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	2^312562-112685	94091	Enzo Doria	06/2014
4002	137^44026-2	94072	Lelio R Paula	10/2017
4003	2^312404-869688105	94043	Lelio R Paula	09/2016
4004	2^312387+2793533	94038	Enzo Doria	03/2016
4006	10^94016+91	94017	Robert Price	04/2011
4005	(15*2^312325-1)/7201	94017	Lelio R Paula	02/2014
4007	10^94016-188963	94016	Patrick De Geest	08/2013
4008	(17*2^312315-1)/45	94016	Lelio R Paula	02/2014
4009	6^120802+7661	94003	Mike Oakes	04/2011
4010	(67607*2^312254+1)/177	94001	Lelio R Paula	06/2014
4011	(11*2^312207+1)/19	93984	Lelio R Paula	09/2013
4012	2^312201+51	93982	Lelio R Paula	11/2012
4013	(4*6^120749+1)/5	93961	Serge Batalov	10/2014
4014	3^196892+58	93942	Lelio R Paula	05/2016
4015	2^312060+18915	93940	Lelio R Paula	03/2016
4016	42^57867-41	93933	Norbert Schneider	08/2018
4017	2^311992-16209	93919	Enzo Doria	04/2013
4018	(85^48677+1)/86	93917	Paul Bourdelais	08/2017
4019	2^311965-39	93911	Lelio R Paula	11/2012
4020	2^311920-111689	93898	Enzo Doria	05/2014
4021	7*10^93887-47	93888	Robert Price	02/2017
4022	12^86965-13	93851	Lelio R Paula	06/2016
4023	2^311705+16095	93833	Lelio R Paula	03/2016
4024	2^311665-81	93821	Lelio R Paula	11/2012
4025	730^32761+32761^730	93806	Norbert Schneider	09/2017
4026	11^90073+92	93802	Lelio R Paula	05/2016
4027	6*10^93792+41	93793	Robert Price	01/2017
4028	(2^311580+7)/591329	93790	Lelio R Paula	06/2013
4029	12^86900-77	93781	Lelio R Paula	06/2016
4030	2^311508-109769	93774	Enzo Doria	04/2014
4031	2^311486-1859621	93767	Enzo Doria	03/2016
4032	Phi(93811,10)/968129521/2109997013/3280113810431/639637782545831	93765	Kurt Beschorner	04/2015
4033	(10^93811-1)/(996812952121099970133280113810431639637782545831)	93765	Gord Palameta	10/2018
4034	2^311471+311469	93763	Renaud Lifchitz	01/2003
4035	(88*10^93760-1)/3	93762	Robert Price	10/2017
4036	2^311426+79459	93749	Enzo Doria	06/2016
4037	2^311294+5775	93709	Lelio R Paula	03/2016
4038	2^311252-1017	93697	Lelio R Paula	03/2016
4039	2^311247-112041	93695	Enzo Doria	06/2014
4040	7*10^93692-83	93693	Robert Price	09/2017
4041	2^311205-109645	93683	Enzo Doria	04/2014
4042	5^134027-84	93681	Lelio R Paula	04/2016
4043	(2^311148-1017)/557	93663	Lelio R Paula	06/2013
4044	(2^311027-2^155514+1)/5	93628		11/2006
4045	3^196192-28	93608	Robert Price	12/2013
4046	216091#+261433	93606	Makoto Morimoto	12/2015
4047	5^133917+68	93604	Lelio R Paula	04/2016
4048	2^310924-1709	93598	Yves Minet	03/2013
4049	(266*10^93577-11)/3	93579	Robert Price	09/2016
4050	(16*10^93577+161)/3	93578	Robert Price	05/2016
4051	3^196113-56	93570	Lelio R Paula	04/2016
4052	2^310806-110345	93562	Enzo Doria	05/2014
4053	3^196093+86	93561	Lelio R Paula	04/2016
4054	2^310780-2327	93555	Yves Minet	10/2013
4055	30^63332+41	93550	Lelio R Paula	08/2012
4056	(21181*2^310707+1)/21	93536	Lelio R Paula	06/2014
4057	8*5^133807+7	93528	Lelio R Paula	10/2014
4058	2^310686+8193	93526	Lelio R Paula	03/2016
4059	2^310646+63	93514	Lelio R Paula	11/2012
4060	(77*10^93508+31)/9	93509	Robert Price	10/2015
4061	(1000907^15583+1)/1000908	93499	Faysal YAtim	04/2009
