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 ?
5751	1000001^13159-1000000^13159	78953	Jean-Louis Charton	10/2003
5752	2^262199-110287	78930	Enzo Doria	05/2014
5753	(19*2^262180-1)/177	78924	Lelio R Paula	02/2014
5754	(3^165403+4)/7	78917	Lelio R Paula	10/2012
5755	2^21068*(2^241076+1)-1	78914	Makoto Morimoto	03/2014
5756	2^29258*(2^232886+1)-1	78914	Makoto Morimoto	03/2014
5757	2^262144+18531	78914	Makoto Morimoto	12/2015
5758	(2^(2^18)+2450)/(23^2137*577)	78908	Makoto Morimoto	08/2017
5759	(2^(2^18)-5719)/(35993623)	78907	Makoto Morimoto	08/2017
5760	14^68837+75	78897	Lelio R Paula	02/2015
5761	106^38949+105	78884	Norbert Schneider	12/2016
5762	(70^42737+1)/71	78853	Paul Bourdelais	08/2017
5763	(25*2^261917-1)/20927	78842	Lelio R Paula	02/2014
5764	2^261881-1859713	78835	Enzo Doria	03/2016
5765	2^261874+1915	78832	Lelio R Paula	07/2013
5766	2^261856+98765331	78827	Jason Earls	01/2009
5767	(5*2^261857-1)/20501277	78821	Lelio R Paula	02/2014
5768	2^261724+92691	78787	Tony Prest / Never Odd Or Even	03/2014
5769	2^261724+285111	78787	Tony Prest / Never Odd Or Even	04/2014
5770	2^261724+293713	78787	Tony Prest / Never Odd Or Even	04/2014
5771	(2^261724+381949)/5	78787	Tony Prest / Never Odd Or Even	04/2014
5772	2^261724+572971	78787	Tony Prest / Never Odd Or Even	05/2014
5773	(2^261724+392705)/3/7	78786	Tony Prest / Never Odd Or Even	04/2014
5774	(2^261724+629709)/5/5	78786	Tony Prest / Never Odd Or Even	05/2014
5775	(2^261724+67397)/3/103	78785	Tony Prest / Never Odd Or Even	04/2014
5776	(2^261724+323043)/11/103	78784	Tony Prest / Never Odd Or Even	04/2014
5777	(2^261724+370143)/1289	78784	Tony Prest / Never Odd Or Even	04/2014
5778	(2^261724+560259)/5/5/73	78784	Tony Prest / Never Odd Or Even	05/2014
5779	(2^261724+64109)/3/3/3/5/5/19	78783	Tony Prest / Never Odd Or Even	04/2014
5780	(2^261724+394491)/55787	78783	Tony Prest / Never Odd Or Even	04/2014
5781	(2^261724+625897)/23/883	78783	Tony Prest / Never Odd Or Even	05/2014
5782	(2^261724+292471)/13/97/151	78782	Tony Prest / Never Odd Or Even	04/2014
5783	(2^261724+154303)/11/67/127	78782	Tony Prest / Never Odd Or Even	04/2014
5784	(2^261724+313319)/3/3/3/3/5/11/113	78782	Tony Prest / Never Odd Or Even	04/2014
5785	(2^261724+383949)/5/41/43/83	78781	Tony Prest / Never Odd Or Even	04/2014
5786	(2^261724+626567)/3/331/631	78781	Tony Prest / Never Odd Or Even	05/2014
5787	(2^261724+32987)/3/3/19/223/1031	78780	Tony Prest / Never Odd Or Even	04/2014
5788	(2^261724+5813)/3/5991397	78780	Tony Prest / Never Odd Or Even	04/2014
5789	(2^261724+13481)/3/11/239/2087	78780	Tony Prest / Never Odd Or Even	04/2014
5790	(2^261724+103399)/5/13/37/10607	78780	Tony Prest / Never Odd Or Even	04/2014
5791	(2^261724+18477)/367/65111	78780	Tony Prest / Never Odd Or Even	04/2014
5792	(2^261724+121285)/167/227/1217	78780	Tony Prest / Never Odd Or Even	04/2014
5793	(2^261724+262037)/3/3/11/23/18517	78780	Tony Prest / Never Odd Or Even	04/2014
