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 ?
6751	2^266630-131	80264	Lelio R Paula	05/2012
6752	(2^266627+1278)/2	80263	Stefano Morozzi	01/2020
6753	2^266598+76819	80254	Enzo Doria	05/2016
6754	24463^1908+1908^24463	80253	Hans Havermann	01/2020
6755	2^266587+1880633	80251	Enzo Doria	10/2016
6756	(2^266570+3942)/2	80246	Stefano Morozzi	01/2020
6757	2^266541-110049	80237	Enzo Doria	04/2014
6758	38635!2-8	80222	Robert Price	06/2015
6759	(2^266465+986)/2	80214	Stefano Morozzi	01/2020
6760	3^168111+168111^3-1	80210	Robert Price	04/2014
6761	(2^266447+758)/2	80209	Stefano Morozzi	01/2020
6762	2^266443+513	80208	Lelio R Paula	07/2013
6763	(26*10^80200+61)/3	80201	Robert Price	06/2017
6765	2^266412-109913	80199	Enzo Doria	04/2014
6766	(10223*2^266417+1)/45091	80199	Lelio R Paula	06/2014
6764	2^266413-4693	80199	Yves Minet	05/2019
6767	13^71988+66	80191	Lelio R Paula	11/2015
6768	11^77002-4320	80190	Enzo Doria	01/2013
6769	18^63879-13	80186	Lelio R Paula	11/2015
6770	(2^266371+1814)/2	80186	Stefano Morozzi	01/2020
6772	2^266368-112295	80185	Enzo Doria	06/2014
6771	19217^14880+14880^19217	80185	Hans Havermann	03/2020
6773	(3^168050+5)/1021454	80175	Lelio R Paula	10/2012
6774	(2^266324+1386)/2	80172	Stefano Morozzi	01/2020
6775	(22*10^80167+41)/9	80168	Robert Price	02/2015
6776	(2^266308+1618)/2	80167	Stefano Morozzi	01/2020
6777	(34*10^80162-43)/9	80163	Ray Chandler	12/2010
6778	(2^266276+762)/2	80157	Stefano Morozzi	01/2020
6779	(38*10^80150-11)/9	80151	Robert Price	05/2015
6780	(598*10^80149-31)/9	80151	Robert Price	02/2017
6781	19^62678-80	80150	Lelio R Paula	12/2015
6782	10^80139+32343	80140	Patrick De Geest	02/2011
6783	10^80139-9	80139	Alexander Gramolin	01/2011
6784	3^167955-106	80135	Lelio R Paula	12/2015
6785	(2^266137+3782)/2	80115	Stefano Morozzi	01/2020
6786	(2^266121+3846)/2	80111	Stefano Morozzi	01/2020
6787	(197*10^80089-11)/3	80091	Robert Price	10/2017
6789	2^265998+75559	80074	Enzo Doria	04/2016
6788	(2^265999+3290)/2	80074	Stefano Morozzi	01/2020
6790	2^265969-109801	80065	Enzo Doria	04/2014
6791	(2^265956+3378)/2	80061	Stefano Morozzi	01/2020
6792	2^265888-112757	80041	Enzo Doria	06/2014
6793	2^265809+1701	80017	Lelio R Paula	07/2013
6794	gcd(V(957175),5F(191435)(F(191435)+1)+1)	80014	Serge Batalov	04/2015
6795	3^167687-104	80008	Lelio R Paula	02/2015
6796	11^76826-5790	80007	Enzo Doria	01/2013
6797	10^80000+85731	80001	Patrick De Geest	10/2009
6798	10^80000-7169	80000	Patrick De Geest	09/2009
6799	10^79999+22399	80000	Patrick De Geest	09/2009
6800	10^79999-74873	79999	Patrick De Geest	09/2009
6801	3^167668+58	79998	Lelio R Paula	02/2015
6802	(2^265728+3742)/2	79992	Stefano Morozzi	01/2020
6803	155^36506-2	79961	Lelio R Paula	10/2017
6804	(2^265621+3882)/2	79960	Stefano Morozzi	01/2020
6806	2^265612+4257	79958	Lelio R Paula	07/2013
6805	(2^265613+1470)/2	79958	Stefano Morozzi	01/2020
6807	5*3^167577+4	79956	Lelio R Paula	06/2014
6808	(9179*2^265593-1)/9	79955	Lelio R Paula	04/2015
6809	6^102723-43	79935	Lelio R Paula	04/2015
6810	11^76748-3360	79925	Enzo Doria	12/2012
6811	19430^12981+12981^19430	79922	Hans Havermann	03/2020
6812	(2^265490+870)/2	79921	Stefano Morozzi	01/2020
6813	(13*2^265498-1)/187119	79919	Lelio R Paula	02/2014
