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	6^124433-124433	96828	Robert Price	01/2014
4002	2^321631+69	96821	Lelio R Paula	12/2012
4003	(13*2^321606+1)/119	96813	Lelio R Paula	11/2013
4004	(46*10^96798-1)/9	96799	Serge Batalov	10/2014
4005	(59*10^96798+31)/9	96799	Robert Price	09/2015
4006	223319#+231223	96790	Makoto Morimoto	02/2016
4007	2^321519-28635	96787	Lelio R Paula	06/2016
4008	2^321487-1867237	96778	Enzo Doria	03/2016
4009	2^321461-63	96770	Lelio R Paula	12/2012
4010	2^321439+123	96763	Lelio R Paula	12/2012
4011	2^321434+709	96762	Lelio R Paula	02/2013
4012	14^84413+89	96749	Lelio R Paula	07/2016
4013	(28*10^96743+71)/9	96744	Serge Batalov	12/2008
4014	13^86847+96	96743	Lelio R Paula	06/2016
4015	9*2^321336-7	96733	Lelio R Paula	08/2014
4016	(209*10^96722-17)/3	96724	Robert Price	05/2017
4017	2^321187-1159	96687	Yves Minet	11/2012
4018	2^321182-1850081	96686	Enzo Doria	08/2015
4019	2^321116-112829	96666	Enzo Doria	06/2014
4020	2^321108-109499	96664	Enzo Doria	04/2014
4021	2^321098+2793859	96661	Enzo Doria	03/2016
4022	2^321057+4097	96648	Lelio R Paula	06/2016
4023	(4435*29^66081-4)/7	96640	Curtis Bright	05/2015
4024	p(19849)#/2-64	96581	Robert Price	04/2017
4025	2^320817+189	96576	Lelio R Paula	12/2012
4026	(361*10^96567-163)/9	96569	Robert Price	10/2017
4027	2^320788-110327	96567	Enzo Doria	05/2014
4028	2^320764+793	96560	Lelio R Paula	02/2013
4029	(9179*2^320652-1)/221	96528	Lelio R Paula	05/2015
4030	2^320616-78795	96516	Lelio R Paula	03/2016
4031	2^320612-461939	96514	Enzo Doria	07/2015
4032	5*2^320431+7	96461	Lelio R Paula	08/2014
4033	19^75431-90	96458	Lelio R Paula	06/2016
4034	(2^320370+3)/67	96440	Lelio R Paula	10/2013
4035	2^320309+1871477	96423	Enzo Doria	05/2016
4036	tau(809^6028)	96410	Nik Lygeros / Olivier Rozier / LR team	10/2013
4037	(21*2^320252-1)/1895	96404	Lelio R Paula	02/2014
4038	2^320232-173	96400	Lelio R Paula	12/2012
4039	175^42975-2	96395	Lelio R Paula	10/2017
4040	10^96377+199911	96378	Patrick De Geest	12/2016
4041	10^96377-20001	96377	Robert Price	11/2016
4042	2^320124-2790449	96367	Enzo Doria	03/2016
4043	2^320043-108775	96343	Enzo Doria	04/2014
4044	10^96338+424939	96339	Patrick De Geest	03/2016
4045	10^96338-9281	96338	Robert Price	09/2015
4046	(3*2^320008+1)/7	96332	Lelio R Paula	09/2013
4047	2^319838+4257	96281	Lelio R Paula	03/2016
4048	2^319830-16995	96279	Lelio R Paula	03/2016
4049	6^123713+143	96268	Lelio R Paula	05/2016
4050	(28*10^96265-97)/3	96266	Robert Price	07/2016
4051	103^47825-102	96264	Norbert Schneider	10/2016
4052	2^319713-81	96244	Lelio R Paula	11/2012
4053	(55459*2^319706+1)/20167	96242	Lelio R Paula	07/2014
4054	12^89153-43	96213	Lelio R Paula	06/2016
4055	(2*10^96195-59)/3	96195	Robert Price	05/2017
4056	2^319545+147	96193	Lelio R Paula	11/2012
4057	(50^56597+1)/51	96155	Robert Price	03/2014
4058	(41*10^96137-59)/9	96138	Robert Price	10/2017
4059	2^319353-110343	96135	Enzo Doria	05/2014
4060	11^92309-42	96130	Lelio R Paula	05/2016
4061	14^83869-13^83869	96125	Jean-Louis Charton	01/2009
4062	(7*10^96112+143)/3	96113	Robert Price	04/2016
