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 ?
5251	11^78108-2040	81342	Enzo Doria	12/2012
5252	3^170400-58	81302	Lelio R Paula	12/2015
5253	(17*10^81300-131)/3	81301	Robert Price	12/2017
5254	10^81297+36991	81298	Patrick De Geest	06/2013
5255	10^81297-57	81297	Robert Price	05/2011
5256	2^270055-113047	81295	Enzo Doria	07/2014
5257	18^64759-55	81291	Lelio R Paula	11/2015
5258	(2^269987+1)/3	81274	H.&R. Lifchitz	10/2000
5259	(31^54493-1)/30	81268	Alexander Zhirkov	10/2010
5260	(2^270059-1)/540119/6481417/7124976157756725967	81265	Dario Alpern	09/2014
5261	(2^269816+7)/424901	81218	Lelio R Paula	12/2012
5262	(23*10^81214+1)/3	81215	Serge Batalov	06/2009
5263	(17*2^269720+1)/303	81193	Lelio R Paula	07/2012
5264	56^46441-55^46441	81188	Robert Price	10/2013
5265	2^269664+177	81177	Lelio R Paula	06/2012
5266	(13*2^269665-1)/185	81177	Lelio R Paula	02/2014
5267	2^269539-112249	81140	Enzo Doria	06/2014
5268	((2170026-3)3^(170026-1)+1)/4	81128	Robert Price	01/2015
5269	(2^269495-5)/9	81126	Lelio R Paula	12/2012
5270	2^269490-3623	81125	Yves Minet	10/2009
5271	(55459*2^269444+1)/35	81114	Lelio R Paula	06/2014
5272	(2^269417+78557)/5257	81099	Lelio R Paula	12/2012
5273	4*5^116011-7	81089	Lelio R Paula	10/2014
5274	7*10^81058+79	81059	Robert Price	02/2017
5275	2^269236-109907	81049	Enzo Doria	04/2014
5276	(8*10^81029-11)/3	81030	Erik Branger	03/2014
5277	3*10^81021+7	81022	Erik Branger	11/2013
5278	6^104115+103	81018	Lelio R Paula	12/2015
5279	2^269120+1869151	81014	Enzo Doria	05/2016
5280	5^115901+12	81012	Lelio R Paula	10/2015
5281	(2^269083-9)/320369	80997	Lelio R Paula	12/2012
5282	17^65810-20	80976	Lelio R Paula	11/2015
5283	20^62236-23	80971	Lelio R Paula	01/2016
5284	2^268974-112181	80970	Enzo Doria	06/2014
5286	L(387433)	80969	Renaud Lifchitz	11/2003
5285	V(387433)	80969	Serge Batalov	03/2015
5287	(2^268955-509203)/5	80963	Lelio R Paula	12/2012
5288	(87398^16384+1)/65537	80957	Lelio R Paula	11/2011
5289	329^32160+32160^329	80954	Norbert Schneider	11/2014
5290	2^268859-159	80935	Lelio R Paula	05/2012
5291	(2^268841-lucasV(1,2,268841)+1)/2	80929	Mike Oakes	11/2016
5292	2^268827+5775	80925	Lelio R Paula	07/2013
5293	2^268824-110255	80925	Enzo Doria	05/2014
5294	2^268798-1868321	80917	Enzo Doria	04/2016
5295	2^268753-114621	80903	Enzo Doria	05/2015
5296	2^268743+1605	80900	Lelio R Paula	07/2013
5297	6^103954-139	80892	Lelio R Paula	12/2015
5298	10^80883+49	80884	Robert Price	03/2011
5299	10^80883-80327	80883	Patrick De Geest	07/2013
5300	6^103937+121	80879	Lelio R Paula	12/2015
5301	(26*10^80875-119)/3	80876	Robert Price	07/2016
5302	(22699*2^268657+1)/6351	80875	Lelio R Paula	06/2014
5303	2^268581-869688105	80851	Lelio R Paula	05/2016
5304	(11*2^268521-1)/3	80834	Lelio R Paula	02/2014
5305	2^268516-249	80832	Yves Minet	02/2012
5306	2^268500+16095	80827	Lelio R Paula	07/2013
5307	3^169402+100	80826	Lelio R Paula	12/2015
5308	9^84698+8^(84698-1)	80823	Robert Price	03/2016
5309	2^268472-109739	80819	Enzo Doria	04/2014
5310	(9*2^268454+1)/37	80813	Lelio R Paula	12/2012
5311	(3*2^268502+1)/377902188435353647	80811	Lelio R Paula	12/2012
