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	961^32831-960^32831	97926	Jean-Louis Charton	02/2011
4002	2^325215+12909	97900	Lelio R Paula	07/2016
4003	7*10^97874-69	97875	Robert Price	01/2017
4005	(17^79537+5^79537)/22	97865	Robert Price	06/2013
4004	15^83212+22	97865	Lelio R Paula	08/2016
4006	2^325087-109057	97861	Enzo Doria	04/2014
4007	2^325074+1870657	97858	Enzo Doria	05/2016
4009	2^325066-2111	97855	Yves Minet	08/2013
4008	CopelandErdos(97855)	97855	Eric W. Weisstein	10/2015
4010	18^77944-89	97841	Lelio R Paula	07/2016
4011	119^47136+118	97833	Norbert Schneider	09/2018
4012	6^125720-17663	97830	Enzo Doria	02/2013
4013	2^324972-2069	97827	Yves Minet	05/2013
4014	2^324958-4691	97823	Yves Minet	05/2019
4015	2^324944-2788319	97818	Enzo Doria	03/2016
4017	4*10^97799-9	97800	Erik Branger	11/2013
4016	2^324882+577294575	97800	Lelio R Paula	09/2016
4018	2^324863-1867921	97794	Enzo Doria	04/2016
4019	6^125662-18473	97785	Enzo Doria	03/2013
4020	12^90604+11	97779	Lelio R Paula	07/2016
4021	5^139830+24	97737	Lelio R Paula	04/2016
4022	2^324612+1155	97718	Lelio R Paula	07/2016
4023	19^76404-44	97702	Lelio R Paula	07/2016
4024	2^324505-2983	97686	Yves Minet	04/2011
4025	(31*2^324496-1)/45	97683	Lelio R Paula	02/2014
4026	6^125488-17843	97649	Enzo Doria	02/2013
4027	7^115515-2	97622	Lelio R Paula	09/2013
4028	(89^50069-1)/88	97603	Paul Bourdelais	08/2017
4029	6^125418-5	97595	Lelio R Paula	11/2014
4030	2^324076+1155	97557	Lelio R Paula	07/2016
4031	(2^324074+9)/13	97555	Lelio R Paula	10/2013
4032	(55459*2^323993+1)/21	97536	Lelio R Paula	07/2014
4033	13^87557-12^87557	97534	Jean-Louis Charton	12/2008
4034	2^323946+73939	97518	Enzo Doria	04/2016
4035	2^323937+1866947	97515	Enzo Doria	03/2016
4036	6^125290-18533	97495	Enzo Doria	03/2013
4037	2^323845+101	97488	Lelio R Paula	12/2012
4038	18^77662+65	97487	Lelio R Paula	07/2016
4039	2^323772+76771	97466	Enzo Doria	05/2016
4040	2^323765-112213	97463	Enzo Doria	06/2014
4041	2^323720-6555	97450	Lelio R Paula	07/2016
4042	2^323694-1860401	97442	Enzo Doria	03/2016
4043	20^74886+3	97429	Lelio R Paula	06/2016
4045	3*10^97399+73	97400	Robert Price	04/2016
4044	7^115252-50	97400	Lelio R Paula	07/2016
4046	224737#+393581	97389	Nicolas PALAU	12/2016
4047	(26*10^97353+31)/3	97354	Robert Price	07/2016
4048	61^54517-60^54517	97331	Jean-Louis Charton	09/2005
4049	(38*10^97329+187)/9	97330	Robert Price	11/2017
4050	p(19982)#/2-1024	97293	Robert Price	09/2017
4051	6^125021-85	97286	Lelio R Paula	08/2016
4052	2^323164-47355	97283	Lelio R Paula	07/2016
4053	(3^203902+4)/36051015157	97276	Lelio R Paula	09/2013
4054	2^323054-6555	97249	Lelio R Paula	07/2016
4055	9*10^97247-29	97248	Robert Price	05/2017
4056	(31*10^97242+41)/9	97243	Robert Price	04/2015
4057	GoldenRatioPrime[97241]	97241	Eric W. Weisstein	06/2009
4058	12^90098-41	97233	Lelio R Paula	07/2016
4059	2^322928-216929	97212	Enzo Doria	05/2014
4060	(7*2^322896-1)/57	97201	Lelio R Paula	02/2014
4061	(2^322897+5)/3146107489	97193	Lelio R Paula	10/2013
4062	2^322725+75761	97150	Enzo Doria	04/2016
4063	(13*2^322686+1)/119	97138	Lelio R Paula	11/2013
