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 (> 50000)	Who ?	When ?
5251	19522^19283+19283^19522	83656	Hans Havermann	04/2017
5252	8*5^119664-3	83643	Lelio R Paula	10/2014
5253	8*3^175299-7	83640	Lelio R Paula	07/2014
5254	(26*10^83638-413)/9	83639	Robert Price	10/2017
5255	3^175250+22	83616	Robert Price	12/2013
5257	11^80285+30	83609	Lelio R Paula	10/2015
5256	26870^1293+1293^26870	83609	Hans Havermann	03/2017
5258	2^277691+1874423	83594	Enzo Doria	06/2016
5259	13^75022-60	83571	Lelio R Paula	11/2015
5260	14^72905-51	83559	Lelio R Paula	11/2015
5261	(17*2^277565-1)/543	83554	Lelio R Paula	02/2014
5262	5^119532-12	83550	Lelio R Paula	10/2015
5263	6^107358-16253	83541	Enzo Doria	02/2013
5264	2^277478-460211	83530	Enzo Doria	06/2015
5265	(22*10^83525-7)/3	83526	Erik Branger	09/2014
5266	(30^56543+1)/31	83520	Robert Price	07/2013
5267	2^277417-460783	83511	Paul Bourdelais	04/2013
5268	(22699*2^277387+1)/219	83504	Lelio R Paula	06/2014
5269	(31*2^277383-1)/247	83500	Lelio R Paula	02/2014
5270	21368^8085+8085^21368	83500	Hans Havermann	04/2017
5271	(9*2^277342+1)/13	83489	Lelio R Paula	12/2012
5272	5^119439-66	83485	Lelio R Paula	10/2015
5273	(14*10^83471-101)/3	83472	Robert Price	04/2017
5274	5*6^107263+7	83468	Lelio R Paula	10/2014
5275	(64*10^83461-1)/9	83462	Serge Batalov	11/2010
5276	2^277244-175709	83459	Hans Havermann	10/2018
5277	17^67796-92	83420	Lelio R Paula	11/2015
5278	2^277106-110057	83418	Enzo Doria	04/2014
5279	6^107200-19	83418	Lelio R Paula	12/2015
5280	11^80096-1830	83412	Enzo Doria	12/2012
5281	3^174801+56	83402	Lelio R Paula	12/2015
5282	2^277033-111973	83396	Enzo Doria	05/2014
5283	120^40105-119	83386	Norbert Schneider	09/2018
5284	20519^11572+11572^20519	83378	Hans Havermann	03/2017
5285	20850^9971+9971^20850	83374	Hans Havermann	03/2017
5286	6^107122-18863	83358	Enzo Doria	03/2013
5287	4*10^83354-89	83355	Robert Price	08/2017
5288	3^174697-34	83352	Robert Price	11/2013
5289	(9787*2^276855-1)/2345	83343	Lelio R Paula	04/2015
5290	2^276825+75227	83333	Enzo Doria	04/2016
5291	5^119214+84	83328	Lelio R Paula	10/2015
5292	2^276803-159	83327	Lelio R Paula	06/2012
5293	(3*2^276753-1)/25	83311	Lelio R Paula	02/2014
5294	114^40495+40495^114	83295	Norbert Schneider	12/2014
5295	39967!2+1024	83282	Robert Price	02/2015
5297	2^276641+57	83278	Lelio R Paula	06/2012
5296	35^53934-3414	83278	Enzo Doria	03/2013
5298	(2^276655+78557)/365425	83276	Lelio R Paula	12/2012
5299	2^276615-4035	83270	Lelio R Paula	08/2013
5300	2^276588+1155	83262	Lelio R Paula	08/2013
5302	2^276587-937	83261	Yves Minet	10/2009
5301	2^276584-113183	83261	Enzo Doria	07/2014
5303	(2^276592-1017)/13843739	83256	Lelio R Paula	12/2012
5304	2^276547-109591	83249	Enzo Doria	04/2014
5305	13^74733-32	83249	Lelio R Paula	11/2015
5306	2^276523-2587	83242	Yves Minet	07/2014
5307	18^66311-43	83239	Lelio R Paula	11/2015
5308	11^79919-1530	83228	Enzo Doria	12/2012
5309	2^276468-109745	83226	Enzo Doria	04/2014
5310	2^276462+5385	83224	Lelio R Paula	08/2013
5311	(9787*2^276422-1)/3	83215	Lelio R Paula	04/2015
5312	2^276391-15	83202	Lelio R Paula	06/2012
5313	(4*10^83201+173)/3	83202	Robert Price	01/2017
