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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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	8^99702+7^(99702-1)	90040	Robert Price	02/2016
4252	5*10^90033+3	90034	Dmitry Domanov	11/2010
4253	243^37738+37738^243	90029	Norbert Schneider	01/2015
4254	2^299048-113297	90023	Enzo Doria	07/2014
4255	3^188648+92	90008	Lelio R Paula	12/2015
4256	5*2^298991+7	90006	Lelio R Paula	08/2014
4257	(25*2^298997+1)/3267	90005	Lelio R Paula	01/2013
4258	10^90000+8869	90001	Patrick De Geest	12/2009
4260	10^89999+82939	90000	Dirk Augustin	04/2007
4259	10^90000-140343	90000	Patrick De Geest	12/2009
4261	10^89999-194891	89999	Patrick De Geest	11/2009
4262	19^70365-78	89980	Lelio R Paula	12/2015
4263	NaturalLogarithmOf2(89973)	89973	Eric W. Weisstein	10/2015
4264	2^298852-64875	89964	Lelio R Paula	11/2013
4265	18^71659+37	89952	Lelio R Paula	12/2015
4266	(2908*29^61501-3)/7	89942	Curtis Bright	05/2015
4267	17^73067+20	89906	Lelio R Paula	11/2015
4268	2^298637-99	89899	Lelio R Paula	10/2012
4269	9^94188+38^94188-24^94188-3*2^94188	89879	Mike Oakes	01/2011
4270	9*10^89858+19	89859	Robert Price	05/2016
4271	2^298501+1870067	89858	Enzo Doria	05/2016
4272	11^86280-98	89852	Lelio R Paula	11/2015
4273	2^298473-110059	89850	Enzo Doria	04/2014
4274	19^70263-32	89850	Lelio R Paula	12/2015
4275	(299*10^89836-17)/3	89838	Robert Price	01/2017
4276	3^188286+14	89836	Robert Price	09/2013
4277	gcd(V(1091095),5F(218219)(F(218219)+1)+1)	89822	Serge Batalov	04/2015
4278	2^298367+58905	89818	Lelio R Paula	11/2013
4279	2^298319-109657	89803	Enzo Doria	04/2014
4280	8*10^89800+81	89801	Robert Price	05/2017
4281	18^71505-91	89759	Lelio R Paula	12/2015
4282	(7^106187+1)/8	89738	Paul Bourdelais	04/2008
4283	2^298079-109531	89731	Enzo Doria	04/2014
4284	(22699*2^298016+1)/385	89714	Lelio R Paula	06/2014
4285	156(10^(422427)-1)/101-1	89709	Robert Price	05/2014
4286	2^298003-66945	89708	Lelio R Paula	11/2013
4287	(23*10^89705-83)/3	89706	Robert Price	09/2017
4288	17^72900-54	89700	Lelio R Paula	11/2015
4289	3*2^297956+5	89695	Lelio R Paula	08/2014
4290	20^68938-11	89691	Lelio R Paula	01/2016
4291	89*10^89687-7	89689	Robert Price	03/2017
4292	2^297923+77783	89684	Enzo Doria	05/2016
4293	11^86107-24576000	89672	Enzo Doria	02/2013
4294	2^297878-111911	89671	Enzo Doria	05/2014
4295	7^106084+40	89652	Lelio R Paula	10/2015
4296	(86*10^89640-311)/9	89641	Robert Price	10/2017
4297	3*10^89608-59	89609	Robert Price	10/2017
4298	3^187780-11038	89594	Enzo Doria	05/2014
4299	(13*2^297560-1)/49151787	89568	Lelio R Paula	02/2014
4300	5^128141-36	89567	Lelio R Paula	10/2015
4301	4*7^105951+9	89540	Lelio R Paula	10/2014
4302	(7*10^89539-439)/9	89539	Robert Price	09/2017
4303	2^297397+177257	89526	Enzo Doria	05/2016
4304	2^297346-16241	89511	Enzo Doria	04/2013
4305	(5*10^89510+79)/3	89511	Robert Price	11/2017
4307	4^148663-3^148663	89505	Jean-Louis Charton	11/2005
4306	2^297328-869688105	89505	Lelio R Paula	07/2016
4308	2^297325-459043	89504	Enzo Doria	05/2015
4309	2^297310-112391	89500	Enzo Doria	06/2014