4062	(2*10^93497+7)/9	93497	Erik Branger	03/2011
4063	3^195958-112852	93496	Enzo Doria	07/2014
4064	2^310583+16385	93495	Lelio R Paula	03/2016
4065	(9913*2^310557-1)/35	93490	Lelio R Paula	04/2015
4066	9*7^110614+2	93481	Lelio R Paula	11/2014
4067	2^310469-8295	93461	Lelio R Paula	03/2016
4068	2^310459-1159	93458	Yves Minet	11/2012
4069	6^120075-95	93437	Lelio R Paula	05/2016
4070	2^310289+98327	93407	Yves Minet	11/2010
4071	2^310217-113143	93385	Enzo Doria	07/2014
4072	7^110494-68	93379	Lelio R Paula	04/2016
4073	2^310184-113093	93375	Enzo Doria	07/2014
4074	2^310180-110417	93374	Enzo Doria	05/2014
4075	gcd(V(1124905),5F(224981)(F(224981)-1)+1)	93372	Serge Batalov	04/2015
4076	3^195669+68	93358	Lelio R Paula	04/2016
4077	10^93356+91	93357	Robert Price	04/2011
4078	10^93356-28313	93356	Patrick De Geest	08/2013
4079	(85*10^93346+23)/9	93347	Robert Price	11/2015
4080	(3^195648-5)/3158276	93342	Lelio R Paula	04/2013
4081	3^195556+8680	93304	Lelio R Paula	04/2016
4082	2^309942-109991	93302	Enzo Doria	04/2014
4083	2^309926-1867301	93298	Enzo Doria	03/2016
4084	2^309924+85951	93297	Yves Minet	03/2011
4085	2^309896-4229	93288	Yves Minet	08/2018
4086	(86*10^93263-77)/9	93264	Robert Price	05/2016
4087	6^119836-125	93251	Lelio R Paula	05/2016
4088	(77*10^93249-257)/9	93250	Robert Price	10/2017
4089	3^195430-2	93244	Theodore Burton	02/2007
4090	(13*10^93236+47)/3	93237	Robert Price	01/2017
4091	(67*10^93226-7)/3	93228	Robert Price	10/2017
4092	(86*10^93217-221)/9	93218	Robert Price	06/2017
4093	2^309637-16329	93211	Enzo Doria	04/2013
4094	(41*10^93207+49)/9	93208	Robert Price	04/2016
4095	14^81312-57	93194	Lelio R Paula	06/2016
4096	41^57783-40	93192	Theodore Burton	02/2007
4097	3*10^93179-97	93180	Robert Price	08/2017
4098	5*7^110252-4	93175	Lelio R Paula	11/2014
4099	2^309380-27	93133	Lelio R Paula	11/2012
4100	23*10^93116-7	93118	Robert Price	03/2016
4101	(29*10^93082+1)/3	93083	Robert Price	11/2015
4102	(58*10^93062-13)/9	93063	Robert Price	09/2015
4103	2^309131+1869383	93058	Enzo Doria	05/2016
4104	2^309066-93	93039	Lelio R Paula	11/2012
4105	2^309063-113269	93038	Enzo Doria	07/2014
4106	3^194965+16	93022	Robert Price	10/2013
4107	2^308979+1869143	93012	Enzo Doria	05/2016
4108	5^133064+54	93008	Lelio R Paula	04/2016
4109	(2^308905-509203)/119	92988	Lelio R Paula	06/2013
4110	(94*10^92981-49)/99	92981	Ray Chandler	07/2011
4111	(2*10^92976-17)/3	92976	Robert Price	08/2014
4112	2^308809+37967	92961	Phil Moore	03/2008
4113	(3^194825+5)/11656	92952	Lelio R Paula	04/2013
4114	(2^308679+5)/1573	92919	Lelio R Paula	06/2013
4115	2^308650+513	92913	Lelio R Paula	02/2016
4116	5*7^109936+6	92908	Lelio R Paula	10/2014
4117	2*10^92897+89	92898	Robert Price	07/2016
4118	12^86073-29	92889	Lelio R Paula	06/2016
4119	2^308566-117	92888	Lelio R Paula	11/2012
4120	(17*10^92869-11)/3	92870	Robert Price	07/2015
4121	2^308459+75431	92856	Enzo Doria	04/2016
4122	2^308426-1866377	92846	Enzo Doria	03/2016
4123	(96^46831-1)/95	92830	Paul Bourdelais	09/2017
4124	2^308349-112111	92823	Enzo Doria	06/2014
4125	9*10^92821+19	92822	Robert Price	05/2016