5312	134^37987-133^37987	80803	Jean-Louis Charton	12/2005
5313	15^68702-76	80800	Lelio R Paula	11/2015
5314	2^268408+7	80799	Lelio R Paula	05/2012
5315	2^268375+141	80789	Lelio R Paula	05/2012
5316	12^74856-47	80784	Lelio R Paula	11/2015
5317	6^103770-107	80749	Lelio R Paula	12/2015
5319	3^169224-62	80741	Lelio R Paula	12/2015
5318	p(16866)#/2+64	80741	Robert Price	03/2017
5320	5^115502-72	80733	Lelio R Paula	10/2015
5321	2^268079-1927	80700	Yves Minet	10/2009
5322	2^268028+117	80685	Lelio R Paula	05/2012
5323	121^38738+120	80683	Norbert Schneider	01/2015
5324	(3^169097-8)/835	80677	Lelio R Paula	12/2012
5325	2^267918+67	80652	Lelio R Paula	05/2012
5326	(89*10^80650-179)/9	80651	Robert Price	11/2017
5327	(302*10^80638+13)/9	80640	Robert Price	01/2017
5328	3^169004+2660	80636	Lelio R Paula	12/2015
5329	2^267860-112859	80634	Enzo Doria	06/2014
5330	2^267828-110705	80625	Enzo Doria	05/2014
5331	2^267743+12705	80599	Lelio R Paula	07/2013
5332	(22*10^80595+23)/9	80596	Robert Price	03/2015
5333	2^267674-51	80578	Lelio R Paula	05/2012
5334	(86*10^80571-41)/9	80572	Robert Price	11/2015
5335	2^267612-1965	80560	Lelio R Paula	07/2013
5336	2^267553+4097	80542	Lelio R Paula	07/2013
5337	7^95276-8	80518	Robert Price	01/2014
5338	(15185*2^267457-1)/47829	80513	Lelio R Paula	04/2015
5339	6^103467+163	80513	Lelio R Paula	12/2015
5340	(7*10^80490+143)/3	80491	Robert Price	04/2016
5341	86^41597-85^41597	80470	Robert Price	04/2015
5342	13^72237+30	80468	Lelio R Paula	11/2015
5343	17^65389+14	80458	Lelio R Paula	11/2015
5344	423^30634+30634^423	80456	Norbert Schneider	05/2017
5345	2^267232+105	80445	Lelio R Paula	05/2012
5346	11^77237-3072000	80435	Enzo Doria	01/2013
5347	2^267116-459959	80410	Enzo Doria	06/2015
5348	38715!2+8	80406	Robert Price	01/2015
5349	(2^267017+1)/3	80380	H.&R. Lifchitz	09/2000
5350	2^266968-45	80366	Lelio R Paula	05/2012
5351	20^61768-63	80363	Lelio R Paula	01/2016
5352	2^266920-112967	80351	Enzo Doria	06/2014
5353	8*10^80342+87	80343	Robert Price	10/2017
5354	12^74428-13	80322	Lelio R Paula	11/2015
5355	2^266680+27	80279	Lelio R Paula	05/2012
5356	2^266630-131	80264	Lelio R Paula	05/2012
5357	2^266598+76819	80254	Enzo Doria	05/2016
5358	2^266587+1880633	80251	Enzo Doria	10/2016
5359	2^266541-110049	80237	Enzo Doria	04/2014
5360	38635!2-8	80222	Robert Price	06/2015
5361	3^168111+168111^3-1	80210	Robert Price	04/2014
5362	2^266443+513	80208	Lelio R Paula	07/2013
5363	(26*10^80200+61)/3	80201	Robert Price	06/2017
5364	2^266412-109913	80199	Enzo Doria	04/2014
5365	(10223*2^266417+1)/45091	80199	Lelio R Paula	06/2014
5366	13^71988+66	80191	Lelio R Paula	11/2015
5367	11^77002-4320	80190	Enzo Doria	01/2013
5368	18^63879-13	80186	Lelio R Paula	11/2015
5369	2^266368-112295	80185	Enzo Doria	06/2014
5370	(3^168050+5)/1021454	80175	Lelio R Paula	10/2012
5371	(22*10^80167+41)/9	80168	Robert Price	02/2015
5372	(34*10^80162-43)/9	80163	Ray Chandler	12/2010
5373	(38*10^80150-11)/9	80151	Robert Price	05/2015
5374	(598*10^80149-31)/9	80151	Robert Price	02/2017
5375	19^62678-80	80150	Lelio R Paula	12/2015
5376	10^80139+32343	80140	Patrick De Geest	02/2011