4310	2^297296-112157	89496	Enzo Doria	06/2014
4311	57^50966-2	89490	Lelio R Paula	08/2013
4312	(266*10^89482+1)/3	89484	Robert Price	02/2016
4313	(14*10^89480-101)/3	89481	Robert Price	04/2017
4314	2^297122+99	89443	Lelio R Paula	10/2012
4315	(3^187435-5)/1286	89427	Lelio R Paula	01/2013
4316	(25*10^89413+161)/3	89414	Robert Price	01/2017
4317	2^296990+1870699	89403	Enzo Doria	05/2016
4318	2^296972-1017	89398	Lelio R Paula	11/2013
4319	(7*10^89383+167)/3	89384	Robert Kinser	10/2017
4320	(85*10^89375-31)/9	89376	Robert Price	11/2015
4321	9*2^296870+7	89368	Lelio R Paula	08/2014
4322	100^44683-99^44683	89366	Robert Price	07/2013
4323	2^296810+76519	89349	Enzo Doria	05/2016
4324	8^98928+7^(98928+1)	89341	Robert Price	06/2016
4325	(3^187247+4)/1027	89337	Lelio R Paula	01/2013
4326	(3^187235-2)/2045	89331	Lelio R Paula	01/2013
4327	2^296736-432149	89327	Paul Bourdelais	05/2013
4328	2^296737-112519	89327	Enzo Doria	06/2014
4329	2^296718-3645	89322	Lelio R Paula	11/2013
4330	2^296681-16221	89310	Enzo Doria	04/2013
4331	2^296669-16513	89307	Enzo Doria	04/2013
4332	2^296619-16357	89292	Enzo Doria	04/2013
4333	2^296614-110051	89290	Enzo Doria	04/2014
4334	(3^187138+8)/83147	89283	Lelio R Paula	01/2013
4335	(2*10^89279+457)/9	89279	Robert Price	01/2017
4336	15^75907-28	89274	Lelio R Paula	11/2015
4337	2^296547-37	89270	Yves Minet	01/2012
4338	2^296485+191	89251	Lelio R Paula	10/2012
4339	2^296467-75	89246	Lelio R Paula	10/2012
4340	2^296416-109535	89231	Enzo Doria	04/2014
4341	(23*2^296406+1)/3	89228	Lelio R Paula	01/2013
4342	66^49037-65	89225	Norbert Schneider	11/2014
4343	2^296377-16245	89219	Enzo Doria	04/2013
4344	2^296372-64875	89217	Lelio R Paula	11/2013
4345	5*6^114648-7	89215	Lelio R Paula	10/2014
4346	3*10^89206+13	89207	Robert Price	08/2017
4347	7*3^186960-4	89204	Lelio R Paula	08/2014
4348	2^296290-112133	89193	Enzo Doria	06/2014
4349	6^114620-17003	89192	Enzo Doria	02/2013
4350	(4*10^89189+41)/9	89189	Robert Price	11/2014
4351	2^296261-161181	89184	Enzo Doria	04/2013
4352	(19*2^296269-1)/530623	89182	Lelio R Paula	02/2014
4353	3^186903-10	89176	Robert Price	09/2013
4356	7*10^89169-3	89170	Dmitry Domanov	11/2010
4354	(2^296221-1017)/35	89170	Lelio R Paula	01/2013
4355	(43*10^89169+47)/9	89170	Robert Price	12/2017
4357	(10^89160+29)/3	89160	Serge Batalov	12/2014
4358	(28*10^89141-97)/3	89142	Robert Price	07/2016
4359	2^296116-734639	89140	Paul Bourdelais	04/2013
4360	6^114544-133	89133	Lelio R Paula	12/2015
4361	2^296076-113297	89128	Enzo Doria	07/2014
4362	(11*2^296060-1)/215	89122	Lelio R Paula	02/2014
4363	5*10^89118+81	89119	Robert Price	08/2017
4364	2^296037-1411	89117	Yves Minet	01/2013
4365	2^296020-2604809	89111	Enzo Doria	05/2015
4366	2^296016+81	89110	Henri Lifchitz	02/2007
4367	2^296010-11	89108	Lelio R Paula	10/2012
4368	2^295998-111911	89105	Enzo Doria	05/2014
4369	(2^296014+47)/93991149	89102	Lelio R Paula	01/2013
4370	2^295939-16621	89087	Enzo Doria	04/2013
4371	2^295934-109691	89086	Enzo Doria	04/2014
4372	(185*10^89063+7)/3	89065	Robert Price	02/2017
4373	2^295831+143	89055	Lelio R Paula	10/2012
4374	31^59713-30	89054	Theodore Burton	02/2007