5314	2^276316-109655	83180	Enzo Doria	04/2014
5315	2^276305-112063	83177	Enzo Doria	06/2014
5316	(10^(241585+1)+5410^41585-1)/9	83171	Robert Price	04/2017
5317	74913!4-2	83161	Robert Price	07/2017
5318	2^276227-1837207	83153	Enzo Doria	05/2015
5319	(2^276227+3)/7	83152	Lelio R Paula	12/2012
5320	2^276184-63389	83140	Paul Bourdelais	02/2012
5321	2^276066-111603	83105	Enzo Doria	05/2014
5322	(2^276028-3)*6-7	83094	Gilbert Mozzo	09/2016
5323	(2^275897+9)/1153	83051	Lelio R Paula	12/2012
5324	2^275879-109807	83048	Enzo Doria	04/2014
5326	F(397379)	83047	Henri Lifchitz	08/2003
5325	U(397379)	83047	Serge Batalov	03/2015
5327	3^174040-14	83039	Robert Price	08/2013
5328	(86*10^83038-221)/9	83039	Robert Price	06/2017
5329	2^275841-6883	83037	Lelio R Paula	07/2011
5330	3^174002-140	83021	Lelio R Paula	12/2015
5331	6^106681+77	83014	Lelio R Paula	12/2015
5332	187^36539-2	83011	Lelio R Paula	10/2017
5333	11^79701-3150	83001	Enzo Doria	12/2012
5334	(55459*2^275657+1)/21	82985	Lelio R Paula	06/2014
5335	(7*10^82960-457)/9	82960	Robert Price	09/2017
5336	2^275535-6855	82945	Lelio R Paula	08/2013
5338	3^173828-14	82938	Robert Price	08/2013
5337	2^275512-109677	82938	Enzo Doria	04/2014
5339	2^275446-110045	82918	Enzo Doria	04/2014
5340	(2^275473+47)/29526097447	82916	Lelio R Paula	12/2012
5341	3^173755-14	82903	Robert Price	08/2013
5342	(182*10^82898+43)/9	82900	Robert Price	11/2017
5343	2^275363-112309	82893	Enzo Doria	06/2014
5344	61^46427-60	82888	Norbert Schneider	10/2014
5345	3*10^82880-7^82880	82881	Mike Oakes	02/2010
5347	2^275290+90195	82871	Lelio R Paula	07/2013
5346	(35*10^82870-71)/9	82871	Robert Price	05/2015
5348	2^275270-1859621	82865	Enzo Doria	03/2016
5349	2^275259+81	82862	Henri Lifchitz	01/2007
5350	(113703^16384+1)/2	82834	Richard Fischer	04/2018
5351	7^98003+98003^7+1	82823	Robert Price	05/2014
5352	10^82790+126043	82791	Patrick De Geest	07/2013
5353	10^82790-47	82790	Robert Price	05/2011
5354	2^274985-112663	82779	Enzo Doria	06/2014
5355	2^274935+15015	82764	Lelio R Paula	07/2013
5356	(17*2^274922+1)/3	82761	Lelio R Paula	12/2012
5357	(43*10^82752-61)/9	82753	Robert Price	06/2015
5358	(3*2^274862+1)/1027	82740	Lelio R Paula	12/2012
5359	(31*2^274848-1)/4065	82736	Lelio R Paula	02/2014
5360	(4^137405+23)/3	82726	Robert Price	02/2017
5361	2^274791-110491	82721	Enzo Doria	05/2014
5362	(11*2^274776-1)/95	82715	Lelio R Paula	02/2014
5363	(47*10^82706-119)/9	82707	Robert Price	09/2017
5364	2^274704-111395	82695	Enzo Doria	05/2014
5365	2^274686-3911	82689	Yves Minet	04/2017
5366	(2^274663-1017)/48871318292279	82669	Lelio R Paula	12/2012
5367	(3^173263-5)/14498	82664	Lelio R Paula	12/2012
5368	2^274511-64875	82637	Lelio R Paula	08/2013
5369	12^76572-83	82636	Lelio R Paula	11/2015
5370	3^173191-2^173191	82634	Mike Oakes	02/2004
5371	14^72072-15	82604	Lelio R Paula	11/2015
5372	(55459*2^274339+1)/3	82589	Lelio R Paula	06/2014
5373	2^274351+123	82588	Lelio R Paula	06/2012
5374	(1017*2^274339-1)/3515	82584	Lelio R Paula	04/2015
5375	6^106086+113	82551	Lelio R Paula	12/2015
5376	(17*10^82540-377)/9	82541	Robert Price	11/2017