5377	10^80139-9	80139	Alexander Gramolin	01/2011
5378	3^167955-106	80135	Lelio R Paula	12/2015
5379	(197*10^80089-11)/3	80091	Robert Price	10/2017
5380	2^265998+75559	80074	Enzo Doria	04/2016
5381	2^265969-109801	80065	Enzo Doria	04/2014
5382	2^265888-112757	80041	Enzo Doria	06/2014
5383	2^265809+1701	80017	Lelio R Paula	07/2013
5384	gcd(V(957175),5F(191435)(F(191435)+1)+1)	80014	Serge Batalov	04/2015
5385	3^167687-104	80008	Lelio R Paula	02/2015
5386	11^76826-5790	80007	Enzo Doria	01/2013
5387	10^80000+85731	80001	Patrick De Geest	10/2009
5388	10^80000-7169	80000	Patrick De Geest	09/2009
5389	10^79999+22399	80000	Patrick De Geest	09/2009
5390	10^79999-74873	79999	Patrick De Geest	09/2009
5391	3^167668+58	79998	Lelio R Paula	02/2015
5392	155^36506-2	79961	Lelio R Paula	10/2017
5393	2^265612+4257	79958	Lelio R Paula	07/2013
5394	5*3^167577+4	79956	Lelio R Paula	06/2014
5395	(9179*2^265593-1)/9	79955	Lelio R Paula	04/2015
5396	6^102723-43	79935	Lelio R Paula	04/2015
5397	11^76748-3360	79925	Enzo Doria	12/2012
5398	(13*2^265498-1)/187119	79919	Lelio R Paula	02/2014
5399	2^265399-109855	79894	Enzo Doria	04/2014
5400	(20^61403-1)/19	79886	Paul Bourdelais	03/2010
5401	18^63635+59	79880	Lelio R Paula	02/2015
5402	(11*10^79867-107)/3	79868	Robert Price	11/2016
5403	3^167375+80	79859	Lelio R Paula	02/2015
5404	5^114240-14486	79851	Enzo Doria	02/2013
5405	49^47238+48	79842	Norbert Schneider	07/2014
5406	2^265212-3779	79837	Yves Minet	04/2017
5407	91^40746+40746^91	79824	Norbert Schneider	12/2014
5408	(68*10^79813-257)/9	79814	Robert Price	06/2017
5409	(5*2^265118-1)/61	79808	Lelio R Paula	02/2014
5410	2^265074+28425	79796	Lelio R Paula	07/2013
5411	2^265072+1185	79795	Lelio R Paula	07/2013
5412	p(16682)#/2-128	79771	Robert Price	05/2017
5413	3^167167-34	79759	Robert Price	11/2013
5414	12^73906+29	79758	Lelio R Paula	02/2015
5415	2^264934+255	79754	Lelio R Paula	07/2013
5416	4*10^79729-87	79730	Robert Price	03/2017
5417	2^264846-111701	79727	Enzo Doria	05/2014
5418	2^264831-112041	79723	Enzo Doria	06/2014
5419	2^264816-455	79718	Yves Minet	03/2012
5420	(55*10^79711+89)/9	79712	Robert Price	09/2017
5421	47^47667-46	79704	Theodore Burton	02/2007
5422	13^71547+96	79700	Lelio R Paula	03/2015
5423	2^264752-112883	79699	Enzo Doria	06/2014
5424	2^264732+133	79693	Lelio R Paula	05/2012
5425	8*3^167010+7	79685	Lelio R Paula	06/2014
5426	42^49087-41	79681	Norbert Schneider	06/2014
5427	(26*10^79678-119)/3	79679	Robert Price	07/2016
5428	2^264683-21	79678	Lelio R Paula	05/2012
5429	7^94279+18	79675	Lelio R Paula	02/2015
5430	2^264655-127	79670	Lelio R Paula	02/2012
5431	2^264597-459043	79652	Enzo Doria	05/2015
5432	(21*2^264566+1)/5	79643	Lelio R Paula	10/2012
5433	2^264536+1870021	79634	Enzo Doria	05/2016
5434	(17*2^264512-1)/359	79625	Lelio R Paula	02/2014
5435	2^264477-109783	79616	Enzo Doria	04/2014
5436	18^63419-1333	79609	Enzo Doria	03/2013
5437	13^71451-36	79593	Lelio R Paula	03/2015
5438	(2^264410-5)/128002609121	79585	Lelio R Paula	10/2012
5439	19^62234+90	79582	Lelio R Paula	03/2015
5440	12^73714+49	79551	Lelio R Paula	02/2015
