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	(10223*2^280881+1)/68419	84553	Lelio R Paula	06/2014
5252	2^280852+97681	84545	Yves Minet	08/2004
5253	2^280848-1203	84544	Lelio R Paula	09/2013
5254	5^120946-24	84538	Lelio R Paula	10/2015
5255	2^280810-2111	84533	Yves Minet	08/2013
5256	11^81161-5160	84521	Enzo Doria	01/2013
5257	2^280737-93	84511	Lelio R Paula	08/2012
5258	2^280698+315	84499	Lelio R Paula	09/2013
5259	3^177099-340	84498	Lelio R Paula	12/2015
5260	(5*10^84469-107)/3	84470	Robert Price	01/2017
5261	(3^177002+7)/6696022272161744	84436	Lelio R Paula	12/2012
5262	(2^280500-1017)/823	84436	Lelio R Paula	01/2013
5263	14^73660-5	84424	Lelio R Paula	11/2015
5264	(19*10^84409-61)/3	84410	Robert Price	04/2017
5265	2^280388+117	84406	Lelio R Paula	08/2012
5266	2^280389-566533	84406	Paul Bourdelais	03/2013
5267	(141584^16384+1)/65537	84390	Syoichiro Yamada	06/2008
5268	119^40652+118	84376	Norbert Schneider	09/2018
5269	2^280240-173	84361	Lelio R Paula	08/2012
5270	(184*10^84348-1)/3	84350	Robert Price	02/2017
5271	4*10^84346+93	84347	Robert Price	01/2017
5272	7*2^280156-5	84337	Lelio R Paula	08/2014
5273	8*7^99782-3	84327	Lelio R Paula	10/2014
5274	2^280116+133	84324	Lelio R Paula	08/2012
5275	2^280118+54615	84324	Lelio R Paula	09/2013
5276	(509203*2^280090-1)/3	84321	Lelio R Paula	04/2015
5277	6^108354+47	84316	Lelio R Paula	12/2015
5278	10^84305+141963	84306	Patrick De Geest	07/2013
5279	10^84305-57	84305	Robert Price	05/2011
5280	9^88339+38^88339-24^88339-3*2^88339	84297	Mike Oakes	01/2011
5281	3^176648-112804	84283	Enzo Doria	06/2014
5282	6^108310+115	84282	Lelio R Paula	12/2015
5283	(11*2^279968-1)/5	84280	Lelio R Paula	02/2014
5284	6^108288-16643	84265	Enzo Doria	02/2013
5285	2^279917-58695	84264	Lelio R Paula	08/2013
5286	65^46477+36	84259	Lelio R Paula	01/2016
5287	2^279866-1907	84249	Yves Minet	05/2013
5288	(3^176580-5)/28076	84246	Lelio R Paula	12/2012
5289	(p(17530)#+4)/2	84246	Robert Price	09/2017
5290	(2*10^84239+1)/3	84239	Serge Batalov	07/2009
5292	18^67103-41	84233	Lelio R Paula	11/2015
5291	20^64743-43	84233	Lelio R Paula	01/2016
5293	143^39070+39070^143	84209	Serge Batalov	05/2014
5294	11^80857-5400	84204	Enzo Doria	01/2013
5295	(13*10^84179+161)/3	84180	Robert Price	04/2017
5296	2^279634-110405	84179	Enzo Doria	05/2014
5297	(74*10^84170+313)/9	84171	Robert Price	11/2017
5298	2^279582-1017	84163	Lelio R Paula	08/2013
5299	(22*10^84159-19)/3	84160	Robert Price	02/2017
5300	p(17513)#/2+512	84156	Robert Price	05/2017
5301	(19*10^84144-43)/3	84145	Robert Price	10/2017
5302	(9*2^279507-1)/137	84139	Lelio R Paula	02/2014
5303	11^80792-810	84137	Enzo Doria	11/2012
5304	(97*10^84134-1)/3	84136	Serge Batalov	12/2014
5305	p(17507)#/2+32	84125	Robert Price	12/2016
5306	21485^8224+8224^21485	84116	Hans Havermann	04/2017
5307	3^176294-340	84114	Lelio R Paula	12/2015
5308	(3^176287+4)/2191	84107	Lelio R Paula	12/2012
5309	2^279388-719	84105	Yves Minet	05/2012
5310	(22699*2^279378+1)/221	84104	Lelio R Paula	06/2014
5311	2^279332-110447	84088	Enzo Doria	05/2014
5312	2^279320+7	84084	Lelio R Paula	06/2012
5313	127^39966-2	84081	Lelio R Paula	10/2017
