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	(32*10^90669+13)/9	90670	Robert Price	04/2015
4252	3*5^129698+8	90656	Lelio R Paula	10/2014
4253	F(433781)	90655	Henri Lifchitz	09/2003
4254	19^70891+82	90653	Lelio R Paula	06/2016
4255	(29*2^301124-1)/13	90648	Lelio R Paula	02/2014
4256	7*3^189953-8	90632	Lelio R Paula	08/2014
4257	11^87022-1800	90625	Enzo Doria	12/2012
4258	(2^301042+47)/12036969	90616	Lelio R Paula	06/2013
4259	2^301004-2786939	90612	Enzo Doria	03/2016
4260	2^300980-27	90605	Lelio R Paula	11/2012
4261	2*10^90597-7	90598	Dmitry Domanov	11/2010
4262	197^39485+2	90597	Lelio R Paula	06/2013
4263	7^107198+48	90593	Lelio R Paula	04/2016
4264	(86*10^90588+121)/9	90589	Robert Price	03/2017
4265	2^300923+53	90587	Lelio R Paula	11/2012
4266	2^300874+7	90573	Lelio R Paula	10/2012
4267	5^129568-56	90565	Lelio R Paula	04/2016
4268	2^300847-112831	90564	Enzo Doria	06/2014
4269	2^300718+255255	90526	Lelio R Paula	02/2016
4270	2^300637+95	90501	Lelio R Paula	11/2012
4271	7^107087-24	90500	Lelio R Paula	04/2016
4272	(10^90499+3^90499)/13	90498	Robert Price	01/2013
4273	13^81241+90	90498	Lelio R Paula	06/2016
4274	6^116273-85	90478	Lelio R Paula	05/2016
4275	6^116256-17573	90465	Enzo Doria	02/2013
4276	2^300502+54615	90461	Lelio R Paula	02/2016
4277	(13*2^300487+1)/45	90456	Lelio R Paula	09/2013
4278	(3^189545-8)/5	90436	Lelio R Paula	01/2013
4279	(7*2^300406-1)/3	90432	Lelio R Paula	02/2014
4280	4*5^129332+3	90400	Lelio R Paula	10/2014
4281	2^300249-16245	90384	Enzo Doria	04/2013
4282	(7*10^90371-313)/9	90371	Robert Price	11/2016
4283	2*6^116118+7	90358	Lelio R Paula	10/2014
4284	(24737*2^300101+1)/25	90343	Lelio R Paula	06/2014
4285	4*10^90334-21	90335	Robert Price	04/2016
4286	2^300019-110335	90315	Enzo Doria	05/2014
4287	2^299949-1005	90294	Lelio R Paula	11/2013
4288	2^299868-109613	90270	Enzo Doria	04/2014
4289	5*2^299799-3	90250	Lelio R Paula	08/2014
4290	13^81008-2	90239	Lelio R Paula	09/2013
4291	64^49957-63^49957	90232	Robert Price	07/2013
4292	10^90227+56281	90228	Patrick De Geest	06/2016
4295	2^299725+315	90227	Lelio R Paula	11/2013
4293	10^90227-1000000001	90227	Robert Price	05/2016
4294	10^90227-68763	90227	Patrick De Geest	06/2016
4296	5^129082+48	90225	Lelio R Paula	03/2016
4297	2^299699+195	90219	Lelio R Paula	10/2012
4298	(55*10^90211-1)/9	90212	Ray Chandler	02/2012
4299	3^189053+280	90202	Lelio R Paula	04/2016
4300	2^299639-187	90201	Lelio R Paula	10/2012
4301	2^299631+183	90198	Lelio R Paula	10/2012
4302	(21*2^299611-1)/29	90192	Lelio R Paula	02/2014
4303	2^299567+113	90179	Lelio R Paula	10/2012
4304	2^299550+189	90174	Lelio R Paula	10/2012
4305	(2^299535+3)/29	90168	Lelio R Paula	01/2013
4306	(97*10^90155-1)/3	90157	Serge Batalov	12/2014
4307	3^188938+8680	90147	Lelio R Paula	04/2016
4308	6^115840-55	90142	Lelio R Paula	05/2016
4309	(5*10^90142-473)/9	90142	Robert Price	12/2017
4310	8*7^106659+5	90139	Lelio R Paula	10/2014
4311	2^299406-16653	90131	Enzo Doria	05/2013
4312	208049#+(216091#)/(208049#)	90128	Makoto Morimoto	04/2016
4313	(F(5)^128941-F(4)^128941)/F(3)	90126	Wayne Halsdorf	03/2012