4064	(41*10^97085+373)/9	97086	Robert Price	04/2017
4065	2^322413+77	97056	Lelio R Paula	12/2012
4066	2^322406+177	97054	Lelio R Paula	12/2012
4067	(14*10^97044+31)/9	97045	Robert Price	02/2015
4068	2^322302+255255	97023	Lelio R Paula	07/2016
4069	2^322196-113093	96991	Enzo Doria	07/2014
4070	2^322000-1861469	96932	Enzo Doria	03/2016
4071	2^321971-112747	96923	Enzo Doria	06/2014
4072	11^93062-92	96915	Lelio R Paula	06/2016
4073	(11*2^321841-7)/15	96884	Renaud Lifchitz	03/2011
4074	3^203051+34	96880	Lelio R Paula	05/2016
4075	2*10^96867-51	96868	Robert Price	11/2017
4076	(64*10^96863-1)/27	96864	Serge Batalov	05/2010
4077	2^321716-2786939	96847	Enzo Doria	03/2016
4078	2^321701-113053	96842	Enzo Doria	07/2014
4079	2^321700-28635	96842	Lelio R Paula	06/2016
4080	(5*2^321691-1)/27	96838	Lelio R Paula	02/2014
4081	6^124433-124433	96828	Robert Price	01/2014
4082	2^321631+69	96821	Lelio R Paula	12/2012
4083	(13*2^321606+1)/119	96813	Lelio R Paula	11/2013
4084	(46*10^96798-1)/9	96799	Serge Batalov	10/2014
4085	(59*10^96798+31)/9	96799	Robert Price	09/2015
4086	223319#+231223	96790	Makoto Morimoto	02/2016
4087	2^321519-28635	96787	Lelio R Paula	06/2016
4088	2^321487-1867237	96778	Enzo Doria	03/2016
4089	2^321461-63	96770	Lelio R Paula	12/2012
4090	2^321439+123	96763	Lelio R Paula	12/2012
4091	2^321434+709	96762	Lelio R Paula	02/2013
4092	14^84413+89	96749	Lelio R Paula	07/2016
4093	(28*10^96743+71)/9	96744	Serge Batalov	12/2008
4094	13^86847+96	96743	Lelio R Paula	06/2016
4095	9*2^321336-7	96733	Lelio R Paula	08/2014
4096	(209*10^96722-17)/3	96724	Robert Price	05/2017
4097	2^321237-4615	96702	Yves Minet	05/2019
4098	2^321187-1159	96687	Yves Minet	11/2012
4099	2^321182-1850081	96686	Enzo Doria	08/2015
4100	2^321116-112829	96666	Enzo Doria	06/2014
4101	2^321108-109499	96664	Enzo Doria	04/2014
4102	2^321098+2793859	96661	Enzo Doria	03/2016
4103	2^321057+4097	96648	Lelio R Paula	06/2016
4104	(4435*29^66081-4)/7	96640	Curtis Bright	05/2015
4105	p(19849)#/2-64	96581	Robert Price	04/2017
4106	2^320817+189	96576	Lelio R Paula	12/2012
4107	2^320816-4685	96576	Yves Minet	05/2019
4108	(361*10^96567-163)/9	96569	Robert Price	10/2017
4109	2^320788-110327	96567	Enzo Doria	05/2014
4110	2^320764+793	96560	Lelio R Paula	02/2013
4111	(9179*2^320652-1)/221	96528	Lelio R Paula	05/2015
4112	2^320616-78795	96516	Lelio R Paula	03/2016
4113	2^320612-461939	96514	Enzo Doria	07/2015
4114	5*2^320431+7	96461	Lelio R Paula	08/2014
4115	19^75431-90	96458	Lelio R Paula	06/2016
4116	(2^320370+3)/67	96440	Lelio R Paula	10/2013
4117	2^320309+1871477	96423	Enzo Doria	05/2016
4118	tau(809^6028)	96410	Nik Lygeros / Olivier Rozier / LR team	10/2013
4119	(21*2^320252-1)/1895	96404	Lelio R Paula	02/2014
4120	2^320232-173	96400	Lelio R Paula	12/2012
4121	175^42975-2	96395	Lelio R Paula	10/2017
4122	10^96377+199911	96378	Patrick De Geest	12/2016
4123	10^96377-20001	96377	Robert Price	11/2016
4124	2^320124-2790449	96367	Enzo Doria	03/2016
4125	2^320043-108775	96343	Enzo Doria	04/2014
4126	10^96338+424939	96339	Patrick De Geest	03/2016