5314	(11*2^279240-1)/95	84059	Lelio R Paula	02/2014
5315	2^279218-111347	84053	Enzo Doria	05/2014
5316	35^54435+2	84052	Lelio R Paula	05/2013
5317	(31*2^279191-1)/12511523	84040	Lelio R Paula	02/2014
5318	20996^10059+10059^20996	84038	Hans Havermann	05/2017
5319	97*10^84033-3	84035	Robert Price	01/2017
5320	21234^9067+9067^21234	84033	Hans Havermann	05/2017
5321	(134569^16384+1)/2	84033	Richard Fischer	06/2018
5322	2^279095-109717	84016	Enzo Doria	04/2014
5323	14^73282-99	83991	Lelio R Paula	11/2015
5324	21457^8200+8200^21457	83979	Hans Havermann	06/2017
5325	89*10^83976-7	83978	Robert Price	03/2017
5326	2^278955+173	83974	Lelio R Paula	06/2012
5327	(7*2^278851+1)/39	83942	Lelio R Paula	12/2012
5328	(9913*2^278844-1)/40803	83940	Lelio R Paula	04/2015
5329	5^120076-14846	83930	Enzo Doria	02/2013
5330	(85*10^83921-1)/3	83923	Robert Price	07/2017
5331	(2^278770-3)/23	83917	Lelio R Paula	12/2012
5332	(10^83916+449)/9	83916	Serge Batalov	12/2014
5334	2^278715+99	83902	Lelio R Paula	06/2012
5333	(132109^16384+1)/2	83902	Richard Fischer	05/2018
5335	40235!2-2^40235	83899	Robert Price	09/2015
5336	2^278698-171	83897	Lelio R Paula	06/2012
5337	(19*10^83894-43)/3	83895	Robert Price	10/2017
5338	6^107802+25	83887	Lelio R Paula	12/2015
5339	8*10^83880+39	83881	Robert Price	01/2017
5340	(58*10^83878+23)/9	83879	Robert Price	09/2015
5341	7^99244-90	83871	Lelio R Paula	10/2015
5342	2^278554+4257	83854	Lelio R Paula	08/2013
5343	2^278504-109619	83839	Enzo Doria	04/2014
5344	2^278499+1870433	83837	Enzo Doria	05/2016
5345	105^41475+104	83829	Norbert Schneider	11/2016
5346	15^71276-68	83828	Lelio R Paula	11/2015
5347	2^278464-216413	83827	Enzo Doria	04/2013
5348	(76*10^83816-211)/9	83817	Robert Price	10/2017
5349	(8*10^83811-101)/3	83812	Robert Price	10/2017
5350	2^278400+40755	83807	Lelio R Paula	08/2013
5351	(9*2^278381-1)/7	83802	Lelio R Paula	02/2014
5352	39^87813+6^87813+24^87813	83796	Mike Oakes	12/2010
5353	19551^19268+19268^19551	83773	Hans Havermann	05/2017
5354	20625^11522+11522^20625	83770	Hans Havermann	05/2017
5355	(44*10^83768-791)/9	83769	Robert Price	10/2017
5356	(87^43189+1)/88	83764	Paul Bourdelais	08/2017
5357	2^278235-49	83758	Lelio R Paula	06/2012
5358	23543^3610+3610^23543	83755	Hans Havermann	05/2017
5360	18^66711-91	83741	Lelio R Paula	11/2015
5359	4*10^83740-89	83741	Robert Price	08/2017
5361	(3*2^278172-1)/11	83738	Lelio R Paula	02/2014
5362	(15*29^57251+2561)/28	83724	Curtis Bright	05/2015
5363	4*7^99059-9	83716	Lelio R Paula	10/2014
5364	(2^278128-3)/126844724149	83714	Lelio R Paula	12/2012
5365	2^278077+1867211	83710	Enzo Doria	03/2016
5366	2^278059-27	83705	Lelio R Paula	06/2012
5367	214^35917+35917^214	83702	Norbert Schneider	12/2014
5368	(23*10^83693+7)/3	83694	Robert Price	10/2015
5369	85^43375-2	83689	Lelio R Paula	09/2013
5370	5*3^175360+4	83669	Lelio R Paula	07/2014
5371	(23^61441-1)/22	83665	Robert Price	01/2012
5372	20091^14596+14596^20091	83664	Hans Havermann	03/2017
5373	2^277907-110629	83659	Enzo Doria	05/2014
5374	19522^19283+19283^19522	83656	Hans Havermann	04/2017
5375	8*5^119664-3	83643	Lelio R Paula	10/2014