4314	6^115819-53	90125	Lelio R Paula	05/2016
4315	6^115816-16853	90123	Enzo Doria	02/2013
4316	6^115813-23	90121	Lelio R Paula	05/2016
4317	(22*10^90110+161)/3	90111	Robert Price	02/2017
4318	(2^299330-509203)/69	90106	Lelio R Paula	01/2013
4319	(29*10^90096-17)/3	90097	Erik Branger	09/2014
4320	2^299247+1870529	90083	Enzo Doria	05/2016
4321	2^299229-2797783	90077	Enzo Doria	04/2016
4322	2^299220-16317	90075	Enzo Doria	04/2013
4323	11^86491-1350	90072	Enzo Doria	12/2012
4324	(31*10^90064-1)/3	90066	Robert Price	03/2017
4325	L(430949)/861899/1440387561539	90045	Serge Batalov	07/2017
4326	2^299112+73951	90042	Enzo Doria	04/2016
4327	8^99702+7^(99702-1)	90040	Robert Price	02/2016
4328	5*10^90033+3	90034	Dmitry Domanov	11/2010
4329	243^37738+37738^243	90029	Norbert Schneider	01/2015
4330	2^299048-113297	90023	Enzo Doria	07/2014
4331	3^188648+92	90008	Lelio R Paula	12/2015
4332	5*2^298991+7	90006	Lelio R Paula	08/2014
4333	(25*2^298997+1)/3267	90005	Lelio R Paula	01/2013
4334	10^90000+8869	90001	Patrick De Geest	12/2009
4336	10^89999+82939	90000	Dirk Augustin	04/2007
4335	10^90000-140343	90000	Patrick De Geest	12/2009
4337	10^89999-194891	89999	Patrick De Geest	11/2009
4338	19^70365-78	89980	Lelio R Paula	12/2015
4339	NaturalLogarithmOf2(89973)	89973	Eric W. Weisstein	10/2015
4340	2^298852-64875	89964	Lelio R Paula	11/2013
4341	18^71659+37	89952	Lelio R Paula	12/2015
4342	(2908*29^61501-3)/7	89942	Curtis Bright	05/2015
4343	17^73067+20	89906	Lelio R Paula	11/2015
4344	2^298637-99	89899	Lelio R Paula	10/2012
4345	9^94188+38^94188-24^94188-3*2^94188	89879	Mike Oakes	01/2011
4346	9*10^89858+19	89859	Robert Price	05/2016
4347	2^298501+1870067	89858	Enzo Doria	05/2016
4348	11^86280-98	89852	Lelio R Paula	11/2015
4349	2^298473-110059	89850	Enzo Doria	04/2014
4350	19^70263-32	89850	Lelio R Paula	12/2015
4351	(299*10^89836-17)/3	89838	Robert Price	01/2017
4352	3^188286+14	89836	Robert Price	09/2013
4353	gcd(V(1091095),5F(218219)(F(218219)+1)+1)	89822	Serge Batalov	04/2015
4354	2^298367+58905	89818	Lelio R Paula	11/2013
4355	2^298319-109657	89803	Enzo Doria	04/2014
4356	8*10^89800+81	89801	Robert Price	05/2017
4357	18^71505-91	89759	Lelio R Paula	12/2015
4358	(7^106187+1)/8	89738	Paul Bourdelais	04/2008
4359	2^298079-109531	89731	Enzo Doria	04/2014
4360	(22699*2^298016+1)/385	89714	Lelio R Paula	06/2014
4361	156(10^(422427)-1)/101-1	89709	Robert Price	05/2014
4362	2^298003-66945	89708	Lelio R Paula	11/2013
4363	(23*10^89705-83)/3	89706	Robert Price	09/2017
4364	17^72900-54	89700	Lelio R Paula	11/2015
4365	3*2^297956+5	89695	Lelio R Paula	08/2014
4366	20^68938-11	89691	Lelio R Paula	01/2016
4367	89*10^89687-7	89689	Robert Price	03/2017
4368	2^297923+77783	89684	Enzo Doria	05/2016
4369	11^86107-24576000	89672	Enzo Doria	02/2013
4370	2^297878-111911	89671	Enzo Doria	05/2014
4371	7^106084+40	89652	Lelio R Paula	10/2015
4372	(86*10^89640-311)/9	89641	Robert Price	10/2017
4373	3*10^89608-59	89609	Robert Price	10/2017
4374	3^187780-11038	89594	Enzo Doria	05/2014
4375	(13*2^297560-1)/49151787	89568	Lelio R Paula	02/2014