6814	(2^265438+3978)/2	79905	Stefano Morozzi	01/2020
6815	(2^265409+1250)/2	79896	Stefano Morozzi	01/2020
6816	2^265399-109855	79894	Enzo Doria	04/2014
6817	(2^265380+3930)/2	79888	Stefano Morozzi	01/2020
6818	(20^61403-1)/19	79886	Paul Bourdelais	03/2010
6819	(2^265368+2970)/2	79884	Stefano Morozzi	01/2020
6820	18^63635+59	79880	Lelio R Paula	02/2015
6821	(11*10^79867-107)/3	79868	Robert Price	11/2016
6822	3^167375+80	79859	Lelio R Paula	02/2015
6823	5^114240-14486	79851	Enzo Doria	02/2013
6824	49^47238+48	79842	Norbert Schneider	07/2014
6825	2^265212-3779	79837	Yves Minet	04/2017
6826	(2^265201+2790)/2	79834	Stefano Morozzi	01/2020
6827	91^40746+40746^91	79824	Norbert Schneider	12/2014
6828	(68*10^79813-257)/9	79814	Robert Price	06/2017
6829	(5*2^265118-1)/61	79808	Lelio R Paula	02/2014
6830	(2^265102+1462)/2	79804	Stefano Morozzi	01/2020
6831	2^265074+28425	79796	Lelio R Paula	07/2013
6832	2^265072+1185	79795	Lelio R Paula	07/2013
6834	p(16682)#/2-128	79771	Robert Price	05/2017
6833	(2^264994+1714)/2	79771	Stefano Morozzi	01/2020
6836	3^167167-34	79759	Robert Price	11/2013
6835	(2^264952+3258)/2	79759	Stefano Morozzi	01/2020
6837	12^73906+29	79758	Lelio R Paula	02/2015
6838	2^264934+255	79754	Lelio R Paula	07/2013
6839	4*10^79729-87	79730	Robert Price	03/2017
6840	2^264846-111701	79727	Enzo Doria	05/2014
6841	2^264831-112041	79723	Enzo Doria	06/2014
6842	2^264816-455	79718	Yves Minet	03/2012
6843	(55*10^79711+89)/9	79712	Robert Price	09/2017
6844	47^47667-46	79704	Theodore Burton	02/2007
6845	13^71547+96	79700	Lelio R Paula	03/2015
6846	2^264752-112883	79699	Enzo Doria	06/2014
6847	(2^264748+1978)/2	79697	Stefano Morozzi	01/2020
6848	2^264732+133	79693	Lelio R Paula	05/2012
6849	8*3^167010+7	79685	Lelio R Paula	06/2014
6850	42^49087-41	79681	Norbert Schneider	06/2014
6851	(26*10^79678-119)/3	79679	Robert Price	07/2016
6852	2^264683-21	79678	Lelio R Paula	05/2012
6853	7^94279+18	79675	Lelio R Paula	02/2015
6855	2^264655-127	79670	Lelio R Paula	02/2012
6854	(2^264658+3102)/2	79670	Stefano Morozzi	01/2020
6856	(2^264637+1682)/2	79664	Stefano Morozzi	01/2020
6857	2^264597-459043	79652	Enzo Doria	05/2015
6858	(21*2^264566+1)/5	79643	Lelio R Paula	10/2012
6859	2^264536+1870021	79634	Enzo Doria	05/2016
6860	(17*2^264512-1)/359	79625	Lelio R Paula	02/2014
6861	2^264477-109783	79616	Enzo Doria	04/2014
6862	18^63419-1333	79609	Enzo Doria	03/2013
6863	13^71451-36	79593	Lelio R Paula	03/2015
6864	23314^2593+2593^23314	79590	Hans Havermann	03/2020
6865	(2^264410-5)/128002609121	79585	Lelio R Paula	10/2012
6866	19^62234+90	79582	Lelio R Paula	03/2015
6867	(2^264276+2866)/2	79555	Stefano Morozzi	01/2020
6868	12^73714+49	79551	Lelio R Paula	02/2015
6869	(2^264213+1442)/2	79536	Stefano Morozzi	01/2020
6870	(3*2^264184-1)/1433339	79522	Lelio R Paula	02/2014
6871	(2^264160+1590)/2	79520	Stefano Morozzi	01/2020
6872	2^264103-112531	79503	Enzo Doria	06/2014
6873	19^62170+78	79501	Lelio R Paula	03/2015
6874	11^76340-2580	79500	Enzo Doria	12/2012
6875	(2^264084+858)/2	79497	Stefano Morozzi	01/2020
6876	(23*10^79492-11)/3	79493	Robert Price	10/2015
6877	((2^132049+13650)^2+(2^132049+13650)+41)/2003/23841473	79491	Makoto Morimoto	05/2016
6878	2^264060-112133	79490	Enzo Doria	06/2014
