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	(68*10^79813-257)/9	79814	Robert Price	06/2017
5252	(5*2^265118-1)/61	79808	Lelio R Paula	02/2014
5253	2^265074+28425	79796	Lelio R Paula	07/2013
5254	2^265072+1185	79795	Lelio R Paula	07/2013
5255	p(16682)#/2-128	79771	Robert Price	05/2017
5256	3^167167-34	79759	Robert Price	11/2013
5257	12^73906+29	79758	Lelio R Paula	02/2015
5258	2^264934+255	79754	Lelio R Paula	07/2013
5259	4*10^79729-87	79730	Robert Price	03/2017
5260	2^264846-111701	79727	Enzo Doria	05/2014
5261	2^264831-112041	79723	Enzo Doria	06/2014
5262	2^264816-455	79718	Yves Minet	03/2012
5263	(55*10^79711+89)/9	79712	Robert Price	09/2017
5264	47^47667-46	79704	Theodore Burton	02/2007
5265	13^71547+96	79700	Lelio R Paula	03/2015
5266	2^264752-112883	79699	Enzo Doria	06/2014
5267	2^264732+133	79693	Lelio R Paula	05/2012
5268	8*3^167010+7	79685	Lelio R Paula	06/2014
5269	42^49087-41	79681	Norbert Schneider	06/2014
5270	(26*10^79678-119)/3	79679	Robert Price	07/2016
5271	2^264683-21	79678	Lelio R Paula	05/2012
5272	7^94279+18	79675	Lelio R Paula	02/2015
5273	2^264655-127	79670	Lelio R Paula	02/2012
5274	2^264597-459043	79652	Enzo Doria	05/2015
5275	(21*2^264566+1)/5	79643	Lelio R Paula	10/2012
5276	2^264536+1870021	79634	Enzo Doria	05/2016
5277	(17*2^264512-1)/359	79625	Lelio R Paula	02/2014
5278	2^264477-109783	79616	Enzo Doria	04/2014
5279	18^63419-1333	79609	Enzo Doria	03/2013
5280	13^71451-36	79593	Lelio R Paula	03/2015
5281	(2^264410-5)/128002609121	79585	Lelio R Paula	10/2012
5282	19^62234+90	79582	Lelio R Paula	03/2015
5283	12^73714+49	79551	Lelio R Paula	02/2015
5284	(3*2^264184-1)/1433339	79522	Lelio R Paula	02/2014
5285	2^264103-112531	79503	Enzo Doria	06/2014
5286	19^62170+78	79501	Lelio R Paula	03/2015
5287	11^76340-2580	79500	Enzo Doria	12/2012
5288	(23*10^79492-11)/3	79493	Robert Price	10/2015
5289	((2^132049+13650)^2+(2^132049+13650)+41)/2003/23841473	79491	Makoto Morimoto	05/2016
5290	2^264060-112133	79490	Enzo Doria	06/2014
5291	((2^132049+4641)^2+(2^132049+4641)+41)/487/8537/10426147	79488	Makoto Morimoto	05/2016
5292	9^83298+6^83298-2^83298	79487	Mike Oakes	08/2010
5293	18^63319+35	79483	Lelio R Paula	02/2015
5294	38303!2+256	79461	Robert Price	01/2015
5295	(29*10^79445+61)/9	79446	Robert Price	04/2015
5296	2^263902-195	79443	Lelio R Paula	05/2012
5297	3^166499-112696	79441	Enzo Doria	06/2014
5298	11^76279-2760	79437	Enzo Doria	12/2012
5299	6^102077-25	79432	Lelio R Paula	03/2015
5300	2^263852-1017	79428	Lelio R Paula	07/2013
5301	2^263842-33	79425	Lelio R Paula	05/2012
5302	12^73584-55	79411	Lelio R Paula	02/2015
5303	2^263772-185	79404	Lelio R Paula	05/2012
5304	(15^67489+1)/16	79373	Paul Bourdelais	03/2010
5305	2^263664+15015	79371	Lelio R Paula	07/2013
5306	10^79362+3^79363	79363	Mike Oakes	06/2010
5307	Phi(163244,10)/2448661/6856249	79331	Maksym Voznyy	11/2015
5308	3^166262+44	79328	Lelio R Paula	02/2015
5309	4*10^79327-63	79328	Robert Price	12/2016
