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 ?
5001	6^108702+7	84587	Lelio R Paula	11/2014
5002	10^84582+100677	84583	Patrick De Geest	05/2016
5003	10^84582-8001	84582	Robert Price	03/2016
5004	3*5^121004-8	84579	Lelio R Paula	10/2014
5005	5^120996-84	84573	Lelio R Paula	10/2015
5006	(10223*2^280881+1)/68419	84553	Lelio R Paula	06/2014
5007	2^280852+97681	84545	Yves Minet	08/2004
5008	2^280848-1203	84544	Lelio R Paula	09/2013
5009	5^120946-24	84538	Lelio R Paula	10/2015
5010	2^280810-2111	84533	Yves Minet	08/2013
5011	11^81161-5160	84521	Enzo Doria	01/2013
5012	2^280737-93	84511	Lelio R Paula	08/2012
5013	2^280698+315	84499	Lelio R Paula	09/2013
5014	3^177099-340	84498	Lelio R Paula	12/2015
5015	(5*10^84469-107)/3	84470	Robert Price	01/2017
5016	(3^177002+7)/6696022272161744	84436	Lelio R Paula	12/2012
5017	(2^280500-1017)/823	84436	Lelio R Paula	01/2013
5018	14^73660-5	84424	Lelio R Paula	11/2015
5019	(19*10^84409-61)/3	84410	Robert Price	04/2017
5020	2^280388+117	84406	Lelio R Paula	08/2012
5021	2^280389-566533	84406	Paul Bourdelais	03/2013
5022	(141584^16384+1)/65537	84390	Syoichiro Yamada	06/2008
5023	119^40652+118	84376	Norbert Schneider	09/2018
5024	2^280240-173	84361	Lelio R Paula	08/2012
5025	(184*10^84348-1)/3	84350	Robert Price	02/2017
5026	4*10^84346+93	84347	Robert Price	01/2017
5027	7*2^280156-5	84337	Lelio R Paula	08/2014
5028	8*7^99782-3	84327	Lelio R Paula	10/2014
5030	2^280116+133	84324	Lelio R Paula	08/2012
5029	2^280118+54615	84324	Lelio R Paula	09/2013
5031	(509203*2^280090-1)/3	84321	Lelio R Paula	04/2015
5032	6^108354+47	84316	Lelio R Paula	12/2015
5033	10^84305+141963	84306	Patrick De Geest	07/2013
5034	10^84305-57	84305	Robert Price	05/2011
5035	9^88339+38^88339-24^88339-3*2^88339	84297	Mike Oakes	01/2011
5036	3^176648-112804	84283	Enzo Doria	06/2014
5037	6^108310+115	84282	Lelio R Paula	12/2015
5038	(11*2^279968-1)/5	84280	Lelio R Paula	02/2014
5039	6^108288-16643	84265	Enzo Doria	02/2013
5040	2^279917-58695	84264	Lelio R Paula	08/2013
5041	65^46477+36	84259	Lelio R Paula	01/2016
5042	2^279866-1907	84249	Yves Minet	05/2013
5043	(3^176580-5)/28076	84246	Lelio R Paula	12/2012
5044	(p(17530)#+4)/2	84246	Robert Price	09/2017
5045	(2*10^84239+1)/3	84239	Serge Batalov	07/2009
5047	18^67103-41	84233	Lelio R Paula	11/2015
5046	20^64743-43	84233	Lelio R Paula	01/2016
5048	143^39070+39070^143	84209	Serge Batalov	05/2014
5049	11^80857-5400	84204	Enzo Doria	01/2013
5050	(13*10^84179+161)/3	84180	Robert Price	04/2017
5051	2^279634-110405	84179	Enzo Doria	05/2014
5052	(74*10^84170+313)/9	84171	Robert Price	11/2017
5053	2^279582-1017	84163	Lelio R Paula	08/2013
5054	(22*10^84159-19)/3	84160	Robert Price	02/2017
5055	p(17513)#/2+512	84156	Robert Price	05/2017
5056	(19*10^84144-43)/3	84145	Robert Price	10/2017
5057	(9*2^279507-1)/137	84139	Lelio R Paula	02/2014
5058	11^80792-810	84137	Enzo Doria	11/2012
5059	(97*10^84134-1)/3	84136	Serge Batalov	12/2014
5060	p(17507)#/2+32	84125	Robert Price	12/2016
5061	21485^8224+8224^21485	84116	Hans Havermann	04/2017
5062	3^176294-340	84114	Lelio R Paula	12/2015
