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	(2^261724+184549)/5/8699/44053/1409322997	78769	Tony Prest / Never Odd Or Even	04/2014
5002	(2^261724+363351)/937/159683/59523200227	78768	Tony Prest / Never Odd Or Even	04/2014
5003	(2^261724+326501)/3/43/193/263/19403/253501403	78768	Tony Prest / Never Odd Or Even	04/2014
5004	(2^261724+629477)/3/17/17/137/263/1993/16187/57347	78768	Tony Prest / Never Odd Or Even	05/2014
5005	(2^261724+94871)/3/3/13/6734017/1673425245787	78766	Tony Prest / Never Odd Or Even	04/2014
5006	(2^261724+25981)/577/1181/3643/517786334743	78766	Tony Prest / Never Odd Or Even	04/2014
5008	(23*2^261642+1)/93	78762	Lelio R Paula	10/2012
5007	(2^261724+351227)/3/3/3/3/71/13997/9595373/8193978007	78762	Tony Prest / Never Odd Or Even	04/2014
5009	(2^261724+22571)/3/7243/7321/18046081/45730741211	78761	Tony Prest / Never Odd Or Even	04/2014
5010	(2^261724+56495)/3/3/3/7/7/13/9041/512818459/23708589119	78760	Tony Prest / Never Odd Or Even	04/2014
5011	(2^261724+604119)/5/7/7/41/14107/19681/211777/90145981/1036020834127	78750	Tony Prest / Never Odd Or Even	05/2014
5012	2^261507-2287	78722	Yves Minet	04/2009
5013	8*10^78717+39	78718	Robert Price	01/2017
5014	(78557*2^261440+1)/3	78706	Lelio R Paula	06/2014
5015	6^101128-16433	78693	Enzo Doria	02/2013
5016	20^60482+99	78689	Lelio R Paula	03/2015
5017	2^261348-110633	78674	Enzo Doria	05/2014
5018	191^34487+2	78666	Lelio R Paula	05/2013
5019	2^261305-110139	78661	Enzo Doria	04/2014
5020	(82*10^78635-1)/9	78636	Robert Price	12/2014
5021	10^78632+81	78633	Robert Price	03/2011
5022	10^78632-402693	78632	Patrick De Geest	07/2013
5023	3*10^78631+17	78632	Robert Price	03/2017
5024	2^261174-3911	78622	Yves Minet	04/2017
5025	2^261167+74843	78620	Enzo Doria	04/2016
5026	L(376121)+F(376122)	78605	Henri Lifchitz	01/2007
5027	14^68580-29	78602	Lelio R Paula	02/2015
5028	(73*10^78576-1)/9	78577	Robert Price	01/2015
5029	(17*2^261026-1)/40451	78574	Lelio R Paula	02/2014
5030	2^261001-195	78570	Lelio R Paula	05/2012
5031	5*2^260950+9	78555	Lelio R Paula	06/2014
5032	2^260931-7605	78549	Lelio R Paula	07/2013
5033	15^66778-32	78538	Lelio R Paula	02/2015
5034	(11*2^260896-1)/245	78537	Lelio R Paula	02/2014
5035	30^53166+29	78533	Norbert Schneider	03/2017
5036	lucasU(2403,1,23229)-lucasU(2403,1,23228)	78529	Mike Oakes	05/2009
5037	7*3^164574-2	78523	Lelio R Paula	06/2014
5038	2^260830-112133	78518	Enzo Doria	06/2014
5039	13^70486+42	78518	Lelio R Paula	03/2015
5040	11^75386-7080	78507	Enzo Doria	01/2013
5041	2^260711-58695	78482	Lelio R Paula	07/2013
5042	2^260678-111065	78472	Enzo Doria	05/2014
5043	18^62501-97	78456	Lelio R Paula	02/2015
5044	53^45498-2	78452	Lelio R Paula	08/2013
5045	2^260513-111121	78423	Enzo Doria	05/2014
5046	37845!2-64	78412	Robert Price	06/2015
5047	2^260469-110695	78409	Enzo Doria	05/2014
5048	(11*10^78408-113)/3	78409	Robert Price	01/2017
5049	2^260447+8415	78403	Lelio R Paula	07/2013
5050	37837!2-64	78394	Robert Price	06/2015
5051	(19*2^260379-1)/53	78382	Lelio R Paula	02/2014
5052	2^260377-113233	78382	Enzo Doria	07/2014
5053	9^82138+6^82138-2^82138	78380	Mike Oakes	08/2010
5054	69^42624+2	78380	Lelio R Paula	05/2013
5055	2^260369-1859713	78379	Enzo Doria	03/2016
