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 ?
4251	100^44683-99^44683	89366	Robert Price	07/2013
4252	2^296810+76519	89349	Enzo Doria	05/2016
4253	8^98928+7^(98928+1)	89341	Robert Price	06/2016
4254	(3^187247+4)/1027	89337	Lelio R Paula	01/2013
4255	(3^187235-2)/2045	89331	Lelio R Paula	01/2013
4257	2^296736-432149	89327	Paul Bourdelais	05/2013
4256	2^296737-112519	89327	Enzo Doria	06/2014
4258	2^296718-3645	89322	Lelio R Paula	11/2013
4259	2^296681-16221	89310	Enzo Doria	04/2013
4260	2^296669-16513	89307	Enzo Doria	04/2013
4261	2^296619-16357	89292	Enzo Doria	04/2013
4262	2^296614-110051	89290	Enzo Doria	04/2014
4263	(3^187138+8)/83147	89283	Lelio R Paula	01/2013
4264	(2*10^89279+457)/9	89279	Robert Price	01/2017
4265	15^75907-28	89274	Lelio R Paula	11/2015
4266	2^296547-37	89270	Yves Minet	01/2012
4267	2^296485+191	89251	Lelio R Paula	10/2012
4268	2^296467-75	89246	Lelio R Paula	10/2012
4269	2^296416-109535	89231	Enzo Doria	04/2014
4270	(23*2^296406+1)/3	89228	Lelio R Paula	01/2013
4271	66^49037-65	89225	Norbert Schneider	11/2014
4272	2^296377-16245	89219	Enzo Doria	04/2013
4273	2^296372-64875	89217	Lelio R Paula	11/2013
4274	5*6^114648-7	89215	Lelio R Paula	10/2014
4275	3*10^89206+13	89207	Robert Price	08/2017
4276	7*3^186960-4	89204	Lelio R Paula	08/2014
4277	2^296290-112133	89193	Enzo Doria	06/2014
4278	6^114620-17003	89192	Enzo Doria	02/2013
4279	(4*10^89189+41)/9	89189	Robert Price	11/2014
4280	2^296261-161181	89184	Enzo Doria	04/2013
4281	(19*2^296269-1)/530623	89182	Lelio R Paula	02/2014
4282	3^186903-10	89176	Robert Price	09/2013
4284	7*10^89169-3	89170	Dmitry Domanov	11/2010
4283	(2^296221-1017)/35	89170	Lelio R Paula	01/2013
4285	(43*10^89169+47)/9	89170	Robert Price	12/2017
4286	(10^89160+29)/3	89160	Serge Batalov	12/2014
4287	(28*10^89141-97)/3	89142	Robert Price	07/2016
4288	2^296116-734639	89140	Paul Bourdelais	04/2013
4289	6^114544-133	89133	Lelio R Paula	12/2015
4290	2^296076-113297	89128	Enzo Doria	07/2014
4291	(11*2^296060-1)/215	89122	Lelio R Paula	02/2014
4292	5*10^89118+81	89119	Robert Price	08/2017
4293	2^296037-1411	89117	Yves Minet	01/2013
4294	2^296020-2604809	89111	Enzo Doria	05/2015
4295	2^296016+81	89110	Henri Lifchitz	02/2007
4296	2^296010-11	89108	Lelio R Paula	10/2012
4297	2^295998-111911	89105	Enzo Doria	05/2014
4298	(2^296014+47)/93991149	89102	Lelio R Paula	01/2013
4299	2^295939-16621	89087	Enzo Doria	04/2013
4300	2^295934-109691	89086	Enzo Doria	04/2014
4301	(185*10^89063+7)/3	89065	Robert Price	02/2017
4302	2^295831+143	89055	Lelio R Paula	10/2012
4303	31^59713-30	89054	Theodore Burton	02/2007
4304	(7*2^295834-1)/27663	89052	Lelio R Paula	02/2014
4305	123^42608+2	89047	Lelio R Paula	05/2013
4306	6^114433-114433^6	89047	Norbert Schneider	04/2017
4307	2^295800-459659	89045	Enzo Doria	05/2015
4308	(52*10^89037-1)/3	89039	Robert Price	02/2017
4309	(6^114398-11)/5	89019	Paul Bourdelais	11/2011
4310	11^85470-5850	89008	Enzo Doria	02/2013
4311	(27*2^295634+1)/4687	88993	Lelio R Paula	01/2013
4312	(p(18424)#-4)/2	88985	Robert Price	09/2017