5310	2^263486+513	79318	Lelio R Paula	07/2013
5311	2^263448-519509	79306	Paul Bourdelais	03/2013
5312	21^59971-20^59971	79295	Robert Price	05/2012
5313	2^263372+123	79283	Lelio R Paula	05/2012
5314	17^64429+84	79277	Lelio R Paula	03/2015
5315	11^76124-11430	79275	Enzo Doria	12/2012
5316	(206*10^79268-17)/9	79270	Robert Price	03/2017
5317	13^71157+18	79265	Lelio R Paula	03/2015
5318	2^263297+65835	79261	Lelio R Paula	07/2013
5319	19^61980-18	79258	Theodore Burton	12/2005
5320	2*10^79242+93	79243	Robert Price	07/2016
5321	(88^40751-1)/87	79238	Paul Bourdelais	08/2017
5322	(103*29^54179-39)/4	79233	Curtis Bright	05/2015
5323	9^83024-83024^9	79226	Norbert Schneider	08/2017
5324	17^64382-26	79219	Lelio R Paula	03/2015
5325	7^93733-74	79214	Lelio R Paula	02/2015
5326	15^67352+38	79213	Lelio R Paula	02/2015
5327	2^263135-110235	79212	Enzo Doria	05/2014
5328	2^263044+4257	79185	Lelio R Paula	07/2013
5330	2^263032+87517	79181	Yves Minet	11/2010
5329	6^101755+95	79181	Lelio R Paula	03/2015
5331	4^131497-3^131497	79170	Jean-Louis Charton	05/2004
5332	5*7^93674+8	79165	Lelio R Paula	10/2014
5333	lucasU(486,25,29457)-5*lucasU(486,25,29456)	79137	Mike Oakes	05/2009
5334	260^32768+179^32768	79134	Serge Batalov	03/2018
5335	11^75978-42	79123	Lelio R Paula	02/2015
5336	8*5^113180+9	79111	Lelio R Paula	10/2014
5337	(6883*2^262741-1)/4835	79094	Lelio R Paula	04/2015
5338	(9*2^262745+1)/137	79093	Lelio R Paula	10/2012
5339	12^73285+85	79088	Lelio R Paula	02/2015
5340	19^61840+52	79079	Lelio R Paula	03/2015
5341	(10^79067+77)/3	79067	Robert Price	01/2017
5342	(1017*2^262640-1)/11557	79062	Lelio R Paula	04/2015
5343	10^79040+137949	79041	Patrick De Geest	02/2016
5345	10^79040-1007297	79040	Robert Price	02/2015
5344	10^79040-77427	79040	Patrick De Geest	02/2016
5346	2^262551-17295	79036	Lelio R Paula	07/2013
5347	3^165597+340	79010	Lelio R Paula	02/2015
5348	(23*2^262435+1)/55	79001	Lelio R Paula	10/2012
5349	11^75860-2100	79001	Enzo Doria	12/2012
5350	8*7^93463+9	78987	Lelio R Paula	10/2014
5351	67^43240-2	78960	Lelio R Paula	09/2013
5352	1000001^13159-1000000^13159	78953	Jean-Louis Charton	10/2003
5353	2^262199-110287	78930	Enzo Doria	05/2014
5354	(19*2^262180-1)/177	78924	Lelio R Paula	02/2014
5355	(3^165403+4)/7	78917	Lelio R Paula	10/2012
5357	2^21068*(2^241076+1)-1	78914	Makoto Morimoto	03/2014
5358	2^29258*(2^232886+1)-1	78914	Makoto Morimoto	03/2014
5356	2^262144+18531	78914	Makoto Morimoto	12/2015
5359	(2^(2^18)+2450)/(23^2137*577)	78908	Makoto Morimoto	08/2017
5360	(2^(2^18)-5719)/(35993623)	78907	Makoto Morimoto	08/2017
5361	14^68837+75	78897	Lelio R Paula	02/2015
5362	106^38949+105	78884	Norbert Schneider	12/2016
5363	(70^42737+1)/71	78853	Paul Bourdelais	08/2017
5364	(25*2^261917-1)/20927	78842	Lelio R Paula	02/2014
5365	2^261881-1859713	78835	Enzo Doria	03/2016
5366	2^261874+1915	78832	Lelio R Paula	07/2013
5367	2^261856+98765331	78827	Jason Earls	01/2009