5376	8*3^175299-7	83640	Lelio R Paula	07/2014
5377	(26*10^83638-413)/9	83639	Robert Price	10/2017
5378	3^175250+22	83616	Robert Price	12/2013
5380	11^80285+30	83609	Lelio R Paula	10/2015
5379	26870^1293+1293^26870	83609	Hans Havermann	03/2017
5381	2^277691+1874423	83594	Enzo Doria	06/2016
5382	13^75022-60	83571	Lelio R Paula	11/2015
5383	14^72905-51	83559	Lelio R Paula	11/2015
5384	(17*2^277565-1)/543	83554	Lelio R Paula	02/2014
5385	5^119532-12	83550	Lelio R Paula	10/2015
5386	6^107358-16253	83541	Enzo Doria	02/2013
5387	2^277478-460211	83530	Enzo Doria	06/2015
5388	(22*10^83525-7)/3	83526	Erik Branger	09/2014
5389	(30^56543+1)/31	83520	Robert Price	07/2013
5390	2^277417-460783	83511	Paul Bourdelais	04/2013
5391	(22699*2^277387+1)/219	83504	Lelio R Paula	06/2014
5392	(31*2^277383-1)/247	83500	Lelio R Paula	02/2014
5393	21368^8085+8085^21368	83500	Hans Havermann	04/2017
5394	(9*2^277342+1)/13	83489	Lelio R Paula	12/2012
5395	5^119439-66	83485	Lelio R Paula	10/2015
5396	(14*10^83471-101)/3	83472	Robert Price	04/2017
5397	5*6^107263+7	83468	Lelio R Paula	10/2014
5398	(64*10^83461-1)/9	83462	Serge Batalov	11/2010
5399	2^277244-175709	83459	Hans Havermann	10/2018
5400	17^67796-92	83420	Lelio R Paula	11/2015
5401	2^277106-110057	83418	Enzo Doria	04/2014
5402	6^107200-19	83418	Lelio R Paula	12/2015
5403	11^80096-1830	83412	Enzo Doria	12/2012
5404	3^174801+56	83402	Lelio R Paula	12/2015
5405	2^277033-111973	83396	Enzo Doria	05/2014
5406	120^40105-119	83386	Norbert Schneider	09/2018
5407	20519^11572+11572^20519	83378	Hans Havermann	03/2017
5408	20850^9971+9971^20850	83374	Hans Havermann	03/2017
5409	6^107122-18863	83358	Enzo Doria	03/2013
5410	4*10^83354-89	83355	Robert Price	08/2017
5411	3^174697-34	83352	Robert Price	11/2013
5412	(9787*2^276855-1)/2345	83343	Lelio R Paula	04/2015
5413	2^276825+75227	83333	Enzo Doria	04/2016
5414	5^119214+84	83328	Lelio R Paula	10/2015
5415	2^276803-159	83327	Lelio R Paula	06/2012
5416	(3*2^276753-1)/25	83311	Lelio R Paula	02/2014
5417	114^40495+40495^114	83295	Norbert Schneider	12/2014
5418	39967!2+1024	83282	Robert Price	02/2015
5420	2^276641+57	83278	Lelio R Paula	06/2012
5419	35^53934-3414	83278	Enzo Doria	03/2013
5421	(2^276655+78557)/365425	83276	Lelio R Paula	12/2012
5422	2^276615-4035	83270	Lelio R Paula	08/2013
5423	2^276588+1155	83262	Lelio R Paula	08/2013
5425	2^276587-937	83261	Yves Minet	10/2009
5424	2^276584-113183	83261	Enzo Doria	07/2014
5426	(2^276592-1017)/13843739	83256	Lelio R Paula	12/2012
5427	2^276547-109591	83249	Enzo Doria	04/2014
5428	13^74733-32	83249	Lelio R Paula	11/2015
5429	2^276523-2587	83242	Yves Minet	07/2014
5430	18^66311-43	83239	Lelio R Paula	11/2015
5431	11^79919-1530	83228	Enzo Doria	12/2012
5432	2^276468-109745	83226	Enzo Doria	04/2014
5433	2^276462+5385	83224	Lelio R Paula	08/2013
5434	(9787*2^276422-1)/3	83215	Lelio R Paula	04/2015
5436	2^276391-15	83202	Lelio R Paula	06/2012
5435	(4*10^83201+173)/3	83202	Robert Price	01/2017
5437	2^276316-109655	83180	Enzo Doria	04/2014
5438	2^276305-112063	83177	Enzo Doria	06/2014
5439	(10^(241585+1)+5410^41585-1)/9	83171	Robert Price	04/2017