5794	(2^261724+586157)/3/7/457/1259	78780	Tony Prest / Never Odd Or Even	05/2014
5795	(2^261724+315287)/3/45822541	78779	Tony Prest / Never Odd Or Even	04/2014
5796	(2^261724+605675)/3/3/3/103/207481	78779	Tony Prest / Never Odd Or Even	05/2014
5797	(2^261724+60031)/13/31/7024877	78778	Tony Prest / Never Odd Or Even	04/2014
5798	(2^261724+121879)/5/789433217	78778	Tony Prest / Never Odd Or Even	04/2014
5799	(2^261724+290135)/3/3/8467/9059	78778	Tony Prest / Never Odd Or Even	04/2014
5800	(2^261724+79857)/59/3847/165331	78777	Tony Prest / Never Odd Or Even	04/2014
5801	(2^261724+22883)/3/17/23/2351/10079	78777	Tony Prest / Never Odd Or Even	04/2014
5802	(2^261724+154799)/3/5/3655653719	78777	Tony Prest / Never Odd Or Even	04/2014
5803	(2^261724+391001)/3/11/17/41/43/24071	78777	Tony Prest / Never Odd Or Even	04/2014
5804	(2^261724+622383)/34843/550717	78777	Tony Prest / Never Odd Or Even	05/2014
5805	(2^261724+302829)/5/37/37/37078147	78776	Tony Prest / Never Odd Or Even	04/2014
5806	(2^261724+315837)/43/2176136243	78776	Tony Prest / Never Odd Or Even	04/2014
5807	(2^261724+582373)/53/307/311/32117	78776	Tony Prest / Never Odd Or Even	05/2014
5808	(2^261724+295283)/3/3/3/29/43/17812273	78775	Tony Prest / Never Odd Or Even	04/2014
5809	(2^261724+27491)/3/22787/105978449	78774	Tony Prest / Never Odd Or Even	04/2014
5810	(2^261724+392751)/193813/287826689	78774	Tony Prest / Never Odd Or Even	04/2014
5811	(2^261724+328501)/7/1091/31495610519	78773	Tony Prest / Never Odd Or Even	04/2014
5812	(2^261724+111267)/19/4637/15140560427	78772	Tony Prest / Never Odd Or Even	04/2014
5813	(2^261724+572133)/127/131/73787752333	78772	Tony Prest / Never Odd Or Even	05/2014
5814	(2^261724+608733)/59/7079/18451/909151	78771	Tony Prest / Never Odd Or Even	05/2014
5815	(2^261724+255449)/3/3/5/7/1759/10177/33158869	78770	Tony Prest / Never Odd Or Even	04/2014
5816	(2^261724+99509)/3/5/5/6507271/6749659289	78769	Tony Prest / Never Odd Or Even	04/2014
5817	(2^261724+52501)/563/53939/27942831391	78769	Tony Prest / Never Odd Or Even	04/2014
5818	(2^261724+117089)/3/5/37/149/967/2027/4163741	78769	Tony Prest / Never Odd Or Even	04/2014
5819	(2^261724+372571)/1487/9209/21559/2263249	78769	Tony Prest / Never Odd Or Even	04/2014
5820	(2^261724+184549)/5/8699/44053/1409322997	78769	Tony Prest / Never Odd Or Even	04/2014
5821	(2^261724+363351)/937/159683/59523200227	78768	Tony Prest / Never Odd Or Even	04/2014
5822	(2^261724+326501)/3/43/193/263/19403/253501403	78768	Tony Prest / Never Odd Or Even	04/2014
5823	(2^261724+629477)/3/17/17/137/263/1993/16187/57347	78768	Tony Prest / Never Odd Or Even	05/2014
5824	(2^261724+94871)/3/3/13/6734017/1673425245787	78766	Tony Prest / Never Odd Or Even	04/2014
5825	(2^261724+25981)/577/1181/3643/517786334743	78766	Tony Prest / Never Odd Or Even	04/2014
5827	(23*2^261642+1)/93	78762	Lelio R Paula	10/2012