5368	(5*2^261857-1)/20501277	78821	Lelio R Paula	02/2014
5369	2^261724+92691	78787	Tony Prest / Never Odd Or Even	03/2014
5370	2^261724+285111	78787	Tony Prest / Never Odd Or Even	04/2014
5371	2^261724+293713	78787	Tony Prest / Never Odd Or Even	04/2014
5372	(2^261724+381949)/5	78787	Tony Prest / Never Odd Or Even	04/2014
5373	2^261724+572971	78787	Tony Prest / Never Odd Or Even	05/2014
5374	(2^261724+392705)/3/7	78786	Tony Prest / Never Odd Or Even	04/2014
5375	(2^261724+629709)/5/5	78786	Tony Prest / Never Odd Or Even	05/2014
5376	(2^261724+67397)/3/103	78785	Tony Prest / Never Odd Or Even	04/2014
5377	(2^261724+323043)/11/103	78784	Tony Prest / Never Odd Or Even	04/2014
5378	(2^261724+370143)/1289	78784	Tony Prest / Never Odd Or Even	04/2014
5379	(2^261724+560259)/5/5/73	78784	Tony Prest / Never Odd Or Even	05/2014
5380	(2^261724+64109)/3/3/3/5/5/19	78783	Tony Prest / Never Odd Or Even	04/2014
5381	(2^261724+394491)/55787	78783	Tony Prest / Never Odd Or Even	04/2014
5382	(2^261724+625897)/23/883	78783	Tony Prest / Never Odd Or Even	05/2014
5383	(2^261724+292471)/13/97/151	78782	Tony Prest / Never Odd Or Even	04/2014
5384	(2^261724+154303)/11/67/127	78782	Tony Prest / Never Odd Or Even	04/2014
5385	(2^261724+313319)/3/3/3/3/5/11/113	78782	Tony Prest / Never Odd Or Even	04/2014
5386	(2^261724+383949)/5/41/43/83	78781	Tony Prest / Never Odd Or Even	04/2014
5387	(2^261724+626567)/3/331/631	78781	Tony Prest / Never Odd Or Even	05/2014
5388	(2^261724+32987)/3/3/19/223/1031	78780	Tony Prest / Never Odd Or Even	04/2014
5389	(2^261724+5813)/3/5991397	78780	Tony Prest / Never Odd Or Even	04/2014
5390	(2^261724+13481)/3/11/239/2087	78780	Tony Prest / Never Odd Or Even	04/2014
5391	(2^261724+103399)/5/13/37/10607	78780	Tony Prest / Never Odd Or Even	04/2014
5392	(2^261724+18477)/367/65111	78780	Tony Prest / Never Odd Or Even	04/2014
5393	(2^261724+121285)/167/227/1217	78780	Tony Prest / Never Odd Or Even	04/2014
5394	(2^261724+262037)/3/3/11/23/18517	78780	Tony Prest / Never Odd Or Even	04/2014
5395	(2^261724+586157)/3/7/457/1259	78780	Tony Prest / Never Odd Or Even	05/2014
5396	(2^261724+315287)/3/45822541	78779	Tony Prest / Never Odd Or Even	04/2014
5397	(2^261724+605675)/3/3/3/103/207481	78779	Tony Prest / Never Odd Or Even	05/2014
5398	(2^261724+60031)/13/31/7024877	78778	Tony Prest / Never Odd Or Even	04/2014
5399	(2^261724+121879)/5/789433217	78778	Tony Prest / Never Odd Or Even	04/2014
5400	(2^261724+290135)/3/3/8467/9059	78778	Tony Prest / Never Odd Or Even	04/2014
5401	(2^261724+79857)/59/3847/165331	78777	Tony Prest / Never Odd Or Even	04/2014
5402	(2^261724+22883)/3/17/23/2351/10079	78777	Tony Prest / Never Odd Or Even	04/2014
5403	(2^261724+154799)/3/5/3655653719	78777	Tony Prest / Never Odd Or Even	04/2014
5404	(2^261724+391001)/3/11/17/41/43/24071	78777	Tony Prest / Never Odd Or Even	04/2014
5405	(2^261724+622383)/34843/550717	78777	Tony Prest / Never Odd Or Even	05/2014