5441	(3*2^264184-1)/1433339	79522	Lelio R Paula	02/2014
5442	2^264103-112531	79503	Enzo Doria	06/2014
5443	19^62170+78	79501	Lelio R Paula	03/2015
5444	11^76340-2580	79500	Enzo Doria	12/2012
5445	(23*10^79492-11)/3	79493	Robert Price	10/2015
5446	((2^132049+13650)^2+(2^132049+13650)+41)/2003/23841473	79491	Makoto Morimoto	05/2016
5447	2^264060-112133	79490	Enzo Doria	06/2014
5448	((2^132049+4641)^2+(2^132049+4641)+41)/487/8537/10426147	79488	Makoto Morimoto	05/2016
5449	9^83298+6^83298-2^83298	79487	Mike Oakes	08/2010
5450	18^63319+35	79483	Lelio R Paula	02/2015
5451	38303!2+256	79461	Robert Price	01/2015
5452	(29*10^79445+61)/9	79446	Robert Price	04/2015
5453	2^263902-195	79443	Lelio R Paula	05/2012
5454	3^166499-112696	79441	Enzo Doria	06/2014
5455	11^76279-2760	79437	Enzo Doria	12/2012
5456	6^102077-25	79432	Lelio R Paula	03/2015
5457	2^263852-1017	79428	Lelio R Paula	07/2013
5458	2^263842-33	79425	Lelio R Paula	05/2012
5459	12^73584-55	79411	Lelio R Paula	02/2015
5460	2^263772-185	79404	Lelio R Paula	05/2012
5461	(15^67489+1)/16	79373	Paul Bourdelais	03/2010
5462	2^263664+15015	79371	Lelio R Paula	07/2013
5463	10^79362+3^79363	79363	Mike Oakes	06/2010
5464	Phi(163244,10)/2448661/6856249	79331	Maksym Voznyy	11/2015
5465	3^166262+44	79328	Lelio R Paula	02/2015
5466	4*10^79327-63	79328	Robert Price	12/2016
5467	2^263486+513	79318	Lelio R Paula	07/2013
5468	2^263448-519509	79306	Paul Bourdelais	03/2013
5469	21^59971-20^59971	79295	Robert Price	05/2012
5470	2^263372+123	79283	Lelio R Paula	05/2012
5471	17^64429+84	79277	Lelio R Paula	03/2015
5472	11^76124-11430	79275	Enzo Doria	12/2012
5473	(206*10^79268-17)/9	79270	Robert Price	03/2017
5474	13^71157+18	79265	Lelio R Paula	03/2015
5475	2^263297+65835	79261	Lelio R Paula	07/2013
5476	19^61980-18	79258	Theodore Burton	12/2005
5477	2*10^79242+93	79243	Robert Price	07/2016
5478	(88^40751-1)/87	79238	Paul Bourdelais	08/2017
5479	(103*29^54179-39)/4	79233	Curtis Bright	05/2015
5480	9^83024-83024^9	79226	Norbert Schneider	08/2017
5481	17^64382-26	79219	Lelio R Paula	03/2015
5482	7^93733-74	79214	Lelio R Paula	02/2015
5483	15^67352+38	79213	Lelio R Paula	02/2015
5484	2^263135-110235	79212	Enzo Doria	05/2014
5485	2^263044+4257	79185	Lelio R Paula	07/2013
5487	2^263032+87517	79181	Yves Minet	11/2010
5486	6^101755+95	79181	Lelio R Paula	03/2015
5488	4^131497-3^131497	79170	Jean-Louis Charton	05/2004
5489	5*7^93674+8	79165	Lelio R Paula	10/2014
5490	lucasU(486,25,29457)-5*lucasU(486,25,29456)	79137	Mike Oakes	05/2009
5491	260^32768+179^32768	79134	Serge Batalov	03/2018
5492	11^75978-42	79123	Lelio R Paula	02/2015
5493	8*5^113180+9	79111	Lelio R Paula	10/2014
5494	(6883*2^262741-1)/4835	79094	Lelio R Paula	04/2015
5495	(9*2^262745+1)/137	79093	Lelio R Paula	10/2012
5496	12^73285+85	79088	Lelio R Paula	02/2015
5497	19^61840+52	79079	Lelio R Paula	03/2015
5498	(10^79067+77)/3	79067	Robert Price	01/2017
5499	(1017*2^262640-1)/11557	79062	Lelio R Paula	04/2015
5500	10^79040+137949	79041	Patrick De Geest	02/2016

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PRP Records

Probable Primes Top 10000

(218736 PRPs in the top)