5056	14*10^78362+1089	78364	Jens K. Andersen	11/2007
5057	5^112070-54	78334	Lelio R Paula	02/2015
5058	(10^(239165+1)+5410^39165-1)/9	78331	Robert Price	04/2017
5059	2^260182-113453	78323	Enzo Doria	07/2014
5060	(78557*2^260084+1)/519	78296	Lelio R Paula	06/2014
5062	10^78288+9^(78288+1)	78289	Robert Price	08/2016
5061	10^78288+39109	78289	Patrick De Geest	12/2016
5063	10^78288-216299	78288	Patrick De Geest	12/2016
5064	5^111997+36	78283	Lelio R Paula	02/2015
5065	(21^59183+1)/22	78252	Paul Bourdelais	03/2010
5066	(88*10^78242-7)/9	78243	Robert Price	11/2014
5067	2*6^100547+7	78242	Lelio R Paula	10/2014
5068	2^259860-111089	78226	Enzo Doria	05/2014
5069	37^49875-2	78215	Lelio R Paula	09/2013
5070	7*5^111893-4	78211	Lelio R Paula	10/2014
5071	(11*2^259809-1)/1437	78209	Lelio R Paula	02/2014
5072	7^92511-6	78181	Theodore Burton	11/2005
5073	(3^163859-4)/253	78179	Lelio R Paula	10/2012
5074	(27*2^259666-1)/625691	78163	Lelio R Paula	02/2014
5075	3*10^78146+17	78147	Robert Price	03/2017
5076	2^259503+74333	78119	Enzo Doria	04/2016
5077	(31*2^259504-1)/13365	78116	Lelio R Paula	02/2014
5079	(58547^16384+1)/2	78111	Lelio R Paula	11/2011
5078	6^100379+13	78111	Lelio R Paula	03/2015
5080	2^259469-109909	78108	Enzo Doria	04/2014
5081	15^66413-26	78108	Lelio R Paula	02/2015
5082	7^92410-9266	78096	Mike Oakes	02/2010
5083	2^259398+75799	78087	Enzo Doria	04/2016
5084	2^259394+1876189	78086	Enzo Doria	07/2016
5085	PIPrime(78073)	78073	Eric W. Weisstein	07/2006
5086	5*2^259344-7	78072	Lelio R Paula	06/2014
5087	14^68097-87	78048	Lelio R Paula	02/2015
5088	2^259233-475573	78037	Paul Bourdelais	03/2013
5089	3^163500-28	78010	Robert Price	12/2013
5090	(65*10^77992+691)/9	77993	Robert Price	08/2016
5091	2^259013-112591	77971	Enzo Doria	06/2014
5092	6^100193-100193^6	77966	Norbert Schneider	04/2017
5093	2^258863-110235	77926	Enzo Doria	05/2014
5094	2^258852+1605	77923	Lelio R Paula	06/2013
5095	(11*10^77909+49)/3	77910	Robert Price	05/2016
5096	2*7^92187-9	77908	Lelio R Paula	10/2014
5097	2^258763-110155	77896	Enzo Doria	04/2014
5098	2^258694-110387	77875	Enzo Doria	05/2014
5099	11^74773-94	77869	Lelio R Paula	02/2015
5100	6^100067+125	77868	Lelio R Paula	03/2015
5101	15^66205+8	77864	Lelio R Paula	07/2014
5102	5^111373-18136	77847	Enzo Doria	05/2014
5103	2^258524-109877	77824	Enzo Doria	04/2014
5104	6^100002-16643	77817	Enzo Doria	02/2013
5105	65^42916+28	77803	Lelio R Paula	01/2016
5106	(89*10^77781-17)/9	77782	Robert Price	11/2015
5107	2^258382-110405	77781	Enzo Doria	05/2014
5108	5^111278-14996	77780	Enzo Doria	02/2013
5109	14^67862+61	77779	Lelio R Paula	02/2015
5110	10^77777+48483	77778	Patrick De Geest	11/2010
5111	10^77777-183243	77777	Patrick De Geest	11/2010
5112	(27*2^258352+1)/43	77772	Lelio R Paula	08/2012
5113	337^30756-10002	77740	Enzo Doria	07/2012
5114	10^77726+99	77727	Robert Price	03/2011
5115	10^77726-85947	77726	Patrick De Geest	06/2013
5116	89^39870-2	77723	Lelio R Paula	08/2013
5117	7^91966-32	77721	Lelio R Paula	02/2015
5118	35^50327+2	77709	Lelio R Paula	05/2013
5119	24^56298+23	77704	Norbert Schneider	12/2016
5120	(2^258105+78557)/19	77697	Lelio R Paula	10/2012
5121	2^258079+179	77690	Lelio R Paula	03/2012