5406	(2^261724+302829)/5/37/37/37078147	78776	Tony Prest / Never Odd Or Even	04/2014
5407	(2^261724+315837)/43/2176136243	78776	Tony Prest / Never Odd Or Even	04/2014
5408	(2^261724+582373)/53/307/311/32117	78776	Tony Prest / Never Odd Or Even	05/2014
5409	(2^261724+295283)/3/3/3/29/43/17812273	78775	Tony Prest / Never Odd Or Even	04/2014
5410	(2^261724+27491)/3/22787/105978449	78774	Tony Prest / Never Odd Or Even	04/2014
5411	(2^261724+392751)/193813/287826689	78774	Tony Prest / Never Odd Or Even	04/2014
5412	(2^261724+328501)/7/1091/31495610519	78773	Tony Prest / Never Odd Or Even	04/2014
5413	(2^261724+111267)/19/4637/15140560427	78772	Tony Prest / Never Odd Or Even	04/2014
5414	(2^261724+572133)/127/131/73787752333	78772	Tony Prest / Never Odd Or Even	05/2014
5415	(2^261724+608733)/59/7079/18451/909151	78771	Tony Prest / Never Odd Or Even	05/2014
5416	(2^261724+255449)/3/3/5/7/1759/10177/33158869	78770	Tony Prest / Never Odd Or Even	04/2014
5417	(2^261724+99509)/3/5/5/6507271/6749659289	78769	Tony Prest / Never Odd Or Even	04/2014
5418	(2^261724+52501)/563/53939/27942831391	78769	Tony Prest / Never Odd Or Even	04/2014
5419	(2^261724+117089)/3/5/37/149/967/2027/4163741	78769	Tony Prest / Never Odd Or Even	04/2014
5420	(2^261724+372571)/1487/9209/21559/2263249	78769	Tony Prest / Never Odd Or Even	04/2014
5421	(2^261724+184549)/5/8699/44053/1409322997	78769	Tony Prest / Never Odd Or Even	04/2014
5422	(2^261724+363351)/937/159683/59523200227	78768	Tony Prest / Never Odd Or Even	04/2014
5423	(2^261724+326501)/3/43/193/263/19403/253501403	78768	Tony Prest / Never Odd Or Even	04/2014
5424	(2^261724+629477)/3/17/17/137/263/1993/16187/57347	78768	Tony Prest / Never Odd Or Even	05/2014
5425	(2^261724+94871)/3/3/13/6734017/1673425245787	78766	Tony Prest / Never Odd Or Even	04/2014
5426	(2^261724+25981)/577/1181/3643/517786334743	78766	Tony Prest / Never Odd Or Even	04/2014
5428	(23*2^261642+1)/93	78762	Lelio R Paula	10/2012
5427	(2^261724+351227)/3/3/3/3/71/13997/9595373/8193978007	78762	Tony Prest / Never Odd Or Even	04/2014
5429	(2^261724+22571)/3/7243/7321/18046081/45730741211	78761	Tony Prest / Never Odd Or Even	04/2014
5430	(2^261724+56495)/3/3/3/7/7/13/9041/512818459/23708589119	78760	Tony Prest / Never Odd Or Even	04/2014
5431	(2^261724+604119)/5/7/7/41/14107/19681/211777/90145981/1036020834127	78750	Tony Prest / Never Odd Or Even	05/2014
5432	2^261507-2287	78722	Yves Minet	04/2009
5433	8*10^78717+39	78718	Robert Price	01/2017
5434	(78557*2^261440+1)/3	78706	Lelio R Paula	06/2014
5435	6^101128-16433	78693	Enzo Doria	02/2013
5436	20^60482+99	78689	Lelio R Paula	03/2015
5437	2^261348-110633	78674	Enzo Doria	05/2014
5438	191^34487+2	78666	Lelio R Paula	05/2013
5439	2^261305-110139	78661	Enzo Doria	04/2014
5440	(82*10^78635-1)/9	78636	Robert Price	12/2014
5441	10^78632+81	78633	Robert Price	03/2011
5442	10^78632-402693	78632	Patrick De Geest	07/2013