5826	(2^261724+351227)/3/3/3/3/71/13997/9595373/8193978007	78762	Tony Prest / Never Odd Or Even	04/2014
5828	(2^261724+22571)/3/7243/7321/18046081/45730741211	78761	Tony Prest / Never Odd Or Even	04/2014
5829	(2^261724+56495)/3/3/3/7/7/13/9041/512818459/23708589119	78760	Tony Prest / Never Odd Or Even	04/2014
5830	(2^261724+604119)/5/7/7/41/14107/19681/211777/90145981/1036020834127	78750	Tony Prest / Never Odd Or Even	05/2014
5831	2^261507-2287	78722	Yves Minet	04/2009
5832	8*10^78717+39	78718	Robert Price	01/2017
5833	(78557*2^261440+1)/3	78706	Lelio R Paula	06/2014
5834	6^101128-16433	78693	Enzo Doria	02/2013
5835	20^60482+99	78689	Lelio R Paula	03/2015
5836	2^261348-110633	78674	Enzo Doria	05/2014
5837	191^34487+2	78666	Lelio R Paula	05/2013
5838	2^261305-110139	78661	Enzo Doria	04/2014
5839	(82*10^78635-1)/9	78636	Robert Price	12/2014
5840	10^78632+81	78633	Robert Price	03/2011
5841	10^78632-402693	78632	Patrick De Geest	07/2013
5842	3*10^78631+17	78632	Robert Price	03/2017
5843	2^261174-3911	78622	Yves Minet	04/2017
5844	2^261167+74843	78620	Enzo Doria	04/2016
5845	L(376121)+F(376122)	78605	Henri Lifchitz	01/2007
5846	14^68580-29	78602	Lelio R Paula	02/2015
5847	(73*10^78576-1)/9	78577	Robert Price	01/2015
5848	(17*2^261026-1)/40451	78574	Lelio R Paula	02/2014
5849	2^261001-195	78570	Lelio R Paula	05/2012
5850	5*2^260950+9	78555	Lelio R Paula	06/2014
5851	2^260931-7605	78549	Lelio R Paula	07/2013
5852	15^66778-32	78538	Lelio R Paula	02/2015
5853	(11*2^260896-1)/245	78537	Lelio R Paula	02/2014
5854	30^53166+29	78533	Norbert Schneider	03/2017
5855	lucasU(2403,1,23229)-lucasU(2403,1,23228)	78529	Mike Oakes	05/2009
5856	7*3^164574-2	78523	Lelio R Paula	06/2014
5857	2^260830-112133	78518	Enzo Doria	06/2014
5858	13^70486+42	78518	Lelio R Paula	03/2015
5859	11^75386-7080	78507	Enzo Doria	01/2013
5860	(86^40583-1)/85	78506	Paul Bourdelais	08/2017
5861	2^260711-58695	78482	Lelio R Paula	07/2013
5862	2^260678-111065	78472	Enzo Doria	05/2014
5863	18^62501-97	78456	Lelio R Paula	02/2015
5864	53^45498-2	78452	Lelio R Paula	08/2013
5865	2^260513-111121	78423	Enzo Doria	05/2014
5866	37845!2-64	78412	Robert Price	06/2015
5867	2^260469-110695	78409	Enzo Doria	05/2014
5868	(11*10^78408-113)/3	78409	Robert Price	01/2017
5869	2^260447+8415	78403	Lelio R Paula	07/2013
5870	37837!2-64	78394	Robert Price	06/2015
5871	(19*2^260379-1)/53	78382	Lelio R Paula	02/2014
5872	2^260377-113233	78382	Enzo Doria	07/2014
5874	9^82138+6^82138-2^82138	78380	Mike Oakes	08/2010
5873	69^42624+2	78380	Lelio R Paula	05/2013
5875	2^260369-1859713	78379	Enzo Doria	03/2016
5876	14*10^78362+1089	78364	Jens K. Andersen	11/2007
5877	5^112070-54	78334	Lelio R Paula	02/2015
5878	(10^(239165+1)+5410^39165-1)/9	78331	Robert Price	04/2017
5879	2^260182-113453	78323	Enzo Doria	07/2014
5880	f(16405)	78319	Robert Price	09/2017
5881	(78557*2^260084+1)/519	78296	Lelio R Paula	06/2014
5882	10^78288+9^(78288+1)	78289	Robert Price	08/2016
