R Paula	04/2016
4108	2^324612+1155	97718	Lelio R Paula	07/2016
4109	19^76404-44	97702	Lelio R Paula	07/2016
4110	2^324505-2983	97686	Yves Minet	04/2011
4111	(144^45259+1)/145	97684	Paul Bourdelais	08/2019
4112	(31*2^324496-1)/45	97683	Lelio R Paula	02/2014
4113	6^125488-17843	97649	Enzo Doria	02/2013
4114	7^115515-2	97622	Lelio R Paula	09/2013
4115	(89^50069-1)/88	97603	Paul Bourdelais	08/2017
4116	6^125418-5	97595	Lelio R Paula	11/2014
4117	2^324076+1155	97557	Lelio R Paula	07/2016
4118	(2^324074+9)/13	97555	Lelio R Paula	10/2013
4119	(55459*2^323993+1)/21	97536	Lelio R Paula	07/2014
4120	13^87557-12^87557	97534	Jean-Louis Charton	12/2008
4121	2^323946+73939	97518	Enzo Doria	04/2016
4122	2^323937+1866947	97515	Enzo Doria	03/2016
4123	6^125290-18533	97495	Enzo Doria	03/2013
4124	2^323845+101	97488	Lelio R Paula	12/2012
4125	18^77662+65	97487	Lelio R Paula	07/2016
4126	2^323772+76771	97466	Enzo Doria	05/2016
4127	2^323765-112213	97463	Enzo Doria	06/2014
4128	2^323720-6555	97450	Lelio R Paula	07/2016
4129	2^323694-1860401	97442	Enzo Doria	03/2016
4130	20^74886+3	97429	Lelio R Paula	06/2016
4132	3*10^97399+73	97400	Robert Price	04/2016
4131	7^115252-50	97400	Lelio R Paula	07/2016
4133	224737#+393581	97389	Nicolas PALAU	12/2016
4134	(26*10^97353+31)/3	97354	Robert Price	07/2016
4135	61^54517-60^54517	97331	Jean-Louis Charton	09/2005
4136	(38*10^97329+187)/9	97330	Robert Price	11/2017
4137	p(19982)#/2-1024	97293	Robert Price	09/2017
4138	6^125021-85	97286	Lelio R Paula	08/2016
4139	2^323164-47355	97283	Lelio R Paula	07/2016
4140	(3^203902+4)/36051015157	97276	Lelio R Paula	09/2013
4141	2^323054-6555	97249	Lelio R Paula	07/2016
4142	9*10^97247-29	97248	Robert Price	05/2017
4143	(31*10^97242+41)/9	97243	Robert Price	04/2015
4144	GoldenRatioPrime[97241]	97241	Eric W. Weisstein	06/2009
4145	12^90098-41	97233	Lelio R Paula	07/2016
4146	2^322928-216929	97212	Enzo Doria	05/2014
4147	(7*2^322896-1)/57	97201	Lelio R Paula	02/2014
4148	(2^322897+5)/3146107489	97193	Lelio R Paula	10/2013
4149	2^322725+75761	97150	Enzo Doria	04/2016
4150	(13*2^322686+1)/119	97138	Lelio R Paula	11/2013
4151	(41*10^97085+373)/9	97086	Robert Price	04/2017
4152	2^322413+77	97056	Lelio R Paula	12/2012
4153	2^322406+177	97054	Lelio R Paula	12/2012
4154	(14*10^97044+31)/9	97045	Robert Price	02/2015
4155	2^322302+255255	97023	Lelio R Paula	07/2016
4156	2^322196-113093	96991	Enzo Doria	07/2014
4157	2^322000-1861469	96932	Enzo Doria	03/2016
4158	2^321971-112747	96923	Enzo Doria	06/2014
4159	11^93062-92	96915	Lelio R Paula	06/2016
4160	(11*2^321841-7)/15	96884	Renaud Lifchitz	03/2011
4161	3^203051+34	96880	Lelio R Paula	05/2016
4162	2*10^96867-51	96868	Robert Price	11/2017
4163	(64*10^96863-1)/27	96864	Serge Batalov	05/2010
4164	2^321716-2786939	96847	Enzo Doria	03/2016
4165	2^321701-113053	96842	Enzo Doria	07/2014
4166	2^321700-28635	96842	Lelio R Paula	06/2016
4167	(5*2^321691-1)/27	96838	Lelio R Paula	02/2014
4168	6^124433-124433	96828	Robert Price	01/2014
4169	2^321631+69	96821	Lelio R Paula	12/2012
4170	(13*2^321606+1)/119	96813	Lelio R Paula	11/2013
4171	(46*10^96798-1)/9	96799	Serge Batalov	10/2014
4172	(59*10^96798+31)/9	96799	Robert Price	09/2015
4173	223319#+231223	96790	Makoto Morimoto	02/2016
4174	2^321519-28635	96787	Lelio R Paula	06/2016
4175	2^321487-1867237	96778	Enzo Doria	03/2016
4176	2^321461-63	96770	Lelio R Paula	12/2012
4177	2^321439+123	96763	Lelio R Paula	12/2012
4178	2^321434+709	96762	Lelio R Paula	02/2013
4179	14^84413+89	96749	Lelio R Paula	07/2016