5443	3*10^78631+17	78632	Robert Price	03/2017
5444	2^261174-3911	78622	Yves Minet	04/2017
5445	2^261167+74843	78620	Enzo Doria	04/2016
5446	L(376121)+F(376122)	78605	Henri Lifchitz	01/2007
5447	14^68580-29	78602	Lelio R Paula	02/2015
5448	(73*10^78576-1)/9	78577	Robert Price	01/2015
5449	(17*2^261026-1)/40451	78574	Lelio R Paula	02/2014
5450	2^261001-195	78570	Lelio R Paula	05/2012
5451	5*2^260950+9	78555	Lelio R Paula	06/2014
5452	2^260931-7605	78549	Lelio R Paula	07/2013
5453	15^66778-32	78538	Lelio R Paula	02/2015
5454	(11*2^260896-1)/245	78537	Lelio R Paula	02/2014
5455	30^53166+29	78533	Norbert Schneider	03/2017
5456	lucasU(2403,1,23229)-lucasU(2403,1,23228)	78529	Mike Oakes	05/2009
5457	7*3^164574-2	78523	Lelio R Paula	06/2014
5458	2^260830-112133	78518	Enzo Doria	06/2014
5459	13^70486+42	78518	Lelio R Paula	03/2015
5460	11^75386-7080	78507	Enzo Doria	01/2013
5461	(86^40583-1)/85	78506	Paul Bourdelais	08/2017
5462	2^260711-58695	78482	Lelio R Paula	07/2013
5463	2^260678-111065	78472	Enzo Doria	05/2014
5464	18^62501-97	78456	Lelio R Paula	02/2015
5465	53^45498-2	78452	Lelio R Paula	08/2013
5466	2^260513-111121	78423	Enzo Doria	05/2014
5467	37845!2-64	78412	Robert Price	06/2015
5468	2^260469-110695	78409	Enzo Doria	05/2014
5469	(11*10^78408-113)/3	78409	Robert Price	01/2017
5470	2^260447+8415	78403	Lelio R Paula	07/2013
5471	37837!2-64	78394	Robert Price	06/2015
5472	(19*2^260379-1)/53	78382	Lelio R Paula	02/2014
5473	2^260377-113233	78382	Enzo Doria	07/2014
5474	9^82138+6^82138-2^82138	78380	Mike Oakes	08/2010
5475	69^42624+2	78380	Lelio R Paula	05/2013
5476	2^260369-1859713	78379	Enzo Doria	03/2016
5477	14*10^78362+1089	78364	Jens K. Andersen	11/2007
5478	5^112070-54	78334	Lelio R Paula	02/2015
5479	(10^(239165+1)+5410^39165-1)/9	78331	Robert Price	04/2017
5480	2^260182-113453	78323	Enzo Doria	07/2014
5481	f(16405)	78319	Robert Price	09/2017
5482	(78557*2^260084+1)/519	78296	Lelio R Paula	06/2014
5483	10^78288+9^(78288+1)	78289	Robert Price	08/2016
5484	10^78288+39109	78289	Patrick De Geest	12/2016
5485	10^78288-216299	78288	Patrick De Geest	12/2016
5486	5^111997+36	78283	Lelio R Paula	02/2015
5487	(21^59183+1)/22	78252	Paul Bourdelais	03/2010
5488	(88*10^78242-7)/9	78243	Robert Price	11/2014
5489	2*6^100547+7	78242	Lelio R Paula	10/2014
5490	2^259860-111089	78226	Enzo Doria	05/2014
5491	37^49875-2	78215	Lelio R Paula	09/2013
5492	(13*10^78213+401)/9	78214	Robert Price	10/2017
5493	7*5^111893-4	78211	Lelio R Paula	10/2014
5494	(11*2^259809-1)/1437	78209	Lelio R Paula	02/2014
5495	7^92511-6	78181	Theodore Burton	11/2005
5496	(3^163859-4)/253	78179	Lelio R Paula	10/2012
5497	(27*2^259666-1)/625691	78163	Lelio R Paula	02/2014
5498	3*10^78146+17	78147	Robert Price	03/2017
5499	(576^28307+1)/577	78137	Richard Fischer	01/2018
5500	2^259503+74333	78119	Enzo Doria	04/2016

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Probable Primes Top 10000

(205869 PRPs in the top)