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	496^31671+31671^496	85369	Norbert Schneider	07/2017
5252	(15*2^283583-1)/103051	85364	Lelio R Paula	02/2014
5253	15^72572+92	85352	Lelio R Paula	11/2015
5254	2^283473-1615	85334	Lelio R Paula	09/2013
5255	2^283466-15	85332	Lelio R Paula	08/2012
5256	11^81916-7020	85307	Enzo Doria	02/2013
5257	6^109626-7	85306	Lelio R Paula	11/2014
5258	2^283374-110327	85305	Enzo Doria	05/2014
5259	33*10^85297+7	85299	Robert Price	07/2016
5260	18^67933+41	85275	Lelio R Paula	11/2015
5261	2^283271-109341	85274	Enzo Doria	04/2014
5262	(25*10^85249-73)/3	85250	Robert Price	09/2016
5263	2*5^121959+3	85246	Lelio R Paula	10/2014
5264	19834^19834+8947	85235	Henri Lifchitz	11/2004
5265	2^283140+1915	85234	Lelio R Paula	09/2013
5266	3*10^85227-97	85228	Robert Price	08/2017
5267	(16*10^85221-31)/3	85222	Robert Price	03/2016
5268	2^283083+1869383	85217	Enzo Doria	05/2016
5269	(24737*2^283051+1)/17	85211	Lelio R Paula	06/2014
5270	(2^283032+78557)/3	85201	Lelio R Paula	01/2013
5271	2^283026-109893	85200	Enzo Doria	04/2014
5272	(2^283012+78557)/129	85193	Lelio R Paula	01/2013
5273	(10^(242589+1)+7210^42589-1)/9	85179	Robert Price	09/2017
5274	2^282860-109727	85150	Enzo Doria	04/2014
5275	2^282819+1869413	85138	Enzo Doria	05/2016
5276	3^178428+2	85132	Ray Chandler	07/2011
5277	(22699*2^282742+1)/73	85117	Lelio R Paula	06/2014
5278	(16^70687+5^70687)/21	85115	Robert Price	07/2013
5279	(3^178352-2)/7	85095	Lelio R Paula	12/2012
5280	11^81699-2790	85081	Enzo Doria	12/2012
5281	2^282612-95	85075	Lelio R Paula	08/2012
5282	2^282609-4069	85074	Yves Minet	02/2018
5283	75^45366-2	85065	Lelio R Paula	08/2013
5284	2^282511+69	85045	Lelio R Paula	08/2012
5285	69^46249+2	85045	Lelio R Paula	06/2013
5286	3^178226+10	85036	Robert Price	10/2013
5287	(182*10^85017+43)/9	85019	Robert Price	11/2017
5288	(14*10^85010+73)/3	85011	Robert Price	04/2016
5289	9*2^282338-7	84994	Lelio R Paula	08/2014
5290	(9913*2^282330-1)/1578003	84988	Lelio R Paula	04/2015
5291	2^282203+5	84952	Lelio R Paula	08/2012
5292	2^282184+13	84946	Lelio R Paula	08/2012
5293	11^81568-2400	84945	Enzo Doria	12/2012
5294	11^81562-2340	84939	Enzo Doria	12/2012
5295	(41*10^84927+31)/9	84928	Robert Price	05/2015
5296	(2*10^84904-17)/3	84904	Robert Price	08/2014
5297	(4^141017+23)/3	84901	Robert Price	02/2017
5298	6^109100-18653	84897	Enzo Doria	03/2013
5299	2^281973+1025	84883	Lelio R Paula	09/2013
5300	2^281951-109651	84876	Enzo Doria	04/2014
5301	11^81491-5430	84865	Enzo Doria	01/2013
5302	((1+sqrt(3)+sqrt(2))^79357-1)((1+sqrt(3)-sqrt(2))^79357-1)((1-sqrt(3)+sqrt(2))^79357-1)*((1-sqrt(3	84849	Mike Oakes	04/2009
5303	2^281825-1861483	84838	Enzo Doria	03/2016
5304	2^281809-97305	84833	Lelio R Paula	09/2013
5305	2^281780-114893	84825	Enzo Doria	05/2015
5306	3^177719+64	84794	Lelio R Paula	12/2015
5308	2^281675-199	84793	Lelio R Paula	08/2012
5307	2^281673-111223	84793	Enzo Doria	05/2014
5309	(4*10^84779+149)/9	84779	Robert Price	03/2017
5310	129^40167-128	84777	Norbert Schneider	01/2019
5311	(72*10^84772-27)/9	84773	Ray Chandler	01/2011
5312	11^81398-630	84768	Enzo Doria	11/2012