4127	10^96338-9281	96338	Robert Price	09/2015
4128	(3*2^320008+1)/7	96332	Lelio R Paula	09/2013
4129	2^319838+4257	96281	Lelio R Paula	03/2016
4130	2^319830-16995	96279	Lelio R Paula	03/2016
4131	6^123713+143	96268	Lelio R Paula	05/2016
4132	(28*10^96265-97)/3	96266	Robert Price	07/2016
4133	103^47825-102	96264	Norbert Schneider	10/2016
4134	2^319713-81	96244	Lelio R Paula	11/2012
4135	(55459*2^319706+1)/20167	96242	Lelio R Paula	07/2014
4136	12^89153-43	96213	Lelio R Paula	06/2016
4137	(2*10^96195-59)/3	96195	Robert Price	05/2017
4138	2^319545+147	96193	Lelio R Paula	11/2012
4139	(50^56597+1)/51	96155	Robert Price	03/2014
4140	(41*10^96137-59)/9	96138	Robert Price	10/2017
4141	2^319353-110343	96135	Enzo Doria	05/2014
4142	11^92309-42	96130	Lelio R Paula	05/2016
4143	14^83869-13^83869	96125	Jean-Louis Charton	01/2009
4144	(7*10^96112+143)/3	96113	Robert Price	04/2016
4145	2^319237+65835	96100	Lelio R Paula	03/2016
4146	2^319194-1841	96087	Yves Minet	03/2013
4147	20^73847-31	96078	Lelio R Paula	05/2016
4148	50^56543-49	96065	Norbert Schneider	09/2018
4149	2^319107-109555	96061	Enzo Doria	04/2014
4150	(3*2^319114-1)/2627	96060	Lelio R Paula	02/2014
4151	2^319098-112157	96059	Enzo Doria	06/2014
4152	15^81673+94	96055	Lelio R Paula	07/2016
4153	2^319074+1871749	96051	Enzo Doria	05/2016
4154	2^319007-112111	96031	Enzo Doria	06/2014
4155	2^318946-1421	96013	Yves Minet	01/2013
4156	2^318834-110411	95979	Enzo Doria	05/2014
4157	2^318831-1965	95978	Lelio R Paula	03/2016
4158	(5*10^95976+7)/3	95977	Erik Branger	03/2014
4159	5*3^201089-8	95945	Lelio R Paula	08/2014
4160	2^318711-139	95942	Lelio R Paula	11/2012
4161	2^318635-1167	95919	Lelio R Paula	03/2016
4162	15^81555+16	95917	Lelio R Paula	07/2016
4163	(37*10^95895+377)/9	95896	Robert Price	10/2017
4164	(22699*2^318527+1)/21	95890	Lelio R Paula	07/2014
4165	2^318496-97305	95877	Lelio R Paula	03/2016
4166	2^318466+15015	95868	Lelio R Paula	03/2016
4167	6^123187-173129	95859	Mike Oakes	04/2011
4168	2^318423-487	95855	Yves Minet	03/2012
4169	(10223*2^318350+1)/1563	95834	Lelio R Paula	07/2014
4170	45369!2+1024	95787	Robert Price	02/2015
4171	3^200758-86	95786	Lelio R Paula	05/2016
4172	(2^318271+1)/(346031404238891654090604244843)	95781	Gord Palameta	12/2018
4173	3*10^95776-59	95777	Robert Price	10/2017
4174	193^41901-2	95768	Lelio R Paula	10/2017
4175	4*10^95752-71	95753	Robert Price	11/2017
4176	((10^47850-1)10000/9+6421)10^47850+(10^47850-1)/9	95704	Hans Havermann	05/2019
4177	(509203*2^317881-1)/52805	95693	Lelio R Paula	04/2015
4178	4*10^95672+91	95673	Robert Price	11/2017
4179	(11*10^95641-113)/3	95642	Robert Price	01/2017
4180	(13*10^95588+11)/3	95589	Robert Price	05/2015
4181	Phi(191188,10)/191189	95587	Maksym Voznyy	11/2015
4182	3^200325+70	95580	Lelio R Paula	05/2016
4183	(25*10^95574-7)/9	95575	Robert Price	12/2014
4184	(2^317485-3)/21313	95569	Lelio R Paula	06/2013
4185	2^317464+31	95567	Lelio R Paula	11/2012
4186	7^113073+82	95558	Lelio R Paula	04/2016
4187	2^317251+465	95503	Lelio R Paula	03/2016
4188	19^74684+58	95503	Lelio R Paula	06/2016
4189	(2^317250-7)/339	95500	Lelio R Paula	07/2013