6879	((2^132049+4641)^2+(2^132049+4641)+41)/487/8537/10426147	79488	Makoto Morimoto	05/2016
6880	20158^8775+8775^20158	79488	Hans Havermann	02/2020
6881	9^83298+6^83298-2^83298	79487	Mike Oakes	08/2010
6882	18^63319+35	79483	Lelio R Paula	02/2015
6883	38303!2+256	79461	Robert Price	01/2015
6884	(29*10^79445+61)/9	79446	Robert Price	04/2015
6885	2^263902-195	79443	Lelio R Paula	05/2012
6886	3^166499-112696	79441	Enzo Doria	06/2014
6887	11^76279-2760	79437	Enzo Doria	12/2012
6888	18907^15894+15894^18907	79433	Hans Havermann	03/2020
6889	6^102077-25	79432	Lelio R Paula	03/2015
6890	2^263852-1017	79428	Lelio R Paula	07/2013
6891	2^263842-33	79425	Lelio R Paula	05/2012
6892	(2^263814+3582)/2	79416	Stefano Morozzi	01/2020
6893	12^73584-55	79411	Lelio R Paula	02/2015
6894	(2^263783+3558)/2	79407	Stefano Morozzi	01/2020
6895	2^263772-185	79404	Lelio R Paula	05/2012
6896	(15^67489+1)/16	79373	Paul Bourdelais	03/2010
6897	2^263664+15015	79371	Lelio R Paula	07/2013
6898	(2^263643+1206)/2	79365	Stefano Morozzi	01/2020
6899	(2^263642+3082)/2	79364	Stefano Morozzi	01/2020
6900	10^79362+3^79363	79363	Mike Oakes	06/2010
6901	(2^263591+2910)/2	79349	Stefano Morozzi	01/2020
6902	(2^263589+1922)/2	79348	Stefano Morozzi	01/2020
6903	Phi(163244,10)/2448661/6856249	79331	Maksym Voznyy	11/2015
6904	3^166262+44	79328	Lelio R Paula	02/2015
6905	4*10^79327-63	79328	Robert Price	12/2016
6906	2^263486+513	79318	Lelio R Paula	07/2013
6907	(2^263458+1282)/2	79309	Stefano Morozzi	01/2020
6908	(2^263456+1558)/2	79308	Stefano Morozzi	01/2020
6909	2^263448-519509	79306	Paul Bourdelais	03/2013
6910	69153^16384+2	79296	Matt Stath	01/2019
6911	21^59971-20^59971	79295	Robert Price	05/2012
6912	2^263372+123	79283	Lelio R Paula	05/2012
6913	(2^263366+1974)/2	79281	Stefano Morozzi	01/2020
6914	17^64429+84	79277	Lelio R Paula	03/2015
6915	11^76124-11430	79275	Enzo Doria	12/2012
6916	19294^12845+12845^19294	79274	Hans Havermann	03/2020
6917	(206*10^79268-17)/9	79270	Robert Price	03/2017
6918	13^71157+18	79265	Lelio R Paula	03/2015
6919	2^263297+65835	79261	Lelio R Paula	07/2013
6920	19^61980-18	79258	Theodore Burton	12/2005
6921	(2^263259+2970)/2	79249	Stefano Morozzi	01/2020
6922	2*10^79242+93	79243	Robert Price	07/2016
6923	(2^263226+1074)/2	79239	Stefano Morozzi	01/2020
6924	(88^40751-1)/87	79238	Paul Bourdelais	08/2017
6925	(103*29^54179-39)/4	79233	Curtis Bright	05/2015
6926	9^83024-83024^9	79226	Norbert Schneider	08/2017
6927	17^64382-26	79219	Lelio R Paula	03/2015
6928	7^93733-74	79214	Lelio R Paula	02/2015
6929	15^67352+38	79213	Lelio R Paula	02/2015
6930	2^263135-110235	79212	Enzo Doria	05/2014
6931	(2^263080+3658)/2	79195	Stefano Morozzi	01/2020
6932	2^263044+4257	79185	Lelio R Paula	07/2013
6933	(2^263039+3554)/2	79183	Stefano Morozzi	01/2020
6935	2^263032+87517	79181	Yves Minet	11/2010
6934	6^101755+95	79181	Lelio R Paula	03/2015
6936	(2^263010+1738)/2	79174	Stefano Morozzi	01/2020
6937	4^131497-3^131497	79170	Jean-Louis Charton	05/2004
6938	5*7^93674+8	79165	Lelio R Paula	10/2014
6939	(2^262939+1326)/2	79153	Stefano Morozzi	01/2020
6940	(2^262941+926)/2	79153	Stefano Morozzi	01/2020
6941	lucasU(486,25,29457)-5*lucasU(486,25,29456)	79137	Mike Oakes	05/2009
6942	260^32768+179^32768	79134	Serge Batalov	03/2018