4126	2^308337-75	92819	Lelio R Paula	11/2012
4127	4*3^194508+7	92805	Lelio R Paula	08/2014
4128	22*25^66379-113	92796	Curtis Bright	05/2015
4129	11^89101-1080	92790	Enzo Doria	12/2012
4130	2^308236-1867859	92789	Enzo Doria	04/2016
4131	12^85963+25	92770	Lelio R Paula	06/2016
4132	7^109750-66	92750	Lelio R Paula	04/2016
4133	9*10^92742+11	92743	Robert Kinser	01/2017
4134	(21*2^308046-1)/8857	92729	Lelio R Paula	02/2014
4135	2^307997-110655	92717	Enzo Doria	05/2014
4136	L(443609)	92709	Renaud Lifchitz	11/2003
4137	10^92691+9	92692	Robert Price	03/2011
4138	10^92691-252291	92691	Patrick De Geest	08/2013
4139	2^307879-2521	92681	Yves Minet	07/2014
4140	(2^307780-7)/19959669	92644	Lelio R Paula	06/2013
4141	14^80831+47	92643	Lelio R Paula	06/2016
4142	15^78744+92	92611	Lelio R Paula	07/2016
4143	65^51083-64	92610	Norbert Schneider	11/2014
4144	6^118996-16943	92597	Enzo Doria	02/2013
4145	(16*10^92591+41)/3	92592	Robert Price	10/2017
4146	(3^194014-7)/2	92568	Lelio R Paula	04/2013
4147	(63^51439+1)/64	92555	Paul Bourdelais	08/2017
4148	(26*10^92546-77)/3	92547	Robert Price	02/2017
4149	3^193954+340	92540	Lelio R Paula	04/2016
4150	2^307407-307407^2	92539	Henri Lifchitz	05/2005
4151	(17*10^92513-11)/3	92514	Robert Price	07/2015
4152	2^307318-4211	92512	Yves Minet	06/2011
4153	2^307280+193	92501	Lelio R Paula	11/2012
4154	20^71075-33	92471	Lelio R Paula	05/2016
4155	2^307126-78795	92455	Lelio R Paula	02/2016
4156	2^307125-49789	92454	Henri Lifchitz	08/2005
4157	2^307099+23	92447	Lelio R Paula	11/2012
4158	7*10^92414-69	92415	Robert Price	01/2017
4159	(9787*2^306975-1)/2129155	92407	Lelio R Paula	04/2015
4160	2^306915+1873373	92391	Enzo Doria	06/2016
4161	2^306908+12915	92389	Lelio R Paula	02/2016
4162	19^72244-80	92383	Lelio R Paula	06/2016
4164	2^306849+75	92371	Lelio R Paula	11/2012
4163	(397*10^92369+53)/9	92371	Robert Price	11/2017
4165	2^306813-869688105	92360	Lelio R Paula	08/2016
4166	2^306672-109059	92318	Enzo Doria	04/2014
4167	6^118604-17063	92292	Enzo Doria	02/2013
4168	(31*2^306487-1)/2291	92260	Lelio R Paula	02/2014
4169	2^306467-1835611	92256	Enzo Doria	04/2015
4170	2^306433+76427	92246	Enzo Doria	05/2016
4172	2^306430-113313	92245	Enzo Doria	07/2014
4171	(23*10^92244-59)/9	92245	Robert Price	03/2017
4173	(47*2^306398+1)/1384803	92231	Lelio R Paula	04/2015
4174	(25*10^92186+59)/3	92187	Robert Price	05/2016
4175	2^306213-286183	92180	Enzo Doria	06/2015
4176	10^92178+61	92179	Robert Price	04/2011
4177	10^92178-175509	92178	Patrick De Geest	07/2013
4178	2^306200+1185	92176	Lelio R Paula	02/2016
4179	2^306153+11	92162	Lelio R Paula	11/2012
4180	(2^306141-7)/5	92157	Lelio R Paula	06/2013
4181	(26*10^92152-23)/3	92153	Robert Price	08/2016
4182	(2*10^92152+67)/3	92152	Robert Price	04/2017
4183	410^92099+37^92099	92100	Mike Oakes	12/2010
4184	115^44684+114	92081	Norbert Schneider	07/2018
4185	(2^305867-2^152934+1)/5	92075		11/2006
4186	2^305851-109495	92071	Enzo Doria	04/2014
4187	12^85300+35	92055	Lelio R Paula	06/2016
4188	3^192911+92	92042	Lelio R Paula	04/2016
4189	2^305723-276271	92032	Enzo Doria	07/2015