5122	2^258062-113111	77685	Enzo Doria	07/2014
5123	80^40807-79	77660	Norbert Schneider	03/2015
5124	(10^77637+359)/9	77637	Serge Batalov	12/2014
5125	2^257862-165	77625	Lelio R Paula	03/2012
5126	(25*2^257853+1)/3	77623	Lelio R Paula	07/2012
5127	(2^257869+1)/(3*18645362967379)	77613	Henri Lifchitz	04/2005
5128	6^99728+71	77604	Lelio R Paula	01/2015
5129	2^257778-112767	77599	Enzo Doria	06/2014
5130	(31*2^257771+1)/537	77596	Lelio R Paula	07/2012
5131	2^257729-73	77585	Lelio R Paula	03/2012
5132	2^257689-63	77573	Lelio R Paula	03/2012
5133	(78557*2^257665+1)/6108725	77564	Lelio R Paula	06/2014
5134	(3^162563+8)/2885	77559	Lelio R Paula	10/2012
5136	2^257636-110235	77557	Enzo Doria	05/2014
5135	(23*10^77556+97)/3	77557	Robert Price	02/2017
5137	2^257621-110071	77552	Enzo Doria	04/2014
5138	2^257567-64875	77536	Lelio R Paula	06/2013
5139	2*7^91674+9	77474	Lelio R Paula	10/2014
5140	(17*10^77427-47)/3	77428	Robert Price	05/2017
5141	10^77418+841683	77419	Patrick De Geest	06/2013
5142	10^77418-33	77418	Robert Price	05/2011
5143	19^60539-36	77415	Lelio R Paula	03/2015
5144	37401!!-1024	77397	Robert Price	11/2015
5145	11^74313-18750	77390	Enzo Doria	12/2012
5146	2^257044-112883	77378	Enzo Doria	06/2014
5147	8*10^77377+51	77378	Robert Price	05/2017
5148	2*7^91553+9	77372	Lelio R Paula	10/2014
5149	713^27118+27118^713	77371	Norbert Schneider	12/2016
5150	2^256920-111155	77341	Enzo Doria	05/2014
5151	2^256896-6555	77334	Lelio R Paula	06/2013
5152	(52*10^77322-7)/9	77323	Robert Price	12/2014
5153	2^256849-112939	77320	Enzo Doria	06/2014
5154	(4*10^77309-31)/9	77309	Erik Branger	05/2011
5155	(3^161988+7)/41864	77284	Lelio R Paula	10/2012
5156	(14^67421-1)/13	77272	Paul Bourdelais	09/2008
5157	5*3^161923-4	77258	Lelio R Paula	06/2014
5158	2^256552-1499	77230	Yves Minet	05/2013
5159	2^256460-112757	77203	Enzo Doria	06/2014
5160	2^256398+23299	77184	Yves Minet	02/2011
5161	2^256391-1155*256391	77182	Henri Lifchitz	03/2005
5162	(2^256391-9)/56593	77177	Lelio R Paula	10/2012
5163	(2^256308+9)/10585	77153	Lelio R Paula	10/2012
5165	21^58348-2	77149	Lelio R Paula	08/2013
5164	(17*2^256291-1)/4785	77149	Lelio R Paula	02/2014
5166	(5*2^256274-1)/2141	77144	Lelio R Paula	02/2014
5167	19^60321+82	77136	Lelio R Paula	03/2015
5168	5*2^256233-3	77135	Lelio R Paula	06/2014
5169	3*2^256149+7	77110	Lelio R Paula	06/2014
5170	3^161594-106	77100	Lelio R Paula	02/2015
5171	2^256114-185	77098	Lelio R Paula	03/2012
5172	8^85349-85349^8	77078	Norbert Schneider	05/2017
5173	2^256043-2786377	77077	Enzo Doria	03/2016
5174	2^255973+1869947	77056	Enzo Doria	05/2016
5175	12^71393-43	77046	Lelio R Paula	02/2015
5176	15^65490+44	77023	Lelio R Paula	02/2015
5177	(3^161411-7)/940	77010	Lelio R Paula	10/2012
5179	lucasU(1107,1,25297)-lucasU(1107,1,25296)	77005	Mike Oakes	05/2009
5178	(570^27943-1)/569	77005	Serge Batalov	12/2016
5180	2^255750-75	76989	Lelio R Paula	03/2012
5181	3*6^98926-5	76980	Lelio R Paula	10/2014
5182	18^61320-1433	76974	Enzo Doria	03/2013
5183	6^98916-17093	76972	Enzo Doria	02/2013
5184	2^255659-110131	76962	Enzo Doria	04/2014
5185	12^71303+91	76949	Lelio R Paula	02/2015
5186	18^61298+59	76946	Lelio R Paula	02/2015