5313	(25*2^281577-1)/23	84764	Lelio R Paula	02/2014
5314	2^281500-455	84740	Yves Minet	03/2012
5315	10^84725+1145141919	84726	Marisa Kirisame	03/2015
5316	10^84725+142041	84726	Patrick De Geest	10/2015
5317	10^84725-138677	84725	Patrick De Geest	02/2016
5318	76^45044+75	84720	Norbert Schneider	02/2015
5319	54^48897-53	84709	Norbert Schneider	08/2014
5320	(9913*2^281377-1)/65	84706	Lelio R Paula	04/2015
5321	Phi(171124,10)/29946701/7761329021/58560344041	84700	Maksym Voznyy	11/2015
5322	2^281337-111223	84691	Enzo Doria	05/2014
5323	2^281308+54615	84683	Lelio R Paula	09/2013
5324	7*5^121144-6	84677	Lelio R Paula	10/2014
5325	(2^281252+47)/3	84665	Lelio R Paula	01/2013
5326	11^81297-3150	84663	Enzo Doria	12/2012
5327	2^281208-303	84653	Yves Minet	02/2012
5328	197^36892-2	84648	Lelio R Paula	10/2017
5329	(21*2^281187+1)/2483	84644	Lelio R Paula	01/2013
5330	11^81247-84	84611	Lelio R Paula	10/2015
5331	17^68747-64	84590	Lelio R Paula	11/2015
5332	5^121018-15596	84588	Enzo Doria	02/2013
5333	6^108702+7	84587	Lelio R Paula	11/2014
5334	10^84582+100677	84583	Patrick De Geest	05/2016
5335	10^84582-8001	84582	Robert Price	03/2016
5336	3*5^121004-8	84579	Lelio R Paula	10/2014
5337	5^120996-84	84573	Lelio R Paula	10/2015
5338	(10223*2^280881+1)/68419	84553	Lelio R Paula	06/2014
5339	2^280852+97681	84545	Yves Minet	08/2004
5340	2^280848-1203	84544	Lelio R Paula	09/2013
5341	5^120946-24	84538	Lelio R Paula	10/2015
5342	2^280810-2111	84533	Yves Minet	08/2013
5343	11^81161-5160	84521	Enzo Doria	01/2013
5344	2^280737-93	84511	Lelio R Paula	08/2012
5345	2^280698+315	84499	Lelio R Paula	09/2013
5346	3^177099-340	84498	Lelio R Paula	12/2015
5347	(5*10^84469-107)/3	84470	Robert Price	01/2017
5348	(3^177002+7)/6696022272161744	84436	Lelio R Paula	12/2012
5349	(2^280500-1017)/823	84436	Lelio R Paula	01/2013
5350	14^73660-5	84424	Lelio R Paula	11/2015
5351	(19*10^84409-61)/3	84410	Robert Price	04/2017
5352	2^280388+117	84406	Lelio R Paula	08/2012
5353	2^280389-566533	84406	Paul Bourdelais	03/2013
5354	(141584^16384+1)/65537	84390	Syoichiro Yamada	06/2008
5355	119^40652+118	84376	Norbert Schneider	09/2018
5356	2^280240-173	84361	Lelio R Paula	08/2012
5357	(184*10^84348-1)/3	84350	Robert Price	02/2017
5358	4*10^84346+93	84347	Robert Price	01/2017
5359	7*2^280156-5	84337	Lelio R Paula	08/2014
5360	8*7^99782-3	84327	Lelio R Paula	10/2014
5362	2^280116+133	84324	Lelio R Paula	08/2012
5361	2^280118+54615	84324	Lelio R Paula	09/2013
5363	(509203*2^280090-1)/3	84321	Lelio R Paula	04/2015
5364	6^108354+47	84316	Lelio R Paula	12/2015
5365	10^84305+141963	84306	Patrick De Geest	07/2013
5366	10^84305-57	84305	Robert Price	05/2011
5367	9^88339+38^88339-24^88339-3*2^88339	84297	Mike Oakes	01/2011
5368	3^176648-112804	84283	Enzo Doria	06/2014
5369	6^108310+115	84282	Lelio R Paula	12/2015
5370	(11*2^279968-1)/5	84280	Lelio R Paula	02/2014
5371	6^108288-16643	84265	Enzo Doria	02/2013
5372	2^279917-58695	84264	Lelio R Paula	08/2013
5373	65^46477+36	84259	Lelio R Paula	01/2016
5374	2^279866-1907	84249	Yves Minet	05/2013
5375	(3^176580-5)/28076	84246	Lelio R Paula	12/2012
5376	(p(17530)#+4)/2	84246	Robert Price	09/2017