4375	(7*2^295834-1)/27663	89052	Lelio R Paula	02/2014
4376	123^42608+2	89047	Lelio R Paula	05/2013
4377	6^114433-114433^6	89047	Norbert Schneider	04/2017
4378	2^295800-459659	89045	Enzo Doria	05/2015
4379	(52*10^89037-1)/3	89039	Robert Price	02/2017
4380	(6^114398-11)/5	89019	Paul Bourdelais	11/2011
4381	11^85470-5850	89008	Enzo Doria	02/2013
4382	(27*2^295634+1)/4687	88993	Lelio R Paula	01/2013
4383	(p(18424)#-4)/2	88985	Robert Price	09/2017
4384	2^295564-189	88974	Lelio R Paula	10/2012
4385	2^295557+73097	88972	Enzo Doria	04/2016
4386	11^85433-5760	88970	Enzo Doria	01/2013
4387	6*10^88938-91	88939	Robert Price	11/2017
4388	15^75619-88	88935	Lelio R Paula	11/2015
4389	2^295385-85	88920	Lelio R Paula	10/2012
4390	2^295385-16333	88920	Enzo Doria	04/2013
4391	2^295309+59	88897	Lelio R Paula	10/2012
4392	2^295288-109799	88891	Enzo Doria	04/2014
4393	2^295245+65	88878	Lelio R Paula	10/2012
4394	Padovan(727734)	88874	Eric W. Weisstein	04/2011
4395	18^70793-17	88865	Lelio R Paula	11/2015
4396	6^114196-17573	88862	Enzo Doria	02/2013
4397	302^35829+35829^302	88857	Norbert Schneider	12/2014
4398	3^186223+16	88851	Robert Price	10/2013
4399	3*2^295139+7	88847	Lelio R Paula	08/2014
4400	3^186212-113008	88846	Enzo Doria	07/2014
4401	87^45803-86	88836	Norbert Schneider	11/2015
4402	2^295094-110273	88833	Enzo Doria	05/2014
4403	2^295080+1869151	88828	Enzo Doria	05/2016
4404	2^295027-113407	88812	Enzo Doria	07/2014
4405	(2*10^88808-71)/3	88808	Robert Price	01/2017
4406	13^79722-80	88806	Lelio R Paula	11/2015
4407	3^186103+104	88794	Lelio R Paula	12/2015
4408	(3*2^294971+1)/25565	88792	Lelio R Paula	01/2013
4409	2^294937-115003	88785	Enzo Doria	06/2015
4410	2^294868-109709	88765	Enzo Doria	04/2014
4411	2^294864-2985	88763	Yves Minet	09/2014
4412	(17*10^88761-41)/3	88762	Robert Price	09/2017
4413	2^294754+15015	88730	Lelio R Paula	10/2013
4414	(3^185951-7)/20	88720	Lelio R Paula	01/2013
4415	(2^294661+5)/443693383	88694	Lelio R Paula	01/2013
4416	(10^88680+11)/3	88680	Robert Price	11/2014
4417	2*7^104928-9	88675	Lelio R Paula	10/2014
4418	11^85150+12	88675	Lelio R Paula	11/2015
4419	8*6^113951+5	88673	Lelio R Paula	10/2014
4420	6^113940-18563	88663	Enzo Doria	03/2013
4421	38^56123-56123^38	88663	Norbert Schneider	02/2017
4422	2^294492-65	88651	Lelio R Paula	10/2012
4423	20^68120-53	88627	Lelio R Paula	01/2016
4424	2^294391-113257	88621	Enzo Doria	07/2014
4425	5^126784-15476	88619	Enzo Doria	02/2013
4426	2^294327+9	88602	Lelio R Paula	10/2012
4427	2^294320+18915	88600	Lelio R Paula	10/2013
4428	(98*10^88595-89)/99	88595	Ray Chandler	07/2011
4429	(17*2^294262-1)/13	88582	Lelio R Paula	02/2014
4430	(2*10^88545+7)/9	88545	Erik Branger	03/2011
4431	2^294137-133	88545	Lelio R Paula	10/2012
4432	(2^294092-1017)/1171	88528	Lelio R Paula	01/2013
4433	4^147036+147036^4+1	88525	Robert Price	04/2014
4434	(14^77213-5^77213)/9	88496	Robert Price	04/2013
4435	2^293965+2793377	88493	Enzo Doria	03/2016
4436	11^84971-150	88489	Enzo Doria	08/2012
4437	(2^293956-1017)/39851376696677	88476	Lelio R Paula	01/2013
4438	11^84958-2190	88475	Enzo Doria	12/2012