4376	5^128141-36	89567	Lelio R Paula	10/2015
4377	4*7^105951+9	89540	Lelio R Paula	10/2014
4378	(7*10^89539-439)/9	89539	Robert Price	09/2017
4379	2^297397+177257	89526	Enzo Doria	05/2016
4380	2^297346-16241	89511	Enzo Doria	04/2013
4381	(5*10^89510+79)/3	89511	Robert Price	11/2017
4383	4^148663-3^148663	89505	Jean-Louis Charton	11/2005
4382	2^297328-869688105	89505	Lelio R Paula	07/2016
4384	2^297325-459043	89504	Enzo Doria	05/2015
4385	2^297310-112391	89500	Enzo Doria	06/2014
4386	2^297296-112157	89496	Enzo Doria	06/2014
4387	57^50966-2	89490	Lelio R Paula	08/2013
4388	(266*10^89482+1)/3	89484	Robert Price	02/2016
4389	(14*10^89480-101)/3	89481	Robert Price	04/2017
4390	2^297122+99	89443	Lelio R Paula	10/2012
4391	(3^187435-5)/1286	89427	Lelio R Paula	01/2013
4392	(25*10^89413+161)/3	89414	Robert Price	01/2017
4393	2^296990+1870699	89403	Enzo Doria	05/2016
4394	2^296972-1017	89398	Lelio R Paula	11/2013
4395	(7*10^89383+167)/3	89384	Robert Kinser	10/2017
4396	(85*10^89375-31)/9	89376	Robert Price	11/2015
4397	9*2^296870+7	89368	Lelio R Paula	08/2014
4398	100^44683-99^44683	89366	Robert Price	07/2013
4399	2^296810+76519	89349	Enzo Doria	05/2016
4400	8^98928+7^(98928+1)	89341	Robert Price	06/2016
4401	(3^187247+4)/1027	89337	Lelio R Paula	01/2013
4402	(3^187235-2)/2045	89331	Lelio R Paula	01/2013
4403	2^296736-432149	89327	Paul Bourdelais	05/2013
4404	2^296737-112519	89327	Enzo Doria	06/2014
4405	2^296718-3645	89322	Lelio R Paula	11/2013
4406	2^296681-16221	89310	Enzo Doria	04/2013
4407	2^296669-16513	89307	Enzo Doria	04/2013
4408	2^296619-16357	89292	Enzo Doria	04/2013
4409	2^296614-110051	89290	Enzo Doria	04/2014
4410	(3^187138+8)/83147	89283	Lelio R Paula	01/2013
4411	(2*10^89279+457)/9	89279	Robert Price	01/2017
4412	15^75907-28	89274	Lelio R Paula	11/2015
4413	2^296547-37	89270	Yves Minet	01/2012
4414	2^296485+191	89251	Lelio R Paula	10/2012
4415	2^296467-75	89246	Lelio R Paula	10/2012
4416	2^296416-109535	89231	Enzo Doria	04/2014
4417	(23*2^296406+1)/3	89228	Lelio R Paula	01/2013
4418	66^49037-65	89225	Norbert Schneider	11/2014
4419	2^296377-16245	89219	Enzo Doria	04/2013
4420	2^296372-64875	89217	Lelio R Paula	11/2013
4421	5*6^114648-7	89215	Lelio R Paula	10/2014
4422	3*10^89206+13	89207	Robert Price	08/2017
4423	7*3^186960-4	89204	Lelio R Paula	08/2014
4424	2^296290-112133	89193	Enzo Doria	06/2014
4425	6^114620-17003	89192	Enzo Doria	02/2013
4426	(4*10^89189+41)/9	89189	Robert Price	11/2014
4427	2^296261-161181	89184	Enzo Doria	04/2013
4428	(19*2^296269-1)/530623	89182	Lelio R Paula	02/2014
4429	3^186903-10	89176	Robert Price	09/2013
4432	7*10^89169-3	89170	Dmitry Domanov	11/2010
4430	(2^296221-1017)/35	89170	Lelio R Paula	01/2013
4431	(43*10^89169+47)/9	89170	Robert Price	12/2017
4433	(10^89160+29)/3	89160	Serge Batalov	12/2014
4434	(28*10^89141-97)/3	89142	Robert Price	07/2016
4435	2^296116-734639	89140	Paul Bourdelais	04/2013
4436	6^114544-133	89133	Lelio R Paula	12/2015
4437	2^296076-113297	89128	Enzo Doria	07/2014
4438	(11*2^296060-1)/215	89122	Lelio R Paula	02/2014
4439	5*10^89118+81	89119	Robert Price	08/2017