5377	2^274093-58695	82511	Lelio R Paula	07/2013
5378	7*10^82509-47	82510	Robert Price	02/2017
5379	2^274081-6555	82507	Lelio R Paula	07/2013
5381	2^274074-274074+1	82505	Robert Price	10/2014
5382	14^71985+47	82505	Lelio R Paula	11/2015
5380	5*10^82504+21	82505	Robert Price	01/2017
5383	6^106014-139	82495	Lelio R Paula	12/2015
5384	(2^274046+47)/753	82494	Lelio R Paula	12/2012
5385	2^274008-1838099	82485	Enzo Doria	05/2015
5386	2^273981-110029	82477	Enzo Doria	04/2014
5387	19^64490-30	82467	Lelio R Paula	12/2015
5388	2^273785+11715	82418	Lelio R Paula	07/2013
5389	8*10^82417+51	82418	Robert Price	05/2017
5390	11^79133-10	82409	Theodore Burton	11/2005
5391	91^42063+90	82404	Norbert Schneider	01/2016
5392	2^273662-63	82381	Lelio R Paula	06/2012
5393	2^273661+255	82381	Lelio R Paula	07/2013
5394	(62*10^82377-17)/9	82378	Robert Price	09/2015
5395	2^273608+524287	82365	Paul Underwood	08/2018
5396	8*10^82360-51	82361	Robert Price	10/2017
5397	(79*10^82347-1)/3	82349	Robert Price	11/2017
5398	(11*10^82323+91)/3	82323	Robert Price	02/2017
5399	(189977#+19081)/(19081*17260483)	82317	Makoto Morimoto	10/2017
5400	(189977#+196924)/(271354128874441)	82316	Makoto Morimoto	10/2017
5401	15^69984+32	82308	Lelio R Paula	11/2015
5402	9*6^105746+7	82288	Lelio R Paula	10/2014
5403	89^42211-88	82286	Norbert Schneider	01/2016
5404	gcd(V(1476435),5F(295287)(F(295287)+1)+1)	82281	Serge Batalov	04/2015
5405	(19*10^82270-43)/3	82271	Robert Price	10/2017
5406	2^273282-110241	82267	Enzo Doria	05/2014
5407	(13^73849+4^73849)/17	82263	Robert Price	05/2013
5409	10^82254+9^(82254+1)	82255	Robert Price	08/2016
5408	10^82254+457773	82255	Patrick De Geest	12/2016
5410	10^82254-99609	82254	Patrick De Geest	12/2016
5411	(754*10^82250-7)/9	82252	Robert Price	11/2017
5412	18^65524+13	82251	Lelio R Paula	11/2015
5413	2^273206-107	82244	Lelio R Paula	06/2012
5414	2^273193-459145	82240	Enzo Doria	05/2015
5416	2^273126+36937	82220	Yves Minet	06/2010
5415	39505!2+128	82220	Robert Price	03/2015
5417	2^273053-112111	82198	Enzo Doria	06/2014
5418	2^273016+1185	82187	Lelio R Paula	07/2013
5419	(2^273008+3)/7	82183	Lelio R Paula	12/2012
5420	5^117554-15386	82167	Enzo Doria	02/2013
5421	(38*10^82161+403)/9	82162	Robert Price	11/2017
5422	2^272907-111439	82154	Enzo Doria	05/2014
5423	(67607*2^272901+1)/50790115	82149	Lelio R Paula	06/2014
5424	2^272875-69	82144	Lelio R Paula	06/2012
5425	7^97197+4	82141	Robert Price	01/2014
5426	(4*6^105554+1)/5	82137	Serge Batalov	10/2014
5427	6^105531-109	82120	Lelio R Paula	12/2015
5428	2^272766-65	82111	Lelio R Paula	06/2012
5429	19^64205-78	82103	Lelio R Paula	12/2015
5430	2^272702+1869979	82092	Enzo Doria	05/2016
5431	(29*2^272687-1)/9	82088	Lelio R Paula	02/2014
5432	(5*10^82085-119)/3	82086	Robert Price	04/2016
5433	2^272660-110049	82079	Enzo Doria	04/2014
5434	6^105474+67	82075	Lelio R Paula	12/2015
5435	2^272637+82875	82072	Lelio R Paula	07/2013
5436	2^272587-31	82057	Lelio R Paula	06/2012
5437	(41*10^82044-59)/9	82045	Robert Price	10/2017
5438	8*5^117368+9	82038	Lelio R Paula	10/2014
5439	(101525^16384+1)/131074	82023	Lelio R Paula	11/2011
5440	4*5^117343-7	82020	Lelio R Paula	10/2014
