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 (> 30000)	Who ?	When ?
4001	4^157583+22147	94875	Mike Oakes	01/2011
4002	2^315098+123	94854	Lelio R Paula	11/2012
4003	3^198791-34	94848	Robert Price	11/2013
4004	3*2^315067+7	94846	Lelio R Paula	08/2014
4005	(9*2^315057+1)/73	94841	Lelio R Paula	09/2013
4006	(16*10^94822+53)/3	94823	Robert Price	12/2016
4007	8*6^121849-7	94818	Lelio R Paula	10/2014
4008	(85*10^94802+473)/9	94803	Robert Price	03/2017
4009	2^314870-108761	94786	Enzo Doria	03/2014
4010	5*2^314841-3	94778	Lelio R Paula	08/2014
4011	6^121772+113	94758	Lelio R Paula	05/2016
4012	6^121756-16253	94745	Enzo Doria	02/2013
4013	2^314718-112793	94740	Enzo Doria	06/2014
4014	2^314697-1847293	94734	Enzo Doria	07/2015
4016	2^314548-249	94689	Yves Minet	02/2012
4015	5^135469+42	94689	Lelio R Paula	04/2016
4017	gcd(V(1137755),5F(227551)(F(227551)-1)+1)	94676	Serge Batalov	04/2015
4018	(2*10^94604+547)/9	94604	Robert Price	10/2017
4019	3*2^314152+5	94570	Lelio R Paula	08/2014
4020	2*6^121530-5	94570	Lelio R Paula	10/2014
4021	7*10^94563+87	94564	Robert Price	11/2016
4022	2^314114-109677	94558	Enzo Doria	04/2014
4023	(218389#+240867)/(311811)	94557	Makoto Morimoto	10/2017
4024	2^314059+76583	94542	Enzo Doria	05/2016
4025	2^314041-4035	94536	Lelio R Paula	03/2016
4026	(7*2^314003-11)/15	94524	Renaud Lifchitz	03/2011
4027	11^90760-4710	94517	Enzo Doria	01/2013
4028	(7*2^313926-1)/148821	94497	Lelio R Paula	02/2014
4029	94*10^94493-3	94495	Robert Price	11/2016
4030	(1000547^15749+1)/1000548	94492	Faysal YAtim	12/2008
4031	(F(375345)^2+L(375345)^2)/4	94477	Henri Lifchitz	10/2017
4032	7^111792-32	94476	Lelio R Paula	04/2016
4033	11^90680-5850	94434	Enzo Doria	01/2013
4034	2^313675-110125	94426	Enzo Doria	04/2014
4035	(2999*29^64556-2427)/4	94410	Curtis Bright	05/2015
4036	2^313609-112225	94406	Enzo Doria	06/2014
4037	2^313584+72901	94399	Enzo Doria	04/2016
4038	2^313510-112865	94376	Enzo Doria	06/2014
4039	7*10^94373+87	94374	Robert Price	11/2016
4040	(9^98897+8^98897)/17	94371	Robert Price	12/2012
4041	2^313453-114703	94359	Enzo Doria	04/2015
4042	8*10^94357-51	94358	Robert Price	10/2017
4043	(379*10^94337-1)/9	94339	Robert Price	08/2017
4044	2^313344-313344+1	94326	Robert Price	10/2014
4045	20^72481-49	94300	Lelio R Paula	05/2016
4046	44725!2+128	94289	Robert Price	03/2015
4047	4*10^94286+9	94287	Robert Price	05/2015
4048	17^76621+24	94279	Lelio R Paula	07/2016
4049	2^313156-112859	94270	Enzo Doria	06/2014
4050	6^121130-59	94258	Lelio R Paula	05/2016
4051	3^197542+28	94252	Robert Price	11/2013
4052	(3^197521+2)/51655	94237	Lelio R Paula	04/2013
4053	2^313045-5955	94236	Lelio R Paula	03/2016
4054	(67*10^94212+23)/9	94213	Ray Chandler	02/2011
4055	2^312909-1865203	94195	Enzo Doria	03/2016
4056	2^312848-149	94177	Lelio R Paula	11/2012
4057	4^156403-77597	94164	Mike Oakes	04/2011
4058	18^75004-85	94151	Lelio R Paula	06/2016
4059	19^73622-48	94145	Lelio R Paula	06/2016
4060	(11^90397-3^90397)/8	94138	Robert Price	04/2011
4061	(3^197287+5)/16	94129	Lelio R Paula	04/2013
4062	12^87212-37	94118	Lelio R Paula	06/2016