4063	2^319237+65835	96100	Lelio R Paula	03/2016
4064	2^319194-1841	96087	Yves Minet	03/2013
4065	20^73847-31	96078	Lelio R Paula	05/2016
4066	50^56543-49	96065	Norbert Schneider	09/2018
4067	2^319107-109555	96061	Enzo Doria	04/2014
4068	(3*2^319114-1)/2627	96060	Lelio R Paula	02/2014
4069	2^319098-112157	96059	Enzo Doria	06/2014
4070	15^81673+94	96055	Lelio R Paula	07/2016
4071	2^319074+1871749	96051	Enzo Doria	05/2016
4072	2^319007-112111	96031	Enzo Doria	06/2014
4073	2^318946-1421	96013	Yves Minet	01/2013
4074	2^318834-110411	95979	Enzo Doria	05/2014
4075	2^318831-1965	95978	Lelio R Paula	03/2016
4076	(5*10^95976+7)/3	95977	Erik Branger	03/2014
4077	5*3^201089-8	95945	Lelio R Paula	08/2014
4078	2^318711-139	95942	Lelio R Paula	11/2012
4079	2^318635-1167	95919	Lelio R Paula	03/2016
4080	15^81555+16	95917	Lelio R Paula	07/2016
4081	(37*10^95895+377)/9	95896	Robert Price	10/2017
4082	(22699*2^318527+1)/21	95890	Lelio R Paula	07/2014
4083	2^318496-97305	95877	Lelio R Paula	03/2016
4084	2^318466+15015	95868	Lelio R Paula	03/2016
4085	6^123187-173129	95859	Mike Oakes	04/2011
4086	2^318423-487	95855	Yves Minet	03/2012
4087	(10223*2^318350+1)/1563	95834	Lelio R Paula	07/2014
4088	45369!2+1024	95787	Robert Price	02/2015
4089	3^200758-86	95786	Lelio R Paula	05/2016
4090	(2^318271+1)/(346031404238891654090604244843)	95781	Gord Palameta	12/2018
4091	3*10^95776-59	95777	Robert Price	10/2017
4092	193^41901-2	95768	Lelio R Paula	10/2017
4093	4*10^95752-71	95753	Robert Price	11/2017
4094	(509203*2^317881-1)/52805	95693	Lelio R Paula	04/2015
4095	4*10^95672+91	95673	Robert Price	11/2017
4096	(11*10^95641-113)/3	95642	Robert Price	01/2017
4097	(13*10^95588+11)/3	95589	Robert Price	05/2015
4098	Phi(191188,10)/191189	95587	Maksym Voznyy	11/2015
4099	3^200325+70	95580	Lelio R Paula	05/2016
4100	(25*10^95574-7)/9	95575	Robert Price	12/2014
4101	(2^317485-3)/21313	95569	Lelio R Paula	06/2013
4102	2^317464+31	95567	Lelio R Paula	11/2012
4103	7^113073+82	95558	Lelio R Paula	04/2016
4104	2^317251+465	95503	Lelio R Paula	03/2016
4105	19^74684+58	95503	Lelio R Paula	06/2016
4106	(2^317250-7)/339	95500	Lelio R Paula	07/2013
4107	6^122718-79	95494	Lelio R Paula	05/2016
4108	2^317141-110491	95469	Enzo Doria	05/2014
4109	2^317094+76309	95455	Enzo Doria	05/2016
4110	2^317085+95	95453	Lelio R Paula	11/2012
4111	(17*10^95451-377)/9	95452	Robert Price	11/2017
4112	2^317057-109551	95444	Enzo Doria	04/2014
4113	3^200026+28	95437	Lelio R Paula	05/2016
4114	2^317024+93	95434	Donovan Johnson	06/2008
4115	2^316999+1605	95427	Lelio R Paula	03/2016
4116	2^316995-110427	95426	Enzo Doria	05/2014
4118	2^316937+177	95408	Lelio R Paula	11/2012
4117	4*10^95407+91	95408	Robert Price	11/2017
4119	2^316908+1915	95399	Lelio R Paula	03/2016
4120	2^316894+99	95395	Lelio R Paula	11/2012
4121	6^122547+11	95361	Lelio R Paula	05/2016
4122	2^316771+82875	95358	Lelio R Paula	03/2016
4123	(23*10^95326+1)/3	95327	Serge Batalov	05/2009
4124	1*10^95326+57	95327	Robert Price	03/2011
4125	10^95326-393687	95326	Patrick De Geest	09/2013
4126	(3^199803+4)/479539	95325	Lelio R Paula	04/2013
