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	(63^51439+1)/64	92555	Paul Bourdelais	08/2017
4002	(26*10^92546-77)/3	92547	Robert Price	02/2017
4003	3^193954+340	92540	Lelio R Paula	04/2016
4004	2^307407-307407^2	92539	Henri Lifchitz	05/2005
4005	(17*10^92513-11)/3	92514	Robert Price	07/2015
4006	2^307318-4211	92512	Yves Minet	06/2011
4007	2^307280+193	92501	Lelio R Paula	11/2012
4008	20^71075-33	92471	Lelio R Paula	05/2016
4009	2^307126-78795	92455	Lelio R Paula	02/2016
4010	2^307125-49789	92454	Henri Lifchitz	08/2005
4011	2^307099+23	92447	Lelio R Paula	11/2012
4012	7*10^92414-69	92415	Robert Price	01/2017
4013	(9787*2^306975-1)/2129155	92407	Lelio R Paula	04/2015
4014	2^306915+1873373	92391	Enzo Doria	06/2016
4015	2^306908+12915	92389	Lelio R Paula	02/2016
4016	19^72244-80	92383	Lelio R Paula	06/2016
4018	2^306849+75	92371	Lelio R Paula	11/2012
4017	(397*10^92369+53)/9	92371	Robert Price	11/2017
4019	2^306813-869688105	92360	Lelio R Paula	08/2016
4020	2^306672-109059	92318	Enzo Doria	04/2014
4021	6^118604-17063	92292	Enzo Doria	02/2013
4022	(31*2^306487-1)/2291	92260	Lelio R Paula	02/2014
4023	2^306467-1835611	92256	Enzo Doria	04/2015
4024	2^306433+76427	92246	Enzo Doria	05/2016
4026	2^306430-113313	92245	Enzo Doria	07/2014
4025	(23*10^92244-59)/9	92245	Robert Price	03/2017
4027	(47*2^306398+1)/1384803	92231	Lelio R Paula	04/2015
4028	(25*10^92186+59)/3	92187	Robert Price	05/2016
4029	2^306213-286183	92180	Enzo Doria	06/2015
4030	10^92178+61	92179	Robert Price	04/2011
4031	10^92178-175509	92178	Patrick De Geest	07/2013
4032	2^306200+1185	92176	Lelio R Paula	02/2016
4033	2^306153+11	92162	Lelio R Paula	11/2012
4034	(2^306141-7)/5	92157	Lelio R Paula	06/2013
4035	(26*10^92152-23)/3	92153	Robert Price	08/2016
4036	(2*10^92152+67)/3	92152	Robert Price	04/2017
4037	410^92099+37^92099	92100	Mike Oakes	12/2010
4038	(2^305867-2^152934+1)/5	92075		11/2006
4039	2^305851-109495	92071	Enzo Doria	04/2014
4040	12^85300+35	92055	Lelio R Paula	06/2016
4041	3^192911+92	92042	Lelio R Paula	04/2016
4042	2^305723-276271	92032	Enzo Doria	07/2015
4043	2^305676+93	92018	Donovan Johnson	06/2008
4044	3^192819+4	91999	Lelio R Paula	04/2013
4045	(38*10^91997-83)/99	91997	Ray Chandler	07/2011
4046	2^305539+72911	91977	Enzo Doria	04/2016
4047	(2^305427-5)/1297998213	91934	Lelio R Paula	06/2013
4048	85^47642+84	91922	Norbert Schneider	10/2015
4049	10^91920+187651	91921	Patrick De Geest	07/2013
4050	10^91920-39	91920	Robert Price	05/2011
4051	(22*10^91903+41)/9	91904	Robert Price	02/2015
4053	2^305275-27	91897	Lelio R Paula	11/2012
4052	3^192607-7726	91897	Enzo Doria	05/2014
4054	(7*10^91856-61)/9	91856	Erik Branger	12/2009
4055	(89*10^91839-53)/9	91840	Robert Price	11/2015
4056	8*5^131351+7	91812	Lelio R Paula	10/2014
4057	3^192426-68	91811	Lelio R Paula	04/2016
4058	2^304973+117	91807	Lelio R Paula	11/2012
4059	2^304939-1863727	91796	Enzo Doria	03/2016
4060	2^304902+8415	91785	Lelio R Paula	02/2016
4061	18^73119+61	91785	Lelio R Paula	06/2016
4062	(78557*2^304740+1)/159	91739	Lelio R Paula	06/2014