4190	6^122718-79	95494	Lelio R Paula	05/2016
4191	2^317141-110491	95469	Enzo Doria	05/2014
4192	2^317094+76309	95455	Enzo Doria	05/2016
4193	2^317085+95	95453	Lelio R Paula	11/2012
4194	(17*10^95451-377)/9	95452	Robert Price	11/2017
4195	2^317057-109551	95444	Enzo Doria	04/2014
4196	3^200026+28	95437	Lelio R Paula	05/2016
4197	2^317024+93	95434	Donovan Johnson	06/2008
4198	2^316999+1605	95427	Lelio R Paula	03/2016
4199	2^316995-110427	95426	Enzo Doria	05/2014
4201	2^316937+177	95408	Lelio R Paula	11/2012
4200	4*10^95407+91	95408	Robert Price	11/2017
4202	2^316908+1915	95399	Lelio R Paula	03/2016
4203	2^316894+99	95395	Lelio R Paula	11/2012
4204	6^122547+11	95361	Lelio R Paula	05/2016
4205	2^316771+82875	95358	Lelio R Paula	03/2016
4207	(23*10^95326+1)/3	95327	Serge Batalov	05/2009
4206	1*10^95326+57	95327	Robert Price	03/2011
4208	10^95326-393687	95326	Patrick De Geest	09/2013
4209	(3^199803+4)/479539	95325	Lelio R Paula	04/2013
4210	2^316654-109481	95323	Enzo Doria	04/2014
4211	8*10^95316+51	95317	Robert Price	05/2017
4212	(50^56099+43^56099)/93	95309	Serge Batalov	12/2016
4213	(23*2^316559+1)/3925	95292	Lelio R Paula	09/2013
4214	(71*10^95277-539)/9	95278	Robert Price	11/2017
4215	19^74503-56	95271	Lelio R Paula	06/2016
4216	11^91475-4380	95262	Enzo Doria	01/2013
4217	(62*10^95251-611)/9	95252	Robert Price	05/2017
4218	(2^316321-509203)/69377	95218	Lelio R Paula	06/2013
4219	(79*10^95214-43)/9	95215	Erik Branger	11/2013
4220	(9*2^316233-1)/1751	95194	Lelio R Paula	02/2014
4221	5*2^316213+9	95191	Lelio R Paula	08/2014
4222	2^316205-1848163	95188	Enzo Doria	07/2015
4223	2^316185-2787913	95182	Enzo Doria	04/2016
4224	(9787*2^316142-1)/3	95172	Lelio R Paula	04/2015
4225	2^316140-5	95168	Henri Lifchitz	02/2006
4226	(15185*2^316117-1)/3	95165	Lelio R Paula	04/2015
4227	(34*10^95153-7)/9/19/19157	95149	Makoto Morimoto	05/2016
4228	2^316069+76817	95147	Enzo Doria	05/2016
4229	(199*10^95134-7)/3	95136	Robert Price	02/2017
4230	2^316027-97305	95134	Lelio R Paula	03/2016
4231	2^316006-2798051	95128	Enzo Doria	04/2016
4232	2^315921-2797603	95102	Enzo Doria	04/2016
4233	2*10^95095+63	95096	Robert Price	10/2017
4234	2^315857+1299	95083	Lelio R Paula	03/2016
4235	14^82955-43	95078	Lelio R Paula	06/2016
4236	(2*10^95072-17)/3	95072	Robert Price	08/2014
4237	2^315727+65	95044	Lelio R Paula	11/2012
4238	2^315725+1885757	95043	Enzo Doria	03/2017
4239	1*10^94983+21	94984	Robert Price	03/2011
4240	10^94983-717	94983	Patrick De Geest	08/2013
4241	17^77187-82	94975	Lelio R Paula	07/2016
4242	3*10^94964+37	94965	Robert Price	10/2017
4243	(2^315481-1017)/20627285	94962	Lelio R Paula	06/2013
4244	2^315423-110329	94952	Enzo Doria	05/2014
4245	11^91169-7230	94943	Enzo Doria	02/2013
4246	7*10^94938+61	94939	Robert Price	02/2017
4247	2^315351+1025	94931	Lelio R Paula	03/2016
4248	2^315350-112253	94930	Enzo Doria	06/2014
4250	((1001327^(15817)+1)/1001328)	94906	Faysal YAtim	10/2010
4249	2^315268+7	94906	Lelio R Paula	10/2012

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PRP Records

Probable Primes Top 10000

(252932 PRPs in the top)