5883	10^78288+39109	78289	Patrick De Geest	12/2016
5884	10^78288-216299	78288	Patrick De Geest	12/2016
5885	5^111997+36	78283	Lelio R Paula	02/2015
5886	(21^59183+1)/22	78252	Paul Bourdelais	03/2010
5887	(88*10^78242-7)/9	78243	Robert Price	11/2014
5888	2*6^100547+7	78242	Lelio R Paula	10/2014
5889	2^259860-111089	78226	Enzo Doria	05/2014
5890	37^49875-2	78215	Lelio R Paula	09/2013
5891	(13*10^78213+401)/9	78214	Robert Price	10/2017
5892	7*5^111893-4	78211	Lelio R Paula	10/2014
5893	(11*2^259809-1)/1437	78209	Lelio R Paula	02/2014
5894	7^92511-6	78181	Theodore Burton	11/2005
5895	(3^163859-4)/253	78179	Lelio R Paula	10/2012
5896	(27*2^259666-1)/625691	78163	Lelio R Paula	02/2014
5897	3*10^78146+17	78147	Robert Price	03/2017
5898	(576^28307+1)/577	78137	Richard Fischer	01/2018
5899	2^259503+74333	78119	Enzo Doria	04/2016
5900	(31*2^259504-1)/13365	78116	Lelio R Paula	02/2014
5902	(58547^16384+1)/2	78111	Lelio R Paula	11/2011
5901	6^100379+13	78111	Lelio R Paula	03/2015
5903	2^259469-109909	78108	Enzo Doria	04/2014
5904	15^66413-26	78108	Lelio R Paula	02/2015
5905	7^92410-9266	78096	Mike Oakes	02/2010
5906	2^259398+75799	78087	Enzo Doria	04/2016
5907	2^259394+1876189	78086	Enzo Doria	07/2016
5908	PIPrime(78073)	78073	Eric W. Weisstein	07/2006
5909	5*2^259344-7	78072	Lelio R Paula	06/2014
5910	14^68097-87	78048	Lelio R Paula	02/2015
5911	2^259233-475573	78037	Paul Bourdelais	03/2013
5912	181^34554-2	78012	Lelio R Paula	10/2017
5913	3^163500-28	78010	Robert Price	12/2013
5914	(65*10^77992+691)/9	77993	Robert Price	08/2016
5915	2^259013-112591	77971	Enzo Doria	06/2014
5916	7*10^77969-11	77970	Robert Price	10/2017
5917	6^100193-100193^6	77966	Norbert Schneider	04/2017
5918	2^258863-110235	77926	Enzo Doria	05/2014
5919	2^258852+1605	77923	Lelio R Paula	06/2013
5920	(11*10^77909+49)/3	77910	Robert Price	05/2016
5921	2*7^92187-9	77908	Lelio R Paula	10/2014
5922	2^258763-110155	77896	Enzo Doria	04/2014
5923	2^258694-110387	77875	Enzo Doria	05/2014
5924	11^74773-94	77869	Lelio R Paula	02/2015
5925	6^100067+125	77868	Lelio R Paula	03/2015
5926	15^66205+8	77864	Lelio R Paula	07/2014
5927	5^111373-18136	77847	Enzo Doria	05/2014
5928	2^258524-109877	77824	Enzo Doria	04/2014
5929	6^100002-16643	77817	Enzo Doria	02/2013
5930	(13*10^77811+347)/9	77812	Robert Price	10/2017
5931	65^42916+28	77803	Lelio R Paula	01/2016
5932	(89*10^77781-17)/9	77782	Robert Price	11/2015
5933	2^258382-110405	77781	Enzo Doria	05/2014
5934	5^111278-14996	77780	Enzo Doria	02/2013
5935	14^67862+61	77779	Lelio R Paula	02/2015
5936	10^77777+48483	77778	Patrick De Geest	11/2010
5937	10^77777-183243	77777	Patrick De Geest	11/2010
5938	(27*2^258352+1)/43	77772	Lelio R Paula	08/2012
5939	337^30756-10002	77740	Enzo Doria	07/2012
5940	10^77726+99	77727	Robert Price	03/2011
5941	10^77726-85947	77726	Patrick De Geest	06/2013
5942	89^39870-2	77723	Lelio R Paula	08/2013
5943	7^91966-32	77721	Lelio R Paula	02/2015