5440	74913!4-2	83161	Robert Price	07/2017
5441	2^276227-1837207	83153	Enzo Doria	05/2015
5442	(2^276227+3)/7	83152	Lelio R Paula	12/2012
5443	2^276184-63389	83140	Paul Bourdelais	02/2012
5444	2^276066-111603	83105	Enzo Doria	05/2014
5445	(2^276028-3)*6-7	83094	Gilbert Mozzo	09/2016
5446	(2^275897+9)/1153	83051	Lelio R Paula	12/2012
5447	2^275879-109807	83048	Enzo Doria	04/2014
5449	F(397379)	83047	Henri Lifchitz	08/2003
5448	U(397379)	83047	Serge Batalov	03/2015
5450	3^174040-14	83039	Robert Price	08/2013
5451	(86*10^83038-221)/9	83039	Robert Price	06/2017
5452	2^275841-6883	83037	Lelio R Paula	07/2011
5453	3^174002-140	83021	Lelio R Paula	12/2015
5454	6^106681+77	83014	Lelio R Paula	12/2015
5455	187^36539-2	83011	Lelio R Paula	10/2017
5456	11^79701-3150	83001	Enzo Doria	12/2012
5457	(55459*2^275657+1)/21	82985	Lelio R Paula	06/2014
5458	(7*10^82960-457)/9	82960	Robert Price	09/2017
5459	2^275535-6855	82945	Lelio R Paula	08/2013
5461	3^173828-14	82938	Robert Price	08/2013
5460	2^275512-109677	82938	Enzo Doria	04/2014
5462	2^275446-110045	82918	Enzo Doria	04/2014
5463	(2^275473+47)/29526097447	82916	Lelio R Paula	12/2012
5464	3^173755-14	82903	Robert Price	08/2013
5465	(182*10^82898+43)/9	82900	Robert Price	11/2017
5466	2^275363-112309	82893	Enzo Doria	06/2014
5467	61^46427-60	82888	Norbert Schneider	10/2014
5468	3*10^82880-7^82880	82881	Mike Oakes	02/2010
5470	2^275290+90195	82871	Lelio R Paula	07/2013
5469	(35*10^82870-71)/9	82871	Robert Price	05/2015
5471	2^275270-1859621	82865	Enzo Doria	03/2016
5472	2^275259+81	82862	Henri Lifchitz	01/2007
5473	(113703^16384+1)/2	82834	Richard Fischer	04/2018
5474	7^98003+98003^7+1	82823	Robert Price	05/2014
5475	10^82790+126043	82791	Patrick De Geest	07/2013
5476	10^82790-47	82790	Robert Price	05/2011
5477	2^274985-112663	82779	Enzo Doria	06/2014
5478	2^274935+15015	82764	Lelio R Paula	07/2013
5479	(17*2^274922+1)/3	82761	Lelio R Paula	12/2012
5480	(43*10^82752-61)/9	82753	Robert Price	06/2015
5481	(3*2^274862+1)/1027	82740	Lelio R Paula	12/2012
5482	(31*2^274848-1)/4065	82736	Lelio R Paula	02/2014
5483	(4^137405+23)/3	82726	Robert Price	02/2017
5484	2^274791-110491	82721	Enzo Doria	05/2014
5485	(11*2^274776-1)/95	82715	Lelio R Paula	02/2014
5486	(47*10^82706-119)/9	82707	Robert Price	09/2017
5487	2^274704-111395	82695	Enzo Doria	05/2014
5488	2^274686-3911	82689	Yves Minet	04/2017
5489	(2^274663-1017)/48871318292279	82669	Lelio R Paula	12/2012
5490	(3^173263-5)/14498	82664	Lelio R Paula	12/2012
5491	2^274511-64875	82637	Lelio R Paula	08/2013
5492	12^76572-83	82636	Lelio R Paula	11/2015
5493	3^173191-2^173191	82634	Mike Oakes	02/2004
5494	14^72072-15	82604	Lelio R Paula	11/2015
5495	(55459*2^274339+1)/3	82589	Lelio R Paula	06/2014
5496	2^274351+123	82588	Lelio R Paula	06/2012
5497	(1017*2^274339-1)/3515	82584	Lelio R Paula	04/2015
5498	6^106086+113	82551	Lelio R Paula	12/2015
5499	(17*10^82540-377)/9	82541	Robert Price	11/2017
5500	2^274093-58695	82511	Lelio R Paula	07/2013

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PRP Records

Probable Primes Top 10000

(252538 PRPs in the top)