5063	(3^176287+4)/2191	84107	Lelio R Paula	12/2012
5064	2^279388-719	84105	Yves Minet	05/2012
5065	(22699*2^279378+1)/221	84104	Lelio R Paula	06/2014
5066	2^279332-110447	84088	Enzo Doria	05/2014
5067	2^279320+7	84084	Lelio R Paula	06/2012
5068	127^39966-2	84081	Lelio R Paula	10/2017
5069	(11*2^279240-1)/95	84059	Lelio R Paula	02/2014
5070	2^279218-111347	84053	Enzo Doria	05/2014
5071	35^54435+2	84052	Lelio R Paula	05/2013
5072	(31*2^279191-1)/12511523	84040	Lelio R Paula	02/2014
5073	20996^10059+10059^20996	84038	Hans Havermann	05/2017
5074	97*10^84033-3	84035	Robert Price	01/2017
5075	21234^9067+9067^21234	84033	Hans Havermann	05/2017
5076	(134569^16384+1)/2	84033	Richard Fischer	06/2018
5077	2^279095-109717	84016	Enzo Doria	04/2014
5078	14^73282-99	83991	Lelio R Paula	11/2015
5079	21457^8200+8200^21457	83979	Hans Havermann	06/2017
5080	89*10^83976-7	83978	Robert Price	03/2017
5081	2^278955+173	83974	Lelio R Paula	06/2012
5082	(7*2^278851+1)/39	83942	Lelio R Paula	12/2012
5083	(9913*2^278844-1)/40803	83940	Lelio R Paula	04/2015
5084	5^120076-14846	83930	Enzo Doria	02/2013
5085	(85*10^83921-1)/3	83923	Robert Price	07/2017
5086	(2^278770-3)/23	83917	Lelio R Paula	12/2012
5087	(10^83916+449)/9	83916	Serge Batalov	12/2014
5088	2^278715+99	83902	Lelio R Paula	06/2012
5089	(132109^16384+1)/2	83902	Richard Fischer	05/2018
5090	40235!2-2^40235	83899	Robert Price	09/2015
5091	2^278698-171	83897	Lelio R Paula	06/2012
5092	(19*10^83894-43)/3	83895	Robert Price	10/2017
5093	6^107802+25	83887	Lelio R Paula	12/2015
5094	8*10^83880+39	83881	Robert Price	01/2017
5095	(58*10^83878+23)/9	83879	Robert Price	09/2015
5096	7^99244-90	83871	Lelio R Paula	10/2015
5097	2^278554+4257	83854	Lelio R Paula	08/2013
5098	2^278504-109619	83839	Enzo Doria	04/2014
5099	2^278499+1870433	83837	Enzo Doria	05/2016
5100	105^41475+104	83829	Norbert Schneider	11/2016
5101	15^71276-68	83828	Lelio R Paula	11/2015
5102	2^278464-216413	83827	Enzo Doria	04/2013
5103	(76*10^83816-211)/9	83817	Robert Price	10/2017
5104	(8*10^83811-101)/3	83812	Robert Price	10/2017
5105	2^278400+40755	83807	Lelio R Paula	08/2013
5106	(9*2^278381-1)/7	83802	Lelio R Paula	02/2014
5107	39^87813+6^87813+24^87813	83796	Mike Oakes	12/2010
5108	19551^19268+19268^19551	83773	Hans Havermann	05/2017
5109	20625^11522+11522^20625	83770	Hans Havermann	05/2017
5110	(44*10^83768-791)/9	83769	Robert Price	10/2017
5111	(87^43189+1)/88	83764	Paul Bourdelais	08/2017
5112	2^278235-49	83758	Lelio R Paula	06/2012
5113	23543^3610+3610^23543	83755	Hans Havermann	05/2017
5115	18^66711-91	83741	Lelio R Paula	11/2015
5114	4*10^83740-89	83741	Robert Price	08/2017
5116	(3*2^278172-1)/11	83738	Lelio R Paula	02/2014
5117	(15*29^57251+2561)/28	83724	Curtis Bright	05/2015
5118	4*7^99059-9	83716	Lelio R Paula	10/2014
5119	(2^278128-3)/126844724149	83714	Lelio R Paula	12/2012
5120	2^278077+1867211	83710	Enzo Doria	03/2016
5121	2^278059-27	83705	Lelio R Paula	06/2012
5122	214^35917+35917^214	83702	Norbert Schneider	12/2014
5123	(23*10^83693+7)/3	83694	Robert Price	10/2015
5124	85^43375-2	83689	Lelio R Paula	09/2013
5125	5*3^175360+4	83669	Lelio R Paula	07/2014