4190	2^305676+93	92018	Donovan Johnson	06/2008
4191	3^192819+4	91999	Lelio R Paula	04/2013
4192	(38*10^91997-83)/99	91997	Ray Chandler	07/2011
4193	2^305539+72911	91977	Enzo Doria	04/2016
4194	(2^305427-5)/1297998213	91934	Lelio R Paula	06/2013
4195	85^47642+84	91922	Norbert Schneider	10/2015
4196	10^91920+187651	91921	Patrick De Geest	07/2013
4197	10^91920-39	91920	Robert Price	05/2011
4198	(22*10^91903+41)/9	91904	Robert Price	02/2015
4200	2^305275-27	91897	Lelio R Paula	11/2012
4199	3^192607-7726	91897	Enzo Doria	05/2014
4201	(7*10^91856-61)/9	91856	Erik Branger	12/2009
4202	(89*10^91839-53)/9	91840	Robert Price	11/2015
4203	8*5^131351+7	91812	Lelio R Paula	10/2014
4204	3^192426-68	91811	Lelio R Paula	04/2016
4205	2^304973+117	91807	Lelio R Paula	11/2012
4206	2^304939-1863727	91796	Enzo Doria	03/2016
4207	2^304902+8415	91785	Lelio R Paula	02/2016
4208	18^73119+61	91785	Lelio R Paula	06/2016
4209	(78557*2^304740+1)/159	91739	Lelio R Paula	06/2014
4210	2^304747+71355	91738	Lelio R Paula	02/2016
4211	8*3^192251+5	91728	Lelio R Paula	08/2014
4212	2^304674-87	91717	Lelio R Paula	11/2012
4213	(28*10^91715+701)/9	91716	Robert Price	11/2017
4214	(2^304698+9)/1362809953	91715	Lelio R Paula	06/2013
4215	(5*10^91707-119)/3	91708	Robert Price	04/2016
4216	2^304633-112771	91704	Enzo Doria	06/2014
4217	9*10^91693+23	91694	Robert Price	11/2017
4218	2^304578-16713	91688	Enzo Doria	05/2013
4219	6^117824-18713	91685	Enzo Doria	03/2013
4220	(17^74509-1)/16	91679	Paul Bourdelais	03/2010
4221	(2^304551-7)/8912231	91673	Lelio R Paula	06/2013
4222	(2^304532-3)/3013	91670	Lelio R Paula	06/2013
4223	2^304507-16645	91666	Enzo Doria	04/2013
4224	(29*2^304489+1)/31	91661	Lelio R Paula	09/2013
4225	2^304471-1836127	91655	Enzo Doria	04/2015
4226	2^304433+32769	91644	Lelio R Paula	02/2016
4227	2^304410-16625	91637	Enzo Doria	04/2013
4228	183^40500-2	91630	Lelio R Paula	10/2017
4229	(203*10^91613+1)/3	91615	Robert Price	09/2017
4230	4*5^131052+7	91603	Lelio R Paula	10/2014
4231	2^304278-4001	91597	Yves Minet	04/2017
4232	2^304272-1866377	91595	Enzo Doria	03/2016
4233	2^304268+19683	91594	Lelio R Paula	02/2016
4234	2^304162-161	91562	Lelio R Paula	11/2012
4235	5*7^108331+6	91552	Lelio R Paula	10/2014
4236	2^304082-2787821	91538	Enzo Doria	03/2016
4237	2^304015+64133	91518	David Broadhurst	06/2002
4238	(7*2^303963+1)/3	91503	Lelio R Paula	09/2013
4239	(2^303945-9)/3617	91494	Lelio R Paula	06/2013
4240	2^303930+1880527	91493	Enzo Doria	10/2016
4241	3^191684-68	91457	Lelio R Paula	04/2016
4242	(21*2^303813-1)/169	91456	Lelio R Paula	02/2014
4243	11^87797-120	91432	Enzo Doria	07/2012
4244	2^303698-1847231	91423	Enzo Doria	07/2015
4245	(38^28933-1)^2-2	91416	Norbert Schneider	06/2016
4246	2^303554+77299	91379	Enzo Doria	05/2016
4247	2^303542+12705	91376	Lelio R Paula	02/2016
4248	31^61269-2	91375	Lelio R Paula	09/2013
4249	2^303516-64875	91368	Lelio R Paula	02/2016
4250	(24737*2^303428+1)/3	91345	Lelio R Paula	06/2014

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Probable Primes Top 10000

(224660 PRPs in the top)