6943	11^75978-42	79123	Lelio R Paula	02/2015
6944	8*5^113180+9	79111	Lelio R Paula	10/2014
6945	(2^262757+3222)/2	79098	Stefano Morozzi	01/2020
6946	(6883*2^262741-1)/4835	79094	Lelio R Paula	04/2015
6947	(9*2^262745+1)/137	79093	Lelio R Paula	10/2012
6948	12^73285+85	79088	Lelio R Paula	02/2015
6949	19^61840+52	79079	Lelio R Paula	03/2015
6951	(10^79067+77)/3	79067	Robert Price	01/2017
6950	(2^262655+678)/2	79067	Stefano Morozzi	01/2020
6952	(1017*2^262640-1)/11557	79062	Lelio R Paula	04/2015
6953	(2^262634+1674)/2	79061	Stefano Morozzi	01/2020
6954	10^79040+137949	79041	Patrick De Geest	02/2016
6956	10^79040-1007297	79040	Robert Price	02/2015
6955	10^79040-77427	79040	Patrick De Geest	02/2016
6957	2^262551-17295	79036	Lelio R Paula	07/2013
6958	3^165597+340	79010	Lelio R Paula	02/2015
6959	19620^10633+10633^19620	79003	Hans Havermann	02/2020
6960	(23*2^262435+1)/55	79001	Lelio R Paula	10/2012
6961	11^75860-2100	79001	Enzo Doria	12/2012
6962	8*7^93463+9	78987	Lelio R Paula	10/2014
6963	(2^262376+3942)/2	78983	Stefano Morozzi	01/2020
6964	67^43240-2	78960	Lelio R Paula	09/2013
6965	1000001^13159-1000000^13159	78953	Jean-Louis Charton	10/2003
6966	(2^262263+3410)/2	78949	Stefano Morozzi	01/2020
6967	2^262199-110287	78930	Enzo Doria	05/2014
6968	(19*2^262180-1)/177	78924	Lelio R Paula	02/2014
6969	(3^165403+4)/7	78917	Lelio R Paula	10/2012
6970	2^21068*(2^241076+1)-1	78914	Makoto Morimoto	03/2014
6971	2^29258*(2^232886+1)-1	78914	Makoto Morimoto	03/2014
6973	2^262144+18531	78914	Makoto Morimoto	12/2015
6972	2^262144-231425	78914	Matthias Baur	03/2020
6974	(2^262137+1730)/2	78911	Stefano Morozzi	01/2020
6975	(2^(2^18)+2450)/(23^2137*577)	78908	Makoto Morimoto	08/2017
6976	(2^(2^18)-5719)/(35993623)	78907	Makoto Morimoto	08/2017
6977	14^68837+75	78897	Lelio R Paula	02/2015
6978	(2^262055+1806)/2	78887	Stefano Morozzi	01/2020
6979	(2^262049+1406)/2	78885	Stefano Morozzi	01/2020
6980	106^38949+105	78884	Norbert Schneider	12/2016
6981	(2^262010+3778)/2	78873	Stefano Morozzi	01/2020
6982	18683^16636+16636^18683	78862	Hans Havermann	03/2020
6983	(2^261964+1450)/2	78859	Stefano Morozzi	01/2020
6984	23288^2433+2433^23288	78857	Hans Havermann	03/2020
6985	(70^42737+1)/71	78853	Paul Bourdelais	08/2017
6986	(2^261919+2474)/2	78846	Stefano Morozzi	01/2020
6987	(25*2^261917-1)/20927	78842	Lelio R Paula	02/2014
6988	2^261881-1859713	78835	Enzo Doria	03/2016
6990	2^261874+1915	78832	Lelio R Paula	07/2013
6989	(2^261872+1582)/2	78832	Stefano Morozzi	01/2020
6991	2^261856+98765331	78827	Jason Earls	01/2009
6992	(5*2^261857-1)/20501277	78821	Lelio R Paula	02/2014
6993	24586^1605+1605^24586	78810	Hans Havermann	02/2020
6994	(2^261786+3538)/2	78806	Stefano Morozzi	01/2020
6995	(2^261780+2290)/2	78804	Stefano Morozzi	01/2020
6996	2^261724+92691	78787	Tony Prest / Never Odd Or Even	03/2014
6997	2^261724+285111	78787	Tony Prest / Never Odd Or Even	04/2014
6998	2^261724+293713	78787	Tony Prest / Never Odd Or Even	04/2014
6999	(2^261724+381949)/5	78787	Tony Prest / Never Odd Or Even	04/2014
7000	2^261724+572971	78787	Tony Prest / Never Odd Or Even	05/2014

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Probable Primes Top 10000

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