5126	(23^61441-1)/22	83665	Robert Price	01/2012
5127	20091^14596+14596^20091	83664	Hans Havermann	03/2017
5128	2^277907-110629	83659	Enzo Doria	05/2014
5129	19522^19283+19283^19522	83656	Hans Havermann	04/2017
5130	8*5^119664-3	83643	Lelio R Paula	10/2014
5131	8*3^175299-7	83640	Lelio R Paula	07/2014
5132	(26*10^83638-413)/9	83639	Robert Price	10/2017
5133	3^175250+22	83616	Robert Price	12/2013
5135	11^80285+30	83609	Lelio R Paula	10/2015
5134	26870^1293+1293^26870	83609	Hans Havermann	03/2017
5136	2^277691+1874423	83594	Enzo Doria	06/2016
5137	13^75022-60	83571	Lelio R Paula	11/2015
5138	14^72905-51	83559	Lelio R Paula	11/2015
5139	(17*2^277565-1)/543	83554	Lelio R Paula	02/2014
5140	5^119532-12	83550	Lelio R Paula	10/2015
5141	6^107358-16253	83541	Enzo Doria	02/2013
5142	2^277478-460211	83530	Enzo Doria	06/2015
5143	(22*10^83525-7)/3	83526	Erik Branger	09/2014
5144	(30^56543+1)/31	83520	Robert Price	07/2013
5145	2^277417-460783	83511	Paul Bourdelais	04/2013
5146	(22699*2^277387+1)/219	83504	Lelio R Paula	06/2014
5147	(31*2^277383-1)/247	83500	Lelio R Paula	02/2014
5148	21368^8085+8085^21368	83500	Hans Havermann	04/2017
5149	(9*2^277342+1)/13	83489	Lelio R Paula	12/2012
5150	5^119439-66	83485	Lelio R Paula	10/2015
5151	(14*10^83471-101)/3	83472	Robert Price	04/2017
5152	5*6^107263+7	83468	Lelio R Paula	10/2014
5153	(64*10^83461-1)/9	83462	Serge Batalov	11/2010
5154	2^277244-175709	83459	Hans Havermann	10/2018
5155	17^67796-92	83420	Lelio R Paula	11/2015
5156	2^277106-110057	83418	Enzo Doria	04/2014
5157	6^107200-19	83418	Lelio R Paula	12/2015
5158	11^80096-1830	83412	Enzo Doria	12/2012
5159	3^174801+56	83402	Lelio R Paula	12/2015
5160	2^277033-111973	83396	Enzo Doria	05/2014
5161	120^40105-119	83386	Norbert Schneider	09/2018
5162	20519^11572+11572^20519	83378	Hans Havermann	03/2017
5163	20850^9971+9971^20850	83374	Hans Havermann	03/2017
5164	6^107122-18863	83358	Enzo Doria	03/2013
5165	4*10^83354-89	83355	Robert Price	08/2017
5166	3^174697-34	83352	Robert Price	11/2013
5167	(9787*2^276855-1)/2345	83343	Lelio R Paula	04/2015
5168	2^276825+75227	83333	Enzo Doria	04/2016
5169	5^119214+84	83328	Lelio R Paula	10/2015
5170	2^276803-159	83327	Lelio R Paula	06/2012
5171	(3*2^276753-1)/25	83311	Lelio R Paula	02/2014
5172	114^40495+40495^114	83295	Norbert Schneider	12/2014
5173	39967!2+1024	83282	Robert Price	02/2015
5175	2^276641+57	83278	Lelio R Paula	06/2012
5174	35^53934-3414	83278	Enzo Doria	03/2013
5176	(2^276655+78557)/365425	83276	Lelio R Paula	12/2012
5177	2^276615-4035	83270	Lelio R Paula	08/2013
5178	2^276588+1155	83262	Lelio R Paula	08/2013
5180	2^276587-937	83261	Yves Minet	10/2009
5179	2^276584-113183	83261	Enzo Doria	07/2014
5181	(2^276592-1017)/13843739	83256	Lelio R Paula	12/2012
5182	2^276547-109591	83249	Enzo Doria	04/2014
5183	13^74733-32	83249	Lelio R Paula	11/2015
5184	2^276523-2587	83242	Yves Minet	07/2014
5185	18^66311-43	83239	Lelio R Paula	11/2015
5186	11^79919-1530	83228	Enzo Doria	12/2012
5187	2^276468-109745	83226	Enzo Doria	04/2014
5188	2^276462+5385	83224	Lelio R Paula	08/2013
5189	(9787*2^276422-1)/3	83215	Lelio R Paula	04/2015