4313	2^295564-189	88974	Lelio R Paula	10/2012
4314	2^295557+73097	88972	Enzo Doria	04/2016
4315	11^85433-5760	88970	Enzo Doria	01/2013
4316	6*10^88938-91	88939	Robert Price	11/2017
4317	15^75619-88	88935	Lelio R Paula	11/2015
4318	2^295385-85	88920	Lelio R Paula	10/2012
4319	2^295385-16333	88920	Enzo Doria	04/2013
4320	2^295309+59	88897	Lelio R Paula	10/2012
4321	2^295288-109799	88891	Enzo Doria	04/2014
4322	2^295245+65	88878	Lelio R Paula	10/2012
4323	Padovan(727734)	88874	Eric W. Weisstein	04/2011
4324	18^70793-17	88865	Lelio R Paula	11/2015
4325	6^114196-17573	88862	Enzo Doria	02/2013
4326	302^35829+35829^302	88857	Norbert Schneider	12/2014
4327	3^186223+16	88851	Robert Price	10/2013
4328	3*2^295139+7	88847	Lelio R Paula	08/2014
4329	3^186212-113008	88846	Enzo Doria	07/2014
4330	87^45803-86	88836	Norbert Schneider	11/2015
4331	2^295094-110273	88833	Enzo Doria	05/2014
4332	2^295080+1869151	88828	Enzo Doria	05/2016
4333	2^295027-113407	88812	Enzo Doria	07/2014
4334	(2*10^88808-71)/3	88808	Robert Price	01/2017
4335	13^79722-80	88806	Lelio R Paula	11/2015
4336	3^186103+104	88794	Lelio R Paula	12/2015
4337	(3*2^294971+1)/25565	88792	Lelio R Paula	01/2013
4338	2^294937-115003	88785	Enzo Doria	06/2015
4339	2^294868-109709	88765	Enzo Doria	04/2014
4340	2^294864-2985	88763	Yves Minet	09/2014
4341	(17*10^88761-41)/3	88762	Robert Price	09/2017
4342	2^294754+15015	88730	Lelio R Paula	10/2013
4343	(3^185951-7)/20	88720	Lelio R Paula	01/2013
4344	(2^294661+5)/443693383	88694	Lelio R Paula	01/2013
4345	(10^88680+11)/3	88680	Robert Price	11/2014
4346	2*7^104928-9	88675	Lelio R Paula	10/2014
4347	11^85150+12	88675	Lelio R Paula	11/2015
4348	8*6^113951+5	88673	Lelio R Paula	10/2014
4349	6^113940-18563	88663	Enzo Doria	03/2013
4350	38^56123-56123^38	88663	Norbert Schneider	02/2017
4351	2^294492-65	88651	Lelio R Paula	10/2012
4352	20^68120-53	88627	Lelio R Paula	01/2016
4353	2^294391-113257	88621	Enzo Doria	07/2014
4354	5^126784-15476	88619	Enzo Doria	02/2013
4355	2^294327+9	88602	Lelio R Paula	10/2012
4356	2^294320+18915	88600	Lelio R Paula	10/2013
4357	(98*10^88595-89)/99	88595	Ray Chandler	07/2011
4358	(17*2^294262-1)/13	88582	Lelio R Paula	02/2014
4359	(2*10^88545+7)/9	88545	Erik Branger	03/2011
4360	2^294137-133	88545	Lelio R Paula	10/2012
4361	(2^294092-1017)/1171	88528	Lelio R Paula	01/2013
4362	4^147036+147036^4+1	88525	Robert Price	04/2014
4363	(14^77213-5^77213)/9	88496	Robert Price	04/2013
4364	2^293965+2793377	88493	Enzo Doria	03/2016
4365	11^84971-150	88489	Enzo Doria	08/2012
4366	(2^293956-1017)/39851376696677	88476	Lelio R Paula	01/2013
4367	11^84958-2190	88475	Enzo Doria	12/2012
4368	2^293880-111347	88467	Enzo Doria	05/2014
4369	(106*10^88459-1)/3	88461	Serge Batalov	12/2014
4370	10^88457+278733	88458	Patrick De Geest	07/2017
4371	10^88457-401	88457	Robert Price	06/2017
4372	11^84908-1680	88423	Enzo Doria	12/2012
4373	2^293679-112075	88407	Enzo Doria	06/2014
4374	6^113608-65	88405	Lelio R Paula	12/2015
4375	2^293624+82875	88390	Lelio R Paula	10/2013
4376	2^293612-112337	88387	Enzo Doria	06/2014