5377	(2*10^84239+1)/3	84239	Serge Batalov	07/2009
5379	18^67103-41	84233	Lelio R Paula	11/2015
5378	20^64743-43	84233	Lelio R Paula	01/2016
5380	143^39070+39070^143	84209	Serge Batalov	05/2014
5381	11^80857-5400	84204	Enzo Doria	01/2013
5382	(13*10^84179+161)/3	84180	Robert Price	04/2017
5383	2^279634-110405	84179	Enzo Doria	05/2014
5384	(74*10^84170+313)/9	84171	Robert Price	11/2017
5385	2^279582-1017	84163	Lelio R Paula	08/2013
5386	(22*10^84159-19)/3	84160	Robert Price	02/2017
5387	p(17513)#/2+512	84156	Robert Price	05/2017
5388	(19*10^84144-43)/3	84145	Robert Price	10/2017
5389	(9*2^279507-1)/137	84139	Lelio R Paula	02/2014
5390	11^80792-810	84137	Enzo Doria	11/2012
5391	(97*10^84134-1)/3	84136	Serge Batalov	12/2014
5392	p(17507)#/2+32	84125	Robert Price	12/2016
5393	21485^8224+8224^21485	84116	Hans Havermann	04/2017
5394	3^176294-340	84114	Lelio R Paula	12/2015
5395	(3^176287+4)/2191	84107	Lelio R Paula	12/2012
5396	2^279388-719	84105	Yves Minet	05/2012
5397	(22699*2^279378+1)/221	84104	Lelio R Paula	06/2014
5398	2^279332-110447	84088	Enzo Doria	05/2014
5399	2^279320+7	84084	Lelio R Paula	06/2012
5400	127^39966-2	84081	Lelio R Paula	10/2017
5401	(11*2^279240-1)/95	84059	Lelio R Paula	02/2014
5402	2^279218-111347	84053	Enzo Doria	05/2014
5403	35^54435+2	84052	Lelio R Paula	05/2013
5404	(31*2^279191-1)/12511523	84040	Lelio R Paula	02/2014
5405	20996^10059+10059^20996	84038	Hans Havermann	05/2017
5406	97*10^84033-3	84035	Robert Price	01/2017
5407	21234^9067+9067^21234	84033	Hans Havermann	05/2017
5408	(134569^16384+1)/2	84033	Richard Fischer	06/2018
5409	2^279095-109717	84016	Enzo Doria	04/2014
5410	14^73282-99	83991	Lelio R Paula	11/2015
5411	21457^8200+8200^21457	83979	Hans Havermann	06/2017
5412	89*10^83976-7	83978	Robert Price	03/2017
5413	2^278955+173	83974	Lelio R Paula	06/2012
5414	(7*2^278851+1)/39	83942	Lelio R Paula	12/2012
5415	(9913*2^278844-1)/40803	83940	Lelio R Paula	04/2015
5416	5^120076-14846	83930	Enzo Doria	02/2013
5417	(85*10^83921-1)/3	83923	Robert Price	07/2017
5418	(2^278770-3)/23	83917	Lelio R Paula	12/2012
5419	(10^83916+449)/9	83916	Serge Batalov	12/2014
5421	2^278715+99	83902	Lelio R Paula	06/2012
5420	(132109^16384+1)/2	83902	Richard Fischer	05/2018
5422	40235!2-2^40235	83899	Robert Price	09/2015
5423	2^278698-171	83897	Lelio R Paula	06/2012
5424	(19*10^83894-43)/3	83895	Robert Price	10/2017
5425	6^107802+25	83887	Lelio R Paula	12/2015
5426	8*10^83880+39	83881	Robert Price	01/2017
5427	(58*10^83878+23)/9	83879	Robert Price	09/2015
5428	7^99244-90	83871	Lelio R Paula	10/2015
5429	2^278554+4257	83854	Lelio R Paula	08/2013
5430	2^278504-109619	83839	Enzo Doria	04/2014
5431	2^278499+1870433	83837	Enzo Doria	05/2016
5432	105^41475+104	83829	Norbert Schneider	11/2016
5433	15^71276-68	83828	Lelio R Paula	11/2015
5434	2^278464-216413	83827	Enzo Doria	04/2013
5435	(76*10^83816-211)/9	83817	Robert Price	10/2017
5436	(8*10^83811-101)/3	83812	Robert Price	10/2017
5437	2^278400+40755	83807	Lelio R Paula	08/2013
5438	(9*2^278381-1)/7	83802	Lelio R Paula	02/2014
5439	39^87813+6^87813+24^87813	83796	Mike Oakes	12/2010