4063	2^304747+71355	91738	Lelio R Paula	02/2016
4064	8*3^192251+5	91728	Lelio R Paula	08/2014
4065	2^304674-87	91717	Lelio R Paula	11/2012
4066	(28*10^91715+701)/9	91716	Robert Price	11/2017
4067	(2^304698+9)/1362809953	91715	Lelio R Paula	06/2013
4068	(5*10^91707-119)/3	91708	Robert Price	04/2016
4069	2^304633-112771	91704	Enzo Doria	06/2014
4070	9*10^91693+23	91694	Robert Price	11/2017
4071	2^304578-16713	91688	Enzo Doria	05/2013
4072	6^117824-18713	91685	Enzo Doria	03/2013
4073	(17^74509-1)/16	91679	Paul Bourdelais	03/2010
4074	(2^304551-7)/8912231	91673	Lelio R Paula	06/2013
4075	(2^304532-3)/3013	91670	Lelio R Paula	06/2013
4076	2^304507-16645	91666	Enzo Doria	04/2013
4077	(29*2^304489+1)/31	91661	Lelio R Paula	09/2013
4078	2^304471-1836127	91655	Enzo Doria	04/2015
4079	2^304433+32769	91644	Lelio R Paula	02/2016
4080	2^304410-16625	91637	Enzo Doria	04/2013
4081	183^40500-2	91630	Lelio R Paula	10/2017
4082	(203*10^91613+1)/3	91615	Robert Price	09/2017
4083	4*5^131052+7	91603	Lelio R Paula	10/2014
4084	2^304278-4001	91597	Yves Minet	04/2017
4085	2^304272-1866377	91595	Enzo Doria	03/2016
4086	2^304268+19683	91594	Lelio R Paula	02/2016
4087	2^304162-161	91562	Lelio R Paula	11/2012
4088	5*7^108331+6	91552	Lelio R Paula	10/2014
4089	2^304082-2787821	91538	Enzo Doria	03/2016
4090	2^304015+64133	91518	David Broadhurst	06/2002
4091	(7*2^303963+1)/3	91503	Lelio R Paula	09/2013
4092	(2^303945-9)/3617	91494	Lelio R Paula	06/2013
4093	2^303930+1880527	91493	Enzo Doria	10/2016
4094	3^191684-68	91457	Lelio R Paula	04/2016
4095	(21*2^303813-1)/169	91456	Lelio R Paula	02/2014
4096	11^87797-120	91432	Enzo Doria	07/2012
4097	2^303698-1847231	91423	Enzo Doria	07/2015
4098	(38^28933-1)^2-2	91416	Norbert Schneider	06/2016
4099	2^303554+77299	91379	Enzo Doria	05/2016
4100	2^303542+12705	91376	Lelio R Paula	02/2016
4101	31^61269-2	91375	Lelio R Paula	09/2013
4102	2^303516-64875	91368	Lelio R Paula	02/2016
4103	(24737*2^303428+1)/3	91345	Lelio R Paula	06/2014
4104	(21181*2^303357+1)/32361	91320	Lelio R Paula	06/2014
4105	2^303344-2786969	91316	Enzo Doria	03/2016
4106	6^117346+65	91313	Lelio R Paula	05/2016
4107	2^303321+855	91309	Lelio R Paula	02/2016
4108	12^84606+47	91306	Lelio R Paula	06/2016
4109	2^303288+1874311	91299	Enzo Doria	06/2016
4110	197^39788-2	91293	Lelio R Paula	10/2017
4111	11^87663-1710	91292	Enzo Doria	12/2012
4112	2^303224+2533	91280	Henri Lifchitz	05/2005
4113	6^117302+143	91279	Lelio R Paula	05/2016
4114	3^191306-112880	91277	Enzo Doria	07/2014
4115	2^303207+12915	91275	Lelio R Paula	02/2016
4116	2^303191-111259	91270	Enzo Doria	05/2014
4117	10^91230+9^(91230+1)	91231	Robert Price	08/2016
4118	10^91230+7921	91231	Patrick De Geest	11/2016
4119	10^91230-911141	91230	Patrick De Geest	11/2016
4120	6^117232-17423	91225	Enzo Doria	02/2013
4121	7*10^91215+3	91216	Erik Branger	11/2009
4122	97*10^91205-3	91207	Robert Price	01/2017
4123	2^302979-161181	91206	Enzo Doria	04/2013
4124	2^302949+81	91197	Henri Lifchitz	02/2007
4125	4*6^117192-5	91194	Lelio R Paula	10/2014
4126	2^302918+99	91188	Lelio R Paula	11/2012