4377	758^30693+30693^758	88386	Norbert Schneider	05/2017
4378	gcd(V(1062695),5F(212539)(F(212539)-1)+1)	88383	Serge Batalov	04/2015
4379	5*10^88377+77	88378	Robert Price	06/2016
4380	(5*2^293526+1)/303	88359	Lelio R Paula	01/2013
4381	2^293461-2785843	88341	Enzo Doria	03/2016
4382	2^293416-1037	88328	Yves Minet	11/2012
4383	(2^293384-7)/3	88317	Lelio R Paula	01/2013
4384	(3^185092-5)/4	88311	Lelio R Paula	01/2013
4385	(5*10^88303-173)/3	88304	Robert Price	11/2017
4386	14^77039-57	88297	Lelio R Paula	11/2015
4387	3*10^88293-59	88294	Robert Price	10/2017
4388	5^126303+42	88283	Lelio R Paula	10/2015
4389	19^69025-18	88266	Theodore Burton	01/2006
4390	5*10^88261-3	88262	Dmitry Domanov	11/2010
4391	8^97731-7^(97731-1)	88260	Robert Price	04/2016
4392	5*10^88254+59	88255	Robert Price	09/2016
4393	4*3^184968-7	88253	Lelio R Paula	08/2014
4394	7^104426+88	88251	Lelio R Paula	10/2015
4395	2^293142+99	88245	Lelio R Paula	10/2012
4396	11^84736-2130	88244	Enzo Doria	12/2012
4397	2^293068-89	88223	Lelio R Paula	10/2012
4398	2^293014-109655	88207	Enzo Doria	04/2014
4399	8*7^104371-3	88205	Lelio R Paula	10/2014
4400	2^292995-2145	88201	Lelio R Paula	10/2013
4401	5*10^88182+77	88183	Robert Price	06/2016
4403	2^292929+43877	88181	Donovan Johnson	04/2005
4402	6^113321+131	88181	Lelio R Paula	12/2015
4404	2^292904-583949	88173	Paul Bourdelais	04/2013
4405	2^292894-111851	88170	Enzo Doria	05/2014
4406	2^292872-2797349	88164	Enzo Doria	03/2016
4407	2^292860-109685	88160	Enzo Doria	04/2014
4408	9*6^113288-5	88157	Lelio R Paula	10/2014
4409	(2*10^88112-23)/3	88112	Robert Price	09/2017
4410	(73*10^88105+17)/9	88106	Robert Price	10/2015
4411	11^84588+78	88090	Lelio R Paula	11/2015
4412	(265*10^88077+11)/3	88079	Robert Price	03/2017
4413	91^44959-90^44959	88077	Robert Price	07/2015
4414	6^113177-5^113177	88069	Jean-Louis Charton	01/2009
4415	(10^88020+101)/3	88020	Robert Price	04/2016
4416	(10^(243982+1)-610^43982-1)/3	87965	Robert Price	02/2016
4417	(424*10^87930-1)/9	87932	Robert Price	11/2017
4418	p(18225)#/2+128	87929	Robert Price	04/2017
4419	4*6^112977+7	87914	Lelio R Paula	10/2014
4420	14^76677+69	87882	Lelio R Paula	11/2015
4421	(22*10^87863-1)/3	87864	Robert Price	12/2014
4422	2^291822-2797811	87848	Enzo Doria	04/2016
4423	2^291716-111389	87816	Enzo Doria	05/2014
4424	(782*10^87809-71)/9	87811	Robert Price	06/2017
4425	3^184039+1820	87809	Lelio R Paula	12/2015
4426	12^81356+41	87798	Lelio R Paula	11/2015
4427	6^112792-18983	87770	Enzo Doria	03/2013
4428	3*6^112787-5	87766	Lelio R Paula	10/2014
4429	7^103848+82	87762	Lelio R Paula	10/2015
4430	(19*2^291534-1)/178696395	87754	Lelio R Paula	02/2014
4431	(3^183915+5)/128	87748	Lelio R Paula	01/2013
4432	19^68619+24	87747	Lelio R Paula	12/2015
4434	2^291480+1185	87745	Lelio R Paula	10/2013
4433	2^291482+1867369	87745	Enzo Doria	03/2016
4435	2^291467-937	87741	Yves Minet	05/2013
4436	(25*10^87726+161)/3	87727	Robert Price	01/2017
4437	11^84239-2850	87726	Enzo Doria	12/2012
4438	10^87720+215541	87721	Patrick De Geest	01/2011
4439	10^87720-3	87720	Markus Tervooren	07/2010