5440	19551^19268+19268^19551	83773	Hans Havermann	05/2017
5441	20625^11522+11522^20625	83770	Hans Havermann	05/2017
5442	(44*10^83768-791)/9	83769	Robert Price	10/2017
5443	(87^43189+1)/88	83764	Paul Bourdelais	08/2017
5444	2^278235-49	83758	Lelio R Paula	06/2012
5445	23543^3610+3610^23543	83755	Hans Havermann	05/2017
5447	18^66711-91	83741	Lelio R Paula	11/2015
5446	4*10^83740-89	83741	Robert Price	08/2017
5448	(3*2^278172-1)/11	83738	Lelio R Paula	02/2014
5449	(15*29^57251+2561)/28	83724	Curtis Bright	05/2015
5450	4*7^99059-9	83716	Lelio R Paula	10/2014
5451	(2^278128-3)/126844724149	83714	Lelio R Paula	12/2012
5452	2^278077+1867211	83710	Enzo Doria	03/2016
5453	2^278059-27	83705	Lelio R Paula	06/2012
5454	214^35917+35917^214	83702	Norbert Schneider	12/2014
5455	(23*10^83693+7)/3	83694	Robert Price	10/2015
5456	85^43375-2	83689	Lelio R Paula	09/2013
5457	5*3^175360+4	83669	Lelio R Paula	07/2014
5458	(23^61441-1)/22	83665	Robert Price	01/2012
5459	20091^14596+14596^20091	83664	Hans Havermann	03/2017
5460	2^277907-110629	83659	Enzo Doria	05/2014
5461	19522^19283+19283^19522	83656	Hans Havermann	04/2017
5462	8*5^119664-3	83643	Lelio R Paula	10/2014
5463	8*3^175299-7	83640	Lelio R Paula	07/2014
5464	(26*10^83638-413)/9	83639	Robert Price	10/2017
5465	3^175250+22	83616	Robert Price	12/2013
5467	11^80285+30	83609	Lelio R Paula	10/2015
5466	26870^1293+1293^26870	83609	Hans Havermann	03/2017
5468	2^277691+1874423	83594	Enzo Doria	06/2016
5469	13^75022-60	83571	Lelio R Paula	11/2015
5470	14^72905-51	83559	Lelio R Paula	11/2015
5471	(17*2^277565-1)/543	83554	Lelio R Paula	02/2014
5472	5^119532-12	83550	Lelio R Paula	10/2015
5473	6^107358-16253	83541	Enzo Doria	02/2013
5474	2^277478-460211	83530	Enzo Doria	06/2015
5475	(22*10^83525-7)/3	83526	Erik Branger	09/2014
5476	(30^56543+1)/31	83520	Robert Price	07/2013
5477	2^277417-460783	83511	Paul Bourdelais	04/2013
5478	(22699*2^277387+1)/219	83504	Lelio R Paula	06/2014
5479	(31*2^277383-1)/247	83500	Lelio R Paula	02/2014
5480	21368^8085+8085^21368	83500	Hans Havermann	04/2017
5481	(9*2^277342+1)/13	83489	Lelio R Paula	12/2012
5482	5^119439-66	83485	Lelio R Paula	10/2015
5483	(14*10^83471-101)/3	83472	Robert Price	04/2017
5484	5*6^107263+7	83468	Lelio R Paula	10/2014
5485	(64*10^83461-1)/9	83462	Serge Batalov	11/2010
5486	2^277244-175709	83459	Hans Havermann	10/2018
5487	17^67796-92	83420	Lelio R Paula	11/2015
5488	2^277106-110057	83418	Enzo Doria	04/2014
5489	6^107200-19	83418	Lelio R Paula	12/2015
5490	11^80096-1830	83412	Enzo Doria	12/2012
5491	3^174801+56	83402	Lelio R Paula	12/2015
5492	2^277033-111973	83396	Enzo Doria	05/2014
5493	120^40105-119	83386	Norbert Schneider	09/2018
5494	20519^11572+11572^20519	83378	Hans Havermann	03/2017
5495	20850^9971+9971^20850	83374	Hans Havermann	03/2017
5496	6^107122-18863	83358	Enzo Doria	03/2013
5497	4*10^83354-89	83355	Robert Price	08/2017
5498	3^174697-34	83352	Robert Price	11/2013
5499	(9787*2^276855-1)/2345	83343	Lelio R Paula	04/2015
5500	2^276825+75227	83333	Enzo Doria	04/2016

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Probable Primes Top 10000

(252675 PRPs in the top)