4127	2^302797+1869587	91151	Enzo Doria	05/2016
4128	265^37614+37614^265	91148	Norbert Schneider	01/2015
4129	7^107852+82	91146	Lelio R Paula	04/2016
4130	(38*10^91144-11)/9	91145	Robert Price	05/2015
4131	(55*10^91142+377)/9	91143	Robert Price	10/2017
4132	249^38030+38030^249	91128	Norbert Schneider	01/2015
4133	6^117094-211049	91117	Mike Oakes	05/2011
4134	2^302602-1867181	91093	Enzo Doria	03/2016
4135	(1017*2^302592-1)/53	91091	Lelio R Paula	04/2015
4136	15^77445-16	91083	Lelio R Paula	07/2016
4137	2^302505+81	91064	Henri Lifchitz	02/2007
4138	2^302496-112349	91061	Enzo Doria	06/2014
4139	17^73999-72	91052	Lelio R Paula	07/2016
4140	(16*10^91032+41)/3	91033	Robert Price	10/2017
4141	2^302332+577294575	91012	Lelio R Paula	08/2016
4142	2^302274+74209	90994	Enzo Doria	04/2016
4143	(311^36497-1)/310	90976	Eric Chen	09/2017
4144	(3^190668+2)/89	90970	Lelio R Paula	04/2013
4145	2^302188+90195	90968	Lelio R Paula	02/2016
4146	(53*10^90965-71)/9	90966	Robert Price	09/2015
4147	2^302113+74105	90946	Enzo Doria	04/2016
4148	2^302102-6555	90942	Lelio R Paula	02/2016
4149	156(10^(422731)-1)/101-1	90925	Robert Price	05/2014
4150	3^190568+38	90925	Lelio R Paula	04/2016
4151	2^302009-16449	90914	Enzo Doria	04/2013
4152	(17*2^301951-1)/165	90896	Lelio R Paula	02/2014
4153	3^190497+74	90891	Lelio R Paula	04/2016
4154	(24737*2^301896+1)/399	90882	Lelio R Paula	06/2014
4155	18^72397+89	90878	Lelio R Paula	06/2016
4156	6^116769-47	90864	Lelio R Paula	05/2016
4157	2^301712-465	90825	Lelio R Paula	02/2016
4158	2^301693-69	90819	Lelio R Paula	11/2012
4159	2^301683-301683^2	90816	Henri Lifchitz	05/2005
4160	11^87187-1710	90796	Enzo Doria	12/2012
4161	5*10^90793+21	90794	Robert Price	01/2017
4162	(22*10^90792-13)/9	90793	Robert Price	03/2015
4163	2^301591-1615	90788	Lelio R Paula	02/2016
4164	(52^52901+1)/53	90777	Paul Bourdelais	08/2017
4165	2^301546-109037	90775	Enzo Doria	04/2014
4166	14^79195-3	90768	Lelio R Paula	06/2016
4167	2^301517-1861693	90766	Enzo Doria	11/2015
4168	2^301460-173	90749	Lelio R Paula	11/2012
4169	(85*10^90745-103)/9	90746	Robert Price	10/2017
4170	2^301312-89	90704	Lelio R Paula	11/2012
4171	2^301285-129	90696	Lelio R Paula	11/2012
4172	2^301282-109991	90695	Enzo Doria	04/2014
4173	2^301228-1854269	90679	Enzo Doria	09/2015
4174	(151*10^90669-1)/3	90671	Robert Price	04/2017
4175	(32*10^90669+13)/9	90670	Robert Price	04/2015
4176	3*5^129698+8	90656	Lelio R Paula	10/2014
4177	F(433781)	90655	Henri Lifchitz	09/2003
4178	19^70891+82	90653	Lelio R Paula	06/2016
4179	(29*2^301124-1)/13	90648	Lelio R Paula	02/2014
4180	7*3^189953-8	90632	Lelio R Paula	08/2014
4181	11^87022-1800	90625	Enzo Doria	12/2012
4182	(2^301042+47)/12036969	90616	Lelio R Paula	06/2013
4183	2^301004-2786939	90612	Enzo Doria	03/2016
4184	2^300980-27	90605	Lelio R Paula	11/2012
4185	2*10^90597-7	90598	Dmitry Domanov	11/2010
4186	197^39485+2	90597	Lelio R Paula	06/2013
4187	7^107198+48	90593	Lelio R Paula	04/2016
4188	(86*10^90588+121)/9	90589	Robert Price	03/2017
4189	2^300923+53	90587	Lelio R Paula	11/2012