5190	2^276391-15	83202	Lelio R Paula	06/2012
5191	(4*10^83201+173)/3	83202	Robert Price	01/2017
5192	2^276316-109655	83180	Enzo Doria	04/2014
5193	2^276305-112063	83177	Enzo Doria	06/2014
5194	(10^(241585+1)+5410^41585-1)/9	83171	Robert Price	04/2017
5195	74913!4-2	83161	Robert Price	07/2017
5196	2^276227-1837207	83153	Enzo Doria	05/2015
5197	(2^276227+3)/7	83152	Lelio R Paula	12/2012
5198	2^276184-63389	83140	Paul Bourdelais	02/2012
5199	2^276066-111603	83105	Enzo Doria	05/2014
5200	(2^276028-3)*6-7	83094	Gilbert Mozzo	09/2016
5201	(2^275897+9)/1153	83051	Lelio R Paula	12/2012
5202	2^275879-109807	83048	Enzo Doria	04/2014
5204	F(397379)	83047	Henri Lifchitz	08/2003
5203	U(397379)	83047	Serge Batalov	03/2015
5205	3^174040-14	83039	Robert Price	08/2013
5206	(86*10^83038-221)/9	83039	Robert Price	06/2017
5207	2^275841-6883	83037	Lelio R Paula	07/2011
5208	3^174002-140	83021	Lelio R Paula	12/2015
5209	6^106681+77	83014	Lelio R Paula	12/2015
5210	187^36539-2	83011	Lelio R Paula	10/2017
5211	11^79701-3150	83001	Enzo Doria	12/2012
5212	(55459*2^275657+1)/21	82985	Lelio R Paula	06/2014
5213	(7*10^82960-457)/9	82960	Robert Price	09/2017
5214	2^275535-6855	82945	Lelio R Paula	08/2013
5216	3^173828-14	82938	Robert Price	08/2013
5215	2^275512-109677	82938	Enzo Doria	04/2014
5217	2^275446-110045	82918	Enzo Doria	04/2014
5218	(2^275473+47)/29526097447	82916	Lelio R Paula	12/2012
5219	3^173755-14	82903	Robert Price	08/2013
5220	(182*10^82898+43)/9	82900	Robert Price	11/2017
5221	2^275363-112309	82893	Enzo Doria	06/2014
5222	61^46427-60	82888	Norbert Schneider	10/2014
5223	3*10^82880-7^82880	82881	Mike Oakes	02/2010
5225	2^275290+90195	82871	Lelio R Paula	07/2013
5224	(35*10^82870-71)/9	82871	Robert Price	05/2015
5226	2^275270-1859621	82865	Enzo Doria	03/2016
5227	2^275259+81	82862	Henri Lifchitz	01/2007
5228	(113703^16384+1)/2	82834	Richard Fischer	04/2018
5229	7^98003+98003^7+1	82823	Robert Price	05/2014
5230	10^82790+126043	82791	Patrick De Geest	07/2013
5231	10^82790-47	82790	Robert Price	05/2011
5232	2^274985-112663	82779	Enzo Doria	06/2014
5233	2^274935+15015	82764	Lelio R Paula	07/2013
5234	(17*2^274922+1)/3	82761	Lelio R Paula	12/2012
5235	(43*10^82752-61)/9	82753	Robert Price	06/2015
5236	(3*2^274862+1)/1027	82740	Lelio R Paula	12/2012
5237	(31*2^274848-1)/4065	82736	Lelio R Paula	02/2014
5238	(4^137405+23)/3	82726	Robert Price	02/2017
5239	2^274791-110491	82721	Enzo Doria	05/2014
5240	(11*2^274776-1)/95	82715	Lelio R Paula	02/2014
5241	(47*10^82706-119)/9	82707	Robert Price	09/2017
5242	2^274704-111395	82695	Enzo Doria	05/2014
5243	2^274686-3911	82689	Yves Minet	04/2017
5244	(2^274663-1017)/48871318292279	82669	Lelio R Paula	12/2012
5245	(3^173263-5)/14498	82664	Lelio R Paula	12/2012
5246	2^274511-64875	82637	Lelio R Paula	08/2013
5247	12^76572-83	82636	Lelio R Paula	11/2015
5248	3^173191-2^173191	82634	Mike Oakes	02/2004
5249	14^72072-15	82604	Lelio R Paula	11/2015
5250	(55459*2^274339+1)/3	82589	Lelio R Paula	06/2014

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Probable Primes Top 10000

(225451 PRPs in the top)