4063	11^90376+76	94117	Lelio R Paula	05/2016
4064	(6^120946-11)/5	94114	Paul Bourdelais	11/2011
4065	(10^94096+191)/3	94096	Robert Price	11/2017
4066	2^312562-112685	94091	Enzo Doria	06/2014
4067	137^44026-2	94072	Lelio R Paula	10/2017
4068	2^312404-869688105	94043	Lelio R Paula	09/2016
4069	2^312387+2793533	94038	Enzo Doria	03/2016
4071	10^94016+91	94017	Robert Price	04/2011
4070	(15*2^312325-1)/7201	94017	Lelio R Paula	02/2014
4073	10^94016-188963	94016	Patrick De Geest	08/2013
4072	(17*2^312315-1)/45	94016	Lelio R Paula	02/2014
4074	6^120802+7661	94003	Mike Oakes	04/2011
4075	(67607*2^312254+1)/177	94001	Lelio R Paula	06/2014
4076	(11*2^312207+1)/19	93984	Lelio R Paula	09/2013
4077	2^312201+51	93982	Lelio R Paula	11/2012
4078	(4*6^120749+1)/5	93961	Serge Batalov	10/2014
4079	3^196892+58	93942	Lelio R Paula	05/2016
4080	2^312060+18915	93940	Lelio R Paula	03/2016
4081	42^57867-41	93933	Norbert Schneider	08/2018
4082	2^311992-16209	93919	Enzo Doria	04/2013
4083	(85^48677+1)/86	93917	Paul Bourdelais	08/2017
4084	2^311965-39	93911	Lelio R Paula	11/2012
4085	2^311920-111689	93898	Enzo Doria	05/2014
4086	7*10^93887-47	93888	Robert Price	02/2017
4087	12^86965-13	93851	Lelio R Paula	06/2016
4088	2^311705+16095	93833	Lelio R Paula	03/2016
4089	2^311665-81	93821	Lelio R Paula	11/2012
4090	730^32761+32761^730	93806	Norbert Schneider	09/2017
4091	11^90073+92	93802	Lelio R Paula	05/2016
4092	6*10^93792+41	93793	Robert Price	01/2017
4093	(2^311580+7)/591329	93790	Lelio R Paula	06/2013
4094	12^86900-77	93781	Lelio R Paula	06/2016
4095	2^311508-109769	93774	Enzo Doria	04/2014
4096	2^311486-1859621	93767	Enzo Doria	03/2016
4097	Phi(93811,10)/968129521/2109997013/3280113810431/639637782545831	93765	Kurt Beschorner	04/2015
4098	(10^93811-1)/(996812952121099970133280113810431639637782545831)	93765	Gord Palameta	10/2018
4099	2^311471+311469	93763	Renaud Lifchitz	01/2003
4100	(88*10^93760-1)/3	93762	Robert Price	10/2017
4101	2^311426+79459	93749	Enzo Doria	06/2016
4102	2^311294+5775	93709	Lelio R Paula	03/2016
4103	2^311252-1017	93697	Lelio R Paula	03/2016
4104	2^311247-112041	93695	Enzo Doria	06/2014
4105	7*10^93692-83	93693	Robert Price	09/2017
4106	2^311205-109645	93683	Enzo Doria	04/2014
4107	5^134027-84	93681	Lelio R Paula	04/2016
4108	(2^311148-1017)/557	93663	Lelio R Paula	06/2013
4109	(2^311027-2^155514+1)/5	93628		11/2006
4110	3^196192-28	93608	Robert Price	12/2013
4111	216091#+261433	93606	Makoto Morimoto	12/2015
4112	5^133917+68	93604	Lelio R Paula	04/2016
4113	2^310924-1709	93598	Yves Minet	03/2013
4114	(266*10^93577-11)/3	93579	Robert Price	09/2016
4115	(16*10^93577+161)/3	93578	Robert Price	05/2016
4116	3^196113-56	93570	Lelio R Paula	04/2016
4117	2^310806-110345	93562	Enzo Doria	05/2014
4118	3^196093+86	93561	Lelio R Paula	04/2016
4119	2^310780-2327	93555	Yves Minet	10/2013
4120	30^63332+41	93550	Lelio R Paula	08/2012
4121	(21181*2^310707+1)/21	93536	Lelio R Paula	06/2014
4122	8*5^133807+7	93528	Lelio R Paula	10/2014
4123	2^310686+8193	93526	Lelio R Paula	03/2016
4124	2^310646+63	93514	Lelio R Paula	11/2012