4127	2^316654-109481	95323	Enzo Doria	04/2014
4128	8*10^95316+51	95317	Robert Price	05/2017
4129	(50^56099+43^56099)/93	95309	Serge Batalov	12/2016
4130	(23*2^316559+1)/3925	95292	Lelio R Paula	09/2013
4131	(71*10^95277-539)/9	95278	Robert Price	11/2017
4132	19^74503-56	95271	Lelio R Paula	06/2016
4133	11^91475-4380	95262	Enzo Doria	01/2013
4134	(62*10^95251-611)/9	95252	Robert Price	05/2017
4135	(2^316321-509203)/69377	95218	Lelio R Paula	06/2013
4136	(79*10^95214-43)/9	95215	Erik Branger	11/2013
4137	(9*2^316233-1)/1751	95194	Lelio R Paula	02/2014
4138	5*2^316213+9	95191	Lelio R Paula	08/2014
4139	2^316205-1848163	95188	Enzo Doria	07/2015
4140	2^316185-2787913	95182	Enzo Doria	04/2016
4141	(9787*2^316142-1)/3	95172	Lelio R Paula	04/2015
4142	2^316140-5	95168	Henri Lifchitz	02/2006
4143	(15185*2^316117-1)/3	95165	Lelio R Paula	04/2015
4144	(34*10^95153-7)/9/19/19157	95149	Makoto Morimoto	05/2016
4145	2^316069+76817	95147	Enzo Doria	05/2016
4146	(199*10^95134-7)/3	95136	Robert Price	02/2017
4147	2^316027-97305	95134	Lelio R Paula	03/2016
4148	2^316006-2798051	95128	Enzo Doria	04/2016
4149	2^315921-2797603	95102	Enzo Doria	04/2016
4150	2*10^95095+63	95096	Robert Price	10/2017
4151	2^315857+1299	95083	Lelio R Paula	03/2016
4152	14^82955-43	95078	Lelio R Paula	06/2016
4153	(2*10^95072-17)/3	95072	Robert Price	08/2014
4154	2^315727+65	95044	Lelio R Paula	11/2012
4155	2^315725+1885757	95043	Enzo Doria	03/2017
4156	1*10^94983+21	94984	Robert Price	03/2011
4157	10^94983-717	94983	Patrick De Geest	08/2013
4158	17^77187-82	94975	Lelio R Paula	07/2016
4159	3*10^94964+37	94965	Robert Price	10/2017
4160	(2^315481-1017)/20627285	94962	Lelio R Paula	06/2013
4161	2^315423-110329	94952	Enzo Doria	05/2014
4162	11^91169-7230	94943	Enzo Doria	02/2013
4163	7*10^94938+61	94939	Robert Price	02/2017
4164	2^315351+1025	94931	Lelio R Paula	03/2016
4165	2^315350-112253	94930	Enzo Doria	06/2014
4166	((1001327^(15817)+1)/1001328)	94906	Faysal YAtim	10/2010
4168	2^315268+7	94906	Lelio R Paula	10/2012
4167	11^91133+62	94906	Lelio R Paula	05/2016
4169	30^64244+41	94897	Lelio R Paula	08/2012
4170	(151*10^94885-7)/9	94887	Robert Price	07/2017
4171	4^157583+22147	94875	Mike Oakes	01/2011
4172	2^315098+123	94854	Lelio R Paula	11/2012
4173	3^198791-34	94848	Robert Price	11/2013
4174	3*2^315067+7	94846	Lelio R Paula	08/2014
4175	(9*2^315057+1)/73	94841	Lelio R Paula	09/2013
4176	(16*10^94822+53)/3	94823	Robert Price	12/2016
4177	8*6^121849-7	94818	Lelio R Paula	10/2014
4178	(85*10^94802+473)/9	94803	Robert Price	03/2017
4179	2^314870-108761	94786	Enzo Doria	03/2014
4180	5*2^314841-3	94778	Lelio R Paula	08/2014
4181	6^121772+113	94758	Lelio R Paula	05/2016
4182	6^121756-16253	94745	Enzo Doria	02/2013
4183	2^314718-112793	94740	Enzo Doria	06/2014
4184	2^314697-1847293	94734	Enzo Doria	07/2015
4186	2^314548-249	94689	Yves Minet	02/2012
4185	5^135469+42	94689	Lelio R Paula	04/2016
4187	gcd(V(1137755),5F(227551)(F(227551)-1)+1)	94676	Serge Batalov	04/2015
4188	(2*10^94604+547)/9	94604	Robert Price	10/2017
4189	3*2^314152+5	94570	Lelio R Paula	08/2014