4180	(28*10^96743+71)/9	96744	Serge Batalov	12/2008
4181	13^86847+96	96743	Lelio R Paula	06/2016
4182	9*2^321336-7	96733	Lelio R Paula	08/2014
4183	(209*10^96722-17)/3	96724	Robert Price	05/2017
4184	2^321237-4615	96702	Yves Minet	05/2019
4185	2^321187-1159	96687	Yves Minet	11/2012
4186	2^321182-1850081	96686	Enzo Doria	08/2015
4187	2^321116-112829	96666	Enzo Doria	06/2014
4188	2^321108-109499	96664	Enzo Doria	04/2014
4189	2^321098+2793859	96661	Enzo Doria	03/2016
4190	2^321057+4097	96648	Lelio R Paula	06/2016
4191	(4435*29^66081-4)/7	96640	Curtis Bright	05/2015
4192	p(19849)#/2-64	96581	Robert Price	04/2017
4193	2^320817+189	96576	Lelio R Paula	12/2012
4194	2^320816-4685	96576	Yves Minet	05/2019
4195	(361*10^96567-163)/9	96569	Robert Price	10/2017
4196	2^320788-110327	96567	Enzo Doria	05/2014
4197	2^320764+793	96560	Lelio R Paula	02/2013
4198	(9179*2^320652-1)/221	96528	Lelio R Paula	05/2015
4199	2^320616-78795	96516	Lelio R Paula	03/2016
4200	2^320612-461939	96514	Enzo Doria	07/2015
4201	5*2^320431+7	96461	Lelio R Paula	08/2014
4202	19^75431-90	96458	Lelio R Paula	06/2016
4203	(2^320370+3)/67	96440	Lelio R Paula	10/2013
4204	2^320309+1871477	96423	Enzo Doria	05/2016
4205	tau(809^6028)	96410	Nik Lygeros / Olivier Rozier / LR team	10/2013
4206	(21*2^320252-1)/1895	96404	Lelio R Paula	02/2014
4207	2^320232-173	96400	Lelio R Paula	12/2012
4208	175^42975-2	96395	Lelio R Paula	10/2017
4209	10^96377+199911	96378	Patrick De Geest	12/2016
4210	10^96377-20001	96377	Robert Price	11/2016
4211	2^320124-2790449	96367	Enzo Doria	03/2016
4212	2^320043-108775	96343	Enzo Doria	04/2014
4213	10^96338+424939	96339	Patrick De Geest	03/2016
4214	10^96338-9281	96338	Robert Price	09/2015
4215	(3*2^320008+1)/7	96332	Lelio R Paula	09/2013
4216	2^319838+4257	96281	Lelio R Paula	03/2016
4217	2^319830-16995	96279	Lelio R Paula	03/2016
4218	6^123713+143	96268	Lelio R Paula	05/2016
4219	(28*10^96265-97)/3	96266	Robert Price	07/2016
4220	103^47825-102	96264	Norbert Schneider	10/2016
4221	2^319713-81	96244	Lelio R Paula	11/2012
4222	(55459*2^319706+1)/20167	96242	Lelio R Paula	07/2014
4223	12^89153-43	96213	Lelio R Paula	06/2016
4224	(2*10^96195-59)/3	96195	Robert Price	05/2017
4225	2^319545+147	96193	Lelio R Paula	11/2012
4226	(50^56597+1)/51	96155	Robert Price	03/2014
4227	(41*10^96137-59)/9	96138	Robert Price	10/2017
4228	2^319353-110343	96135	Enzo Doria	05/2014
4229	11^92309-42	96130	Lelio R Paula	05/2016
4230	14^83869-13^83869	96125	Jean-Louis Charton	01/2009
4231	(7*10^96112+143)/3	96113	Robert Price	04/2016
4232	2^319237+65835	96100	Lelio R Paula	03/2016
4233	2^319194-1841	96087	Yves Minet	03/2013
4234	20^73847-31	96078	Lelio R Paula	05/2016
4235	50^56543-49	96065	Norbert Schneider	09/2018
4236	2^319107-109555	96061	Enzo Doria	04/2014
4237	(3*2^319114-1)/2627	96060	Lelio R Paula	02/2014
4238	2^319098-112157	96059	Enzo Doria	06/2014
4239	15^81673+94	96055	Lelio R Paula	07/2016
4240	2^319074+1871749	96051	Enzo Doria	05/2016
4241	2^319007-112111	96031	Enzo Doria	06/2014
4242	2^318946-1421	96013	Yves Minet	01/2013
4243	2^318834-110411	95979	Enzo Doria	05/2014
4244	2^318831-1965	95978	Lelio R Paula	03/2016
4245	(5*10^95976+7)/3	95977	Erik Branger	03/2014
4246	5*3^201089-8	95945	Lelio R Paula	08/2014
4247	2^318711-139	95942	Lelio R Paula	11/2012
4248	2^318635-1167	95919	Lelio R Paula	03/2016
4249	15^81555+16	95917	Lelio R Paula	07/2016
4250	(37*10^95895+377)/9	95896	Robert Price	10/2017

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PRP Records

Probable Primes Top 10000

(253476 PRPs in the top)