4125	(77*10^93508+31)/9	93509	Robert Price	10/2015
4126	(1000907^15583+1)/1000908	93499	Faysal YAtim	04/2009
4127	(2*10^93497+7)/9	93497	Erik Branger	03/2011
4128	3^195958-112852	93496	Enzo Doria	07/2014
4129	2^310583+16385	93495	Lelio R Paula	03/2016
4130	(9913*2^310557-1)/35	93490	Lelio R Paula	04/2015
4131	9*7^110614+2	93481	Lelio R Paula	11/2014
4132	2^310469-8295	93461	Lelio R Paula	03/2016
4133	2^310459-1159	93458	Yves Minet	11/2012
4134	6^120075-95	93437	Lelio R Paula	05/2016
4135	2^310289+98327	93407	Yves Minet	11/2010
4136	2^310217-113143	93385	Enzo Doria	07/2014
4137	7^110494-68	93379	Lelio R Paula	04/2016
4138	2^310184-113093	93375	Enzo Doria	07/2014
4139	2^310180-110417	93374	Enzo Doria	05/2014
4140	gcd(V(1124905),5F(224981)(F(224981)-1)+1)	93372	Serge Batalov	04/2015
4141	3^195669+68	93358	Lelio R Paula	04/2016
4142	10^93356+91	93357	Robert Price	04/2011
4143	10^93356-28313	93356	Patrick De Geest	08/2013
4144	(85*10^93346+23)/9	93347	Robert Price	11/2015
4145	(3^195648-5)/3158276	93342	Lelio R Paula	04/2013
4146	3^195556+8680	93304	Lelio R Paula	04/2016
4147	2^309942-109991	93302	Enzo Doria	04/2014
4148	2^309926-1867301	93298	Enzo Doria	03/2016
4149	2^309924+85951	93297	Yves Minet	03/2011
4150	2^309896-4229	93288	Yves Minet	08/2018
4151	(86*10^93263-77)/9	93264	Robert Price	05/2016
4152	6^119836-125	93251	Lelio R Paula	05/2016
4153	(77*10^93249-257)/9	93250	Robert Price	10/2017
4154	3^195430-2	93244	Theodore Burton	02/2007
4155	(13*10^93236+47)/3	93237	Robert Price	01/2017
4156	(67*10^93226-7)/3	93228	Robert Price	10/2017
4157	(86*10^93217-221)/9	93218	Robert Price	06/2017
4158	2^309637-16329	93211	Enzo Doria	04/2013
4159	(41*10^93207+49)/9	93208	Robert Price	04/2016
4160	14^81312-57	93194	Lelio R Paula	06/2016
4161	41^57783-40	93192	Theodore Burton	02/2007
4162	3*10^93179-97	93180	Robert Price	08/2017
4163	5*7^110252-4	93175	Lelio R Paula	11/2014
4164	2^309380-27	93133	Lelio R Paula	11/2012
4165	23*10^93116-7	93118	Robert Price	03/2016
4166	(29*10^93082+1)/3	93083	Robert Price	11/2015
4167	(58*10^93062-13)/9	93063	Robert Price	09/2015
4168	2^309131+1869383	93058	Enzo Doria	05/2016
4169	2^309066-93	93039	Lelio R Paula	11/2012
4170	2^309063-113269	93038	Enzo Doria	07/2014
4171	3^194965+16	93022	Robert Price	10/2013
4172	2^308979+1869143	93012	Enzo Doria	05/2016
4173	5^133064+54	93008	Lelio R Paula	04/2016
4174	(2^308905-509203)/119	92988	Lelio R Paula	06/2013
4175	(94*10^92981-49)/99	92981	Ray Chandler	07/2011
4176	(2*10^92976-17)/3	92976	Robert Price	08/2014
4177	2^308809+37967	92961	Phil Moore	03/2008
4178	(3^194825+5)/11656	92952	Lelio R Paula	04/2013
4179	(2^308679+5)/1573	92919	Lelio R Paula	06/2013
4180	2^308650+513	92913	Lelio R Paula	02/2016
4181	5*7^109936+6	92908	Lelio R Paula	10/2014
4182	2*10^92897+89	92898	Robert Price	07/2016
4183	12^86073-29	92889	Lelio R Paula	06/2016
4184	2^308566-117	92888	Lelio R Paula	11/2012
4185	(17*10^92869-11)/3	92870	Robert Price	07/2015
4186	2^308459+75431	92856	Enzo Doria	04/2016
4187	2^308426-1866377	92846	Enzo Doria	03/2016
4188	(96^46831-1)/95	92830	Paul Bourdelais	09/2017