4190	2*6^121530-5	94570	Lelio R Paula	10/2014
4191	7*10^94563+87	94564	Robert Price	11/2016
4192	2^314114-109677	94558	Enzo Doria	04/2014
4193	(218389#+240867)/(311811)	94557	Makoto Morimoto	10/2017
4194	2^314059+76583	94542	Enzo Doria	05/2016
4195	2^314041-4035	94536	Lelio R Paula	03/2016
4196	(7*2^314003-11)/15	94524	Renaud Lifchitz	03/2011
4197	11^90760-4710	94517	Enzo Doria	01/2013
4198	(7*2^313926-1)/148821	94497	Lelio R Paula	02/2014
4199	94*10^94493-3	94495	Robert Price	11/2016
4200	(1000547^15749+1)/1000548	94492	Faysal YAtim	12/2008
4201	(F(375345)^2+L(375345)^2)/4	94477	Henri Lifchitz	10/2017
4202	7^111792-32	94476	Lelio R Paula	04/2016
4203	11^90680-5850	94434	Enzo Doria	01/2013
4204	2^313675-110125	94426	Enzo Doria	04/2014
4205	(2999*29^64556-2427)/4	94410	Curtis Bright	05/2015
4206	2^313609-112225	94406	Enzo Doria	06/2014
4207	2^313584+72901	94399	Enzo Doria	04/2016
4208	2^313510-112865	94376	Enzo Doria	06/2014
4209	7*10^94373+87	94374	Robert Price	11/2016
4210	(9^98897+8^98897)/17	94371	Robert Price	12/2012
4211	2^313453-114703	94359	Enzo Doria	04/2015
4212	8*10^94357-51	94358	Robert Price	10/2017
4213	(379*10^94337-1)/9	94339	Robert Price	08/2017
4214	2^313344-313344+1	94326	Robert Price	10/2014
4215	20^72481-49	94300	Lelio R Paula	05/2016
4216	44725!2+128	94289	Robert Price	03/2015
4217	4*10^94286+9	94287	Robert Price	05/2015
4218	17^76621+24	94279	Lelio R Paula	07/2016
4219	2^313156-112859	94270	Enzo Doria	06/2014
4220	6^121130-59	94258	Lelio R Paula	05/2016
4221	3^197542+28	94252	Robert Price	11/2013
4222	(3^197521+2)/51655	94237	Lelio R Paula	04/2013
4223	2^313045-5955	94236	Lelio R Paula	03/2016
4224	(67*10^94212+23)/9	94213	Ray Chandler	02/2011
4225	2^312909-1865203	94195	Enzo Doria	03/2016
4226	2^312848-149	94177	Lelio R Paula	11/2012
4227	4^156403-77597	94164	Mike Oakes	04/2011
4228	18^75004-85	94151	Lelio R Paula	06/2016
4229	19^73622-48	94145	Lelio R Paula	06/2016
4230	(11^90397-3^90397)/8	94138	Robert Price	04/2011
4231	(3^197287+5)/16	94129	Lelio R Paula	04/2013
4232	12^87212-37	94118	Lelio R Paula	06/2016
4233	11^90376+76	94117	Lelio R Paula	05/2016
4234	(6^120946-11)/5	94114	Paul Bourdelais	11/2011
4235	(10^94096+191)/3	94096	Robert Price	11/2017
4236	2^312562-112685	94091	Enzo Doria	06/2014
4237	137^44026-2	94072	Lelio R Paula	10/2017
4238	2^312404-869688105	94043	Lelio R Paula	09/2016
4239	2^312387+2793533	94038	Enzo Doria	03/2016
4241	10^94016+91	94017	Robert Price	04/2011
4240	(15*2^312325-1)/7201	94017	Lelio R Paula	02/2014
4243	10^94016-188963	94016	Patrick De Geest	08/2013
4242	(17*2^312315-1)/45	94016	Lelio R Paula	02/2014
4244	6^120802+7661	94003	Mike Oakes	04/2011
4245	(67607*2^312254+1)/177	94001	Lelio R Paula	06/2014
4246	(11*2^312207+1)/19	93984	Lelio R Paula	09/2013
4247	2^312201+51	93982	Lelio R Paula	11/2012
4248	(4*6^120749+1)/5	93961	Serge Batalov	10/2014
4249	3^196892+58	93942	Lelio R Paula	05/2016
4250	2^312060+18915	93940	Lelio R Paula	03/2016

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PRP Records

Probable Primes Top 10000

(252675 PRPs in the top)