5187	(223^32768+1)/131074	76945	Lelio R Paula	02/2009
5188	(2^255613-5)/281517	76942	Lelio R Paula	10/2012
5189	18^61290-11	76936	Lelio R Paula	02/2015
5191	63^42752-2	76926	Lelio R Paula	08/2013
5190	(11*2^255545-1)/117	76926	Lelio R Paula	02/2014
5192	2^255517+56387	76919	Yves Minet	02/2011
5193	2^255499-112567	76913	Enzo Doria	06/2014
5194	2^255492+345	76911	Lelio R Paula	06/2013
5195	10^76875+217591	76876	Patrick De Geest	05/2013
5197	10^76875-53	76875	Robert Price	05/2011
5196	11^73819-5880	76875	Enzo Doria	01/2013
5198	2^255313+18915	76857	Lelio R Paula	06/2013
5199	(2^255320-1017)/1446667	76853	Lelio R Paula	10/2012
5200	2^255296+5775	76852	Lelio R Paula	06/2013
5201	14^67052-29	76851	Lelio R Paula	02/2015
5202	(7*10^76818-313)/9	76818	Robert Price	11/2016
5203	10^76801+69	76802	Robert Price	03/2011
5204	10^76801-80943	76801	Patrick De Geest	06/2013
5205	2^255105+57	76795	Lelio R Paula	03/2012
5206	(lucasV(1,2,510187)+2)/(3511)	76789	Mike Oakes	04/2017
5207	(2^255097-7)/20020055	76785	Lelio R Paula	10/2012
5208	2^255055+1869353	76780	Enzo Doria	05/2016
5209	17^62396-90	76776	Lelio R Paula	03/2015
5210	7^90833-60	76763	Lelio R Paula	02/2015
5211	13^68901-56	76752	Lelio R Paula	03/2015
5212	2^254961+1869917	76751	Enzo Doria	05/2016
5213	9*5^109791-8	76742	Lelio R Paula	10/2014
5214	82^40089+40089^82	76723	Serge Batalov	02/2012
5215	2^254861-2790013	76721	Enzo Doria	03/2016
5216	10^76705+13	76706	Robert Price	01/2011
5217	10^76705-94077	76705	Patrick De Geest	06/2013
5218	(5*2^254785-1)/999	76696	Lelio R Paula	02/2014
5219	2^254758-110405	76690	Enzo Doria	05/2014
5220	2^254716-3779	76678	Yves Minet	04/2017
5221	2^254708-110507	76675	Enzo Doria	05/2014
5222	(47*10^76672+133)/9	76673	Robert Price	04/2017
5223	2^254670-112901	76664	Enzo Doria	06/2014
5224	(3^160665+7)/981350	76651	Lelio R Paula	10/2012
5225	2^254598-113183	76642	Enzo Doria	07/2014
5226	19^59932+22	76639	Lelio R Paula	01/2015
5227	2^254569-112213	76633	Enzo Doria	06/2014
5228	2*5^109626+9	76626	Lelio R Paula	10/2014
5229	2^254521+1872527	76619	Enzo Doria	05/2016
5230	(76*10^76615+167)/9	76616	Robert Price	08/2016
5231	25^54799-24^54799	76606	Robert Price	07/2012
5232	(24737*2^254464+1)/9	76605	Lelio R Paula	06/2014
5233	12^70961-85	76580	Lelio R Paula	02/2015
5234	7^90590-38	76558	Lelio R Paula	02/2015
5235	2^254304+5227	76554	Lelio R Paula	06/2013
5236	18^60979-5363	76546	Enzo Doria	03/2013
5237	(21181*2^254264+1)/55314379	76538	Lelio R Paula	06/2014
5238	(34*10^76547-7)/9/61/94529/214807	76536	Makoto Morimoto	05/2016
5239	(7*10^76536-313)/9	76536	Robert Price	11/2016
5241	2^254239-27	76534	Lelio R Paula	03/2012
5240	2^254238-1841	76534	Yves Minet	03/2013
5242	(10^76537-1)/9/66127969	76529	Jens K. Andersen	04/2009
5243	2^254189-112225	76519	Enzo Doria	06/2014
5244	18^60938-1397	76494	Enzo Doria	03/2013
5245	2^254075-2788417	76485	Enzo Doria	03/2016
5246	7*10^76483-23	76484	Robert Price	04/2016
5247	2^254042-112913	76475	Enzo Doria	06/2014
5248	14^66723-37	76474	Lelio R Paula	02/2015
5249	2^254037-110305	76473	Enzo Doria	05/2014
5250	2^253931-111109	76441	Enzo Doria	05/2014

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Probable Primes Top 10000

(174961 PRPs in the top)