4189	2^308349-112111	92823	Enzo Doria	06/2014
4190	9*10^92821+19	92822	Robert Price	05/2016
4191	2^308337-75	92819	Lelio R Paula	11/2012
4192	4*3^194508+7	92805	Lelio R Paula	08/2014
4193	22*25^66379-113	92796	Curtis Bright	05/2015
4194	11^89101-1080	92790	Enzo Doria	12/2012
4195	2^308236-1867859	92789	Enzo Doria	04/2016
4196	12^85963+25	92770	Lelio R Paula	06/2016
4197	7^109750-66	92750	Lelio R Paula	04/2016
4198	9*10^92742+11	92743	Robert Kinser	01/2017
4199	(21*2^308046-1)/8857	92729	Lelio R Paula	02/2014
4200	2^307997-110655	92717	Enzo Doria	05/2014
4201	L(443609)	92709	Renaud Lifchitz	11/2003
4202	10^92691+9	92692	Robert Price	03/2011
4203	10^92691-252291	92691	Patrick De Geest	08/2013
4204	2^307879-2521	92681	Yves Minet	07/2014
4205	(2^307780-7)/19959669	92644	Lelio R Paula	06/2013
4206	14^80831+47	92643	Lelio R Paula	06/2016
4207	15^78744+92	92611	Lelio R Paula	07/2016
4208	65^51083-64	92610	Norbert Schneider	11/2014
4209	6^118996-16943	92597	Enzo Doria	02/2013
4210	(16*10^92591+41)/3	92592	Robert Price	10/2017
4211	(3^194014-7)/2	92568	Lelio R Paula	04/2013
4212	(63^51439+1)/64	92555	Paul Bourdelais	08/2017
4213	(26*10^92546-77)/3	92547	Robert Price	02/2017
4214	3^193954+340	92540	Lelio R Paula	04/2016
4215	2^307407-307407^2	92539	Henri Lifchitz	05/2005
4216	(17*10^92513-11)/3	92514	Robert Price	07/2015
4217	2^307318-4211	92512	Yves Minet	06/2011
4218	2^307280+193	92501	Lelio R Paula	11/2012
4219	20^71075-33	92471	Lelio R Paula	05/2016
4220	2^307126-78795	92455	Lelio R Paula	02/2016
4221	2^307125-49789	92454	Henri Lifchitz	08/2005
4222	2^307099+23	92447	Lelio R Paula	11/2012
4223	7*10^92414-69	92415	Robert Price	01/2017
4224	(9787*2^306975-1)/2129155	92407	Lelio R Paula	04/2015
4225	2^306915+1873373	92391	Enzo Doria	06/2016
4226	2^306908+12915	92389	Lelio R Paula	02/2016
4227	19^72244-80	92383	Lelio R Paula	06/2016
4228	2^306849+75	92371	Lelio R Paula	11/2012
4229	(397*10^92369+53)/9	92371	Robert Price	11/2017
4230	2^306813-869688105	92360	Lelio R Paula	08/2016
4231	2^306672-109059	92318	Enzo Doria	04/2014
4232	6^118604-17063	92292	Enzo Doria	02/2013
4233	(31*2^306487-1)/2291	92260	Lelio R Paula	02/2014
4234	2^306467-1835611	92256	Enzo Doria	04/2015
4235	2^306433+76427	92246	Enzo Doria	05/2016
4236	2^306430-113313	92245	Enzo Doria	07/2014
4237	(23*10^92244-59)/9	92245	Robert Price	03/2017
4238	(47*2^306398+1)/1384803	92231	Lelio R Paula	04/2015
4239	(25*10^92186+59)/3	92187	Robert Price	05/2016
4240	2^306213-286183	92180	Enzo Doria	06/2015
4241	10^92178+61	92179	Robert Price	04/2011
4242	10^92178-175509	92178	Patrick De Geest	07/2013
4243	2^306200+1185	92176	Lelio R Paula	02/2016
4244	2^306153+11	92162	Lelio R Paula	11/2012
4245	(2^306141-7)/5	92157	Lelio R Paula	06/2013
4246	(26*10^92152-23)/3	92153	Robert Price	08/2016
4247	(2*10^92152+67)/3	92152	Robert Price	04/2017
4248	410^92099+37^92099	92100	Mike Oakes	12/2010
4249	115^44684+114	92081	Norbert Schneider	07/2018
4250	(2^305867-2^152934+1)/5	92075		11/2006

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Probable Primes Top 10000

(247113 PRPs in the top)