5441	(265*10^81990+17)/3	81992	Robert Price	05/2016
5442	3^171843+10	81990	Robert Price	10/2013
5443	(7*10^81985+107)/3	81986	Robert Price	02/2017
5444	(3*2^272356+1)/177163	81983	Lelio R Paula	12/2012
5445	2^272296-111149	81970	Enzo Doria	05/2014
5446	(9*2^272243-1)/7	81954	Lelio R Paula	02/2014
5447	2^272177-111223	81934	Enzo Doria	05/2014
5448	(151009^15817+1)/151010	81912	Faysal YAtim	06/2017
5449	(16*10^81896-19)/3	81897	Robert Price	03/2016
5450	(2^271922+78557)/63	81855	Lelio R Paula	12/2012
5451	(10^81848+77)/3	81848	Robert Price	01/2017
5452	(24737*2^271883+1)/3757	81846	Lelio R Paula	06/2014
5453	10^81778+39	81779	Robert Price	03/2011
5454	10^81778-171999	81778	Patrick De Geest	07/2013
5455	(14*10^81767-11)/3	81768	Erik Branger	09/2014
5456	2^271541+1868417	81742	Enzo Doria	04/2016
5457	(2^271549-1)/238749682487	81734	Jens K. Andersen	02/2009
5458	2^271484-167	81725	Lelio R Paula	06/2012
5459	(8*10^81709-611)/9	81709	Robert Price	11/2017
5460	2^271382+12909	81695	Lelio R Paula	07/2013
5461	49^48334+48	81694	Norbert Schneider	07/2014
5462	7^96668+48	81694	Lelio R Paula	10/2015
5463	11^78435-1410	81682	Enzo Doria	12/2012
5464	5*10^81653+9	81654	Dmitry Domanov	11/2010
5465	(2^271211-1)/613961495159	81631	Jens K. Andersen	02/2009
5466	3^171068+52	81621	Lelio R Paula	12/2015
5467	2^271115-110407	81614	Enzo Doria	05/2014
5468	2^271111-110635	81613	Enzo Doria	05/2014
5469	2^271098-111	81609	Lelio R Paula	06/2012
5470	(77*10^81606+13)/9	81607	Robert Price	10/2015
5471	2^271064-2790209	81599	Enzo Doria	03/2016
5472	(13*2^271053-1)/3095	81593	Lelio R Paula	02/2014
5473	2^271040-57	81592	Lelio R Paula	06/2012
5474	(14*10^81585+73)/3	81586	Robert Price	04/2016
5475	127^38779+126	81584	Norbert Schneider	02/2015
5476	18^64966-43	81551	Lelio R Paula	11/2015
5477	(2^270840+47)/591	81529	Lelio R Paula	12/2012
5478	20^62654+87	81515	Lelio R Paula	01/2016
5479	(19*10^81488+191)/3	81489	Robert Price	01/2017
5480	8*10^81487+21	81488	Robert Price	02/2017
5481	(73*10^81485+107)/9	81486	Robert Price	08/2016
5482	536^29847+29847^536	81458	Norbert Schneider	03/2017
5483	8*7^96378+9	81450	Lelio R Paula	10/2014
5484	2^270546-110345	81443	Enzo Doria	05/2014
5485	13^73105-60	81435	Lelio R Paula	11/2015
5486	44^49524+43	81391	Norbert Schneider	06/2014
5487	(3*2^270368-1)/13	81389	Lelio R Paula	02/2014
5488	(10^81363+719)/9	81363	Serge Batalov	12/2014
5489	(10^81353+449)/9	81353	Serge Batalov	12/2014
5490	14^70978-89	81350	Lelio R Paula	11/2015
5491	11^78108-2040	81342	Enzo Doria	12/2012
5492	3^170400-58	81302	Lelio R Paula	12/2015
5493	(17*10^81300-131)/3	81301	Robert Price	12/2017
5494	10^81297+36991	81298	Patrick De Geest	06/2013
5495	10^81297-57	81297	Robert Price	05/2011
5496	2^270055-113047	81295	Enzo Doria	07/2014
5497	18^64759-55	81291	Lelio R Paula	11/2015
5498	(2^269987+1)/3	81274	H.&R. Lifchitz	10/2000
5499	(31^54493-1)/30	81268	Alexander Zhirkov	10/2010
5500	(2^270059-1)/540119/6481417/7124976157756725967	81265	Dario Alpern	09/2014

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Probable Primes Top 10000

(252402 PRPs in the top)