4440	2^296037-1411	89117	Yves Minet	01/2013
4441	2^296020-2604809	89111	Enzo Doria	05/2015
4442	2^296016+81	89110	Henri Lifchitz	02/2007
4443	2^296010-11	89108	Lelio R Paula	10/2012
4444	2^295998-111911	89105	Enzo Doria	05/2014
4445	(2^296014+47)/93991149	89102	Lelio R Paula	01/2013
4446	2^295939-16621	89087	Enzo Doria	04/2013
4447	2^295934-109691	89086	Enzo Doria	04/2014
4448	(185*10^89063+7)/3	89065	Robert Price	02/2017
4449	2^295831+143	89055	Lelio R Paula	10/2012
4450	31^59713-30	89054	Theodore Burton	02/2007
4451	(7*2^295834-1)/27663	89052	Lelio R Paula	02/2014
4452	123^42608+2	89047	Lelio R Paula	05/2013
4453	6^114433-114433^6	89047	Norbert Schneider	04/2017
4454	2^295800-459659	89045	Enzo Doria	05/2015
4455	(52*10^89037-1)/3	89039	Robert Price	02/2017
4456	(6^114398-11)/5	89019	Paul Bourdelais	11/2011
4457	11^85470-5850	89008	Enzo Doria	02/2013
4458	(27*2^295634+1)/4687	88993	Lelio R Paula	01/2013
4459	(p(18424)#-4)/2	88985	Robert Price	09/2017
4460	2^295564-189	88974	Lelio R Paula	10/2012
4461	2^295557+73097	88972	Enzo Doria	04/2016
4462	11^85433-5760	88970	Enzo Doria	01/2013
4463	6*10^88938-91	88939	Robert Price	11/2017
4464	15^75619-88	88935	Lelio R Paula	11/2015
4465	2^295385-85	88920	Lelio R Paula	10/2012
4466	2^295385-16333	88920	Enzo Doria	04/2013
4467	2^295309+59	88897	Lelio R Paula	10/2012
4468	2^295288-109799	88891	Enzo Doria	04/2014
4469	10^88888+170373	88889	Stefano Morozzi	07/2018
4470	10^88888+271399	88889	Stefano Morozzi	07/2018
4471	10^88888+375397	88889	Stefano Morozzi	07/2018
4472	10^88888+548823	88889	Stefano Morozzi	07/2018
4473	10^88888+820861	88889	Stefano Morozzi	07/2018
4474	10^88888+1206349	88889	Stefano Morozzi	07/2018
4475	10^88888+1292047	88889	Stefano Morozzi	07/2018
4476	10^88888+1456029	88889	Stefano Morozzi	07/2018
4477	2^295245+65	88878	Lelio R Paula	10/2012
4478	Padovan(727734)	88874	Eric W. Weisstein	04/2011
4479	18^70793-17	88865	Lelio R Paula	11/2015
4480	6^114196-17573	88862	Enzo Doria	02/2013
4481	302^35829+35829^302	88857	Norbert Schneider	12/2014
4482	3^186223+16	88851	Robert Price	10/2013
4483	3*2^295139+7	88847	Lelio R Paula	08/2014
4484	3^186212-113008	88846	Enzo Doria	07/2014
4485	87^45803-86	88836	Norbert Schneider	11/2015
4486	2^295094-110273	88833	Enzo Doria	05/2014
4487	2^295080+1869151	88828	Enzo Doria	05/2016
4488	2^295027-113407	88812	Enzo Doria	07/2014
4489	(2*10^88808-71)/3	88808	Robert Price	01/2017
4490	13^79722-80	88806	Lelio R Paula	11/2015
4491	3^186103+104	88794	Lelio R Paula	12/2015
4492	(3*2^294971+1)/25565	88792	Lelio R Paula	01/2013
4493	2^294937-115003	88785	Enzo Doria	06/2015
4494	2^294868-109709	88765	Enzo Doria	04/2014
4495	2^294864-2985	88763	Yves Minet	09/2014
4496	(17*10^88761-41)/3	88762	Robert Price	09/2017
4497	2^294754+15015	88730	Lelio R Paula	10/2013
4498	(3^185951-7)/20	88720	Lelio R Paula	01/2013
4499	(2^294661+5)/443693383	88694	Lelio R Paula	01/2013
4500	(10^88680+11)/3	88680	Robert Price	11/2014

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PRP Records

Probable Primes Top 10000

(218736 PRPs in the top)