5944	35^50327+2	77709	Lelio R Paula	05/2013
5945	24^56298+23	77704	Norbert Schneider	12/2016
5946	(2^258105+78557)/19	77697	Lelio R Paula	10/2012
5947	2^258079+179	77690	Lelio R Paula	03/2012
5948	2^258062-113111	77685	Enzo Doria	07/2014
5949	80^40807-79	77660	Norbert Schneider	03/2015
5950	(10^77637+359)/9	77637	Serge Batalov	12/2014
5951	2^257862-165	77625	Lelio R Paula	03/2012
5952	(25*2^257853+1)/3	77623	Lelio R Paula	07/2012
5953	(2^257869+1)/(3*18645362967379)	77613	Henri Lifchitz	04/2005
5954	6^99728+71	77604	Lelio R Paula	01/2015
5955	2^257778-112767	77599	Enzo Doria	06/2014
5956	(31*2^257771+1)/537	77596	Lelio R Paula	07/2012
5957	2^257729-73	77585	Lelio R Paula	03/2012
5958	2^257689-63	77573	Lelio R Paula	03/2012
5959	(47*10^77572+493)/9	77573	Robert Price	11/2017
5960	(78557*2^257665+1)/6108725	77564	Lelio R Paula	06/2014
5961	(3^162563+8)/2885	77559	Lelio R Paula	10/2012
5962	2^257636-110235	77557	Enzo Doria	05/2014
5963	(23*10^77556+97)/3	77557	Robert Price	02/2017
5964	2^257621-110071	77552	Enzo Doria	04/2014
5965	2^257567-64875	77536	Lelio R Paula	06/2013
5966	2*7^91674+9	77474	Lelio R Paula	10/2014
5967	(17*10^77427-47)/3	77428	Robert Price	05/2017
5968	10^77418+841683	77419	Patrick De Geest	06/2013
5969	10^77418-33	77418	Robert Price	05/2011
5970	19^60539-36	77415	Lelio R Paula	03/2015
5971	37401!!-1024	77397	Robert Price	11/2015
5972	11^74313-18750	77390	Enzo Doria	12/2012
5974	2^257044-112883	77378	Enzo Doria	06/2014
5973	8*10^77377+51	77378	Robert Price	05/2017
5975	2*7^91553+9	77372	Lelio R Paula	10/2014
5976	713^27118+27118^713	77371	Norbert Schneider	12/2016
5977	2^256920-111155	77341	Enzo Doria	05/2014
5978	2^256896-6555	77334	Lelio R Paula	06/2013
5979	(52*10^77322-7)/9	77323	Robert Price	12/2014
5980	2^256849-112939	77320	Enzo Doria	06/2014
5981	(4*10^77309-31)/9	77309	Erik Branger	05/2011
5982	(3^161988+7)/41864	77284	Lelio R Paula	10/2012
5983	(14^67421-1)/13	77272	Paul Bourdelais	09/2008
5984	5*3^161923-4	77258	Lelio R Paula	06/2014
5985	2^256552-1499	77230	Yves Minet	05/2013
5986	2^256460-112757	77203	Enzo Doria	06/2014
5987	2^256398+23299	77184	Yves Minet	02/2011
5988	2^256391-1155*256391	77182	Henri Lifchitz	03/2005
5989	(2^256391-9)/56593	77177	Lelio R Paula	10/2012
5990	(2^256308+9)/10585	77153	Lelio R Paula	10/2012
5992	21^58348-2	77149	Lelio R Paula	08/2013
5991	(17*2^256291-1)/4785	77149	Lelio R Paula	02/2014
5993	(5*2^256274-1)/2141	77144	Lelio R Paula	02/2014
5994	19^60321+82	77136	Lelio R Paula	03/2015
5995	5*2^256233-3	77135	Lelio R Paula	06/2014
5996	3*2^256149+7	77110	Lelio R Paula	06/2014
5997	3^161594-106	77100	Lelio R Paula	02/2015
5998	2^256114-185	77098	Lelio R Paula	03/2012
5999	8^85349-85349^8	77078	Norbert Schneider	05/2017
6000	2^256043-2786377	77077	Enzo Doria	03/2016

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Probable Primes Top 10000

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