4440	(5*10^87712-473)/9	87712	Robert Price	12/2017
4441	(2^291357+5)/6847	87704	Lelio R Paula	01/2013
4442	93^44541-2	87679	Lelio R Paula	09/2013
4443	2^291261-109561	87679	Enzo Doria	04/2014
4444	(4*10^87669+149)/9	87669	Robert Price	03/2017
4445	2^291217+4257	87666	Lelio R Paula	10/2013
4446	2*12^81214-5^81214	87645	Mike Oakes	12/2010
4447	(5*10^87622-473)/9	87622	Robert Price	12/2017
4448	12^81188+85	87617	Lelio R Paula	11/2015
4449	(21*2^290980-1)/5	87595	Lelio R Paula	02/2014
4450	2^290958+127	87588	Lelio R Paula	09/2012
4451	2^290923-67	87577	Lelio R Paula	09/2012
4452	3*10^87573-97	87574	Robert Price	08/2017
4453	(13*10^87565+11)/3	87566	Robert Price	05/2015
4454	(2^290857-7)/55	87555	Lelio R Paula	01/2013
4455	2^290802+82875	87541	Lelio R Paula	10/2013
4456	(509203*2^290792-1)/7560987	87536	Lelio R Paula	04/2015
4457	3^183441+236	87524	Lelio R Paula	12/2015
4458	2^290618-33	87485	Lelio R Paula	09/2012
4459	(184*10^87473-1)/3	87475	Robert Price	02/2017
4460	2^290534-115151	87460	Enzo Doria	06/2015
4461	2^290512-109757	87453	Enzo Doria	04/2014
4462	(32*10^87448-41)/9	87449	Robert Price	05/2015
4463	(2^290491+9)/3179	87444	Lelio R Paula	01/2013
4464	(25*2^290489-1)/51809	87443	Lelio R Paula	02/2014
4465	2^290426+82875	87427	Lelio R Paula	11/2013
4466	3*2^290415-7	87425	Lelio R Paula	08/2014
4467	10^87408+57	87409	Robert Price	03/2011
4468	2^290366+74779	87409	Enzo Doria	04/2016
4469	10^87408-123569	87408	Patrick De Geest	07/2013
4470	2^290265+58905	87379	Lelio R Paula	10/2013
4471	7^103391+16	87376	Lelio R Paula	10/2015
4472	(115*10^87368-7)/9	87370	Robert Price	11/2017
4473	(92^44491-1)/91	87369	Paul Bourdelais	08/2017
4474	8*7^103379+3	87367	Lelio R Paula	10/2014
4475	(2^290226+7)/71	87365	Lelio R Paula	01/2013
4476	13^78407-30	87341	Lelio R Paula	11/2015
4477	4*10^87337-99	87338	Robert Price	12/2016
4478	7*10^87319+39	87320	Robert Price	07/2016
4479	3*5^124921+2	87317	Lelio R Paula	10/2014
4480	3^182984+88	87306	Lelio R Paula	12/2015
4481	4*10^87287-99	87288	Robert Price	12/2016
4482	11^83813-1860	87283	Enzo Doria	12/2012
4483	734^30453+30453^734	87270	Norbert Schneider	04/2017
4484	12^80855+29	87258	Lelio R Paula	11/2015
4485	3*6^112119-5	87247	Lelio R Paula	10/2014
4486	12^80806+79	87205	Lelio R Paula	11/2015
4487	91382^9+9^91382	87201	Andrey Kulsha	11/2004
4488	(21181*2^289657+1)/81	87198	Lelio R Paula	06/2014
4489	6^112054-47	87195	Lelio R Paula	12/2015
4490	(55459*2^289632+1)/55	87191	Lelio R Paula	06/2014
4491	15^74131-68	87185	Lelio R Paula	11/2015
4492	2^289583-741	87174	Lelio R Paula	10/2013
4493	7^103146+12	87169	Lelio R Paula	10/2015
4494	5*2^289556-3	87166	Lelio R Paula	08/2014
4495	2^289543-112735	87162	Enzo Doria	06/2014
4496	8*3^182655-7	87150	Lelio R Paula	08/2014
4497	2*10^87144+81	87145	Robert Price	01/2017
4498	7^103106+2*3^103106	87135	Mike Oakes	08/2010
4499	8*3^182614+7	87130	Lelio R Paula	08/2014
4500	(2^289368-509203)/9	87108	Lelio R Paula	01/2013

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PRP Records

Probable Primes Top 10000

(205869 PRPs in the top)