4439	2^293880-111347	88467	Enzo Doria	05/2014
4440	(106*10^88459-1)/3	88461	Serge Batalov	12/2014
4441	10^88457+278733	88458	Patrick De Geest	07/2017
4442	10^88457-401	88457	Robert Price	06/2017
4443	11^84908-1680	88423	Enzo Doria	12/2012
4444	2^293679-112075	88407	Enzo Doria	06/2014
4445	6^113608-65	88405	Lelio R Paula	12/2015
4446	2^293624+82875	88390	Lelio R Paula	10/2013
4447	2^293612-112337	88387	Enzo Doria	06/2014
4448	758^30693+30693^758	88386	Norbert Schneider	05/2017
4449	gcd(V(1062695),5F(212539)(F(212539)-1)+1)	88383	Serge Batalov	04/2015
4450	5*10^88377+77	88378	Robert Price	06/2016
4451	(5*2^293526+1)/303	88359	Lelio R Paula	01/2013
4452	2^293461-2785843	88341	Enzo Doria	03/2016
4453	2^293416-1037	88328	Yves Minet	11/2012
4454	(2^293384-7)/3	88317	Lelio R Paula	01/2013
4455	(3^185092-5)/4	88311	Lelio R Paula	01/2013
4456	(5*10^88303-173)/3	88304	Robert Price	11/2017
4457	14^77039-57	88297	Lelio R Paula	11/2015
4458	3*10^88293-59	88294	Robert Price	10/2017
4459	5^126303+42	88283	Lelio R Paula	10/2015
4460	19^69025-18	88266	Theodore Burton	01/2006
4461	5*10^88261-3	88262	Dmitry Domanov	11/2010
4462	8^97731-7^(97731-1)	88260	Robert Price	04/2016
4463	5*10^88254+59	88255	Robert Price	09/2016
4464	4*3^184968-7	88253	Lelio R Paula	08/2014
4465	7^104426+88	88251	Lelio R Paula	10/2015
4466	2^293142+99	88245	Lelio R Paula	10/2012
4467	11^84736-2130	88244	Enzo Doria	12/2012
4468	2^293068-89	88223	Lelio R Paula	10/2012
4469	2^293014-109655	88207	Enzo Doria	04/2014
4470	8*7^104371-3	88205	Lelio R Paula	10/2014
4471	2^292995-2145	88201	Lelio R Paula	10/2013
4472	5*10^88182+77	88183	Robert Price	06/2016
4474	2^292929+43877	88181	Donovan Johnson	04/2005
4473	6^113321+131	88181	Lelio R Paula	12/2015
4475	2^292904-583949	88173	Paul Bourdelais	04/2013
4476	2^292894-111851	88170	Enzo Doria	05/2014
4477	2^292872-2797349	88164	Enzo Doria	03/2016
4478	2^292860-109685	88160	Enzo Doria	04/2014
4479	9*6^113288-5	88157	Lelio R Paula	10/2014
4480	(2*10^88112-23)/3	88112	Robert Price	09/2017
4481	(73*10^88105+17)/9	88106	Robert Price	10/2015
4482	11^84588+78	88090	Lelio R Paula	11/2015
4483	(265*10^88077+11)/3	88079	Robert Price	03/2017
4484	91^44959-90^44959	88077	Robert Price	07/2015
4485	6^113177-5^113177	88069	Jean-Louis Charton	01/2009
4486	(10^88020+101)/3	88020	Robert Price	04/2016
4487	(10^(243982+1)-610^43982-1)/3	87965	Robert Price	02/2016
4488	(424*10^87930-1)/9	87932	Robert Price	11/2017
4489	p(18225)#/2+128	87929	Robert Price	04/2017
4490	4*6^112977+7	87914	Lelio R Paula	10/2014
4491	14^76677+69	87882	Lelio R Paula	11/2015
4492	(22*10^87863-1)/3	87864	Robert Price	12/2014
4493	2^291822-2797811	87848	Enzo Doria	04/2016
4494	2^291716-111389	87816	Enzo Doria	05/2014
4495	(782*10^87809-71)/9	87811	Robert Price	06/2017
4496	3^184039+1820	87809	Lelio R Paula	12/2015
4497	12^81356+41	87798	Lelio R Paula	11/2015
4498	6^112792-18983	87770	Enzo Doria	03/2013
4499	3*6^112787-5	87766	Lelio R Paula	10/2014
4500	7^103848+82	87762	Lelio R Paula	10/2015

Find by discoverer :

PRP Records

Probable Primes Top 10000

(211563 PRPs in the top)