4190	2^300874+7	90573	Lelio R Paula	10/2012
4191	5^129568-56	90565	Lelio R Paula	04/2016
4192	2^300847-112831	90564	Enzo Doria	06/2014
4193	2^300718+255255	90526	Lelio R Paula	02/2016
4194	2^300637+95	90501	Lelio R Paula	11/2012
4195	7^107087-24	90500	Lelio R Paula	04/2016
4197	(10^90499+3^90499)/13	90498	Robert Price	01/2013
4196	13^81241+90	90498	Lelio R Paula	06/2016
4198	6^116273-85	90478	Lelio R Paula	05/2016
4199	6^116256-17573	90465	Enzo Doria	02/2013
4200	2^300502+54615	90461	Lelio R Paula	02/2016
4201	(13*2^300487+1)/45	90456	Lelio R Paula	09/2013
4202	(3^189545-8)/5	90436	Lelio R Paula	01/2013
4203	(7*2^300406-1)/3	90432	Lelio R Paula	02/2014
4204	4*5^129332+3	90400	Lelio R Paula	10/2014
4205	2^300249-16245	90384	Enzo Doria	04/2013
4206	(7*10^90371-313)/9	90371	Robert Price	11/2016
4207	2*6^116118+7	90358	Lelio R Paula	10/2014
4208	(24737*2^300101+1)/25	90343	Lelio R Paula	06/2014
4209	4*10^90334-21	90335	Robert Price	04/2016
4210	2^300019-110335	90315	Enzo Doria	05/2014
4211	2^299949-1005	90294	Lelio R Paula	11/2013
4212	2^299868-109613	90270	Enzo Doria	04/2014
4213	5*2^299799-3	90250	Lelio R Paula	08/2014
4214	13^81008-2	90239	Lelio R Paula	09/2013
4215	64^49957-63^49957	90232	Robert Price	07/2013
4216	10^90227+56281	90228	Patrick De Geest	06/2016
4219	2^299725+315	90227	Lelio R Paula	11/2013
4217	10^90227-1000000001	90227	Robert Price	05/2016
4218	10^90227-68763	90227	Patrick De Geest	06/2016
4220	5^129082+48	90225	Lelio R Paula	03/2016
4221	2^299699+195	90219	Lelio R Paula	10/2012
4222	(55*10^90211-1)/9	90212	Ray Chandler	02/2012
4223	3^189053+280	90202	Lelio R Paula	04/2016
4224	2^299639-187	90201	Lelio R Paula	10/2012
4225	2^299631+183	90198	Lelio R Paula	10/2012
4226	(21*2^299611-1)/29	90192	Lelio R Paula	02/2014
4227	2^299567+113	90179	Lelio R Paula	10/2012
4228	2^299550+189	90174	Lelio R Paula	10/2012
4229	(2^299535+3)/29	90168	Lelio R Paula	01/2013
4230	(97*10^90155-1)/3	90157	Serge Batalov	12/2014
4231	3^188938+8680	90147	Lelio R Paula	04/2016
4232	6^115840-55	90142	Lelio R Paula	05/2016
4233	(5*10^90142-473)/9	90142	Robert Price	12/2017
4234	8*7^106659+5	90139	Lelio R Paula	10/2014
4235	2^299406-16653	90131	Enzo Doria	05/2013
4236	208049#+(216091#)/(208049#)	90128	Makoto Morimoto	04/2016
4237	(F(5)^128941-F(4)^128941)/F(3)	90126	Wayne Halsdorf	03/2012
4238	6^115819-53	90125	Lelio R Paula	05/2016
4239	6^115816-16853	90123	Enzo Doria	02/2013
4240	6^115813-23	90121	Lelio R Paula	05/2016
4241	(22*10^90110+161)/3	90111	Robert Price	02/2017
4242	(2^299330-509203)/69	90106	Lelio R Paula	01/2013
4243	(29*10^90096-17)/3	90097	Erik Branger	09/2014
4244	2^299247+1870529	90083	Enzo Doria	05/2016
4245	2^299229-2797783	90077	Enzo Doria	04/2016
4246	2^299220-16317	90075	Enzo Doria	04/2013
4247	11^86491-1350	90072	Enzo Doria	12/2012
4248	(31*10^90064-1)/3	90066	Robert Price	03/2017
4249	L(430949)/861899/1440387561539	90045	Serge Batalov	07/2017
4250	2^299112+73951	90042	Enzo Doria	04/2016

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Probable Primes Top 10000

(211563 PRPs in the top)