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 ?
7751	2^266598+76819	80254	Enzo Doria	05/2016
7752	24463^1908+1908^24463	80253	Hans Havermann	01/2020
7753	2^266587+1880633	80251	Enzo Doria	10/2016
7754	(2^266570+3942)/2	80246	Stefano Morozzi	01/2020
7755	2^266541-110049	80237	Enzo Doria	04/2014
7756	38635!2-8	80222	Robert Price	06/2015
7757	(2^266465+986)/2	80214	Stefano Morozzi	01/2020
7758	3^168111+168111^3-1	80210	Robert Price	04/2014
7759	(2^266447+758)/2	80209	Stefano Morozzi	01/2020
7760	2^266443+513	80208	Lelio R Paula	07/2013
7761	(26*10^80200+61)/3	80201	Robert Price	06/2017
7762	2^266412-109913	80199	Enzo Doria	04/2014
7763	(10223*2^266417+1)/45091	80199	Lelio R Paula	06/2014
7764	2^266413-4693	80199	Yves Minet	05/2019
7765	(13737^19381-1)/13736	80193	Serge Batalov	08/2020
7766	13^71988+66	80191	Lelio R Paula	11/2015
7767	11^77002-4320	80190	Enzo Doria	01/2013
7768	19839^11012+11012^19839	80187	Hans Havermann	03/2020
7770	18^63879-13	80186	Lelio R Paula	11/2015
7769	(2^266371+1814)/2	80186	Stefano Morozzi	01/2020
7771	2^266368-112295	80185	Enzo Doria	06/2014
7772	19217^14880+14880^19217	80185	Hans Havermann	03/2020
7773	(3^168050+5)/1021454	80175	Lelio R Paula	10/2012
7774	(2^266324+1386)/2	80172	Stefano Morozzi	01/2020
7775	(22*10^80167+41)/9	80168	Robert Price	02/2015
7776	(2^266308+1618)/2	80167	Stefano Morozzi	01/2020
7777	(34*10^80162-43)/9	80163	Ray Chandler	12/2010
7778	(2^266276+762)/2	80157	Stefano Morozzi	01/2020
7780	(38*10^80150-11)/9	80151	Robert Price	05/2015
7779	(598*10^80149-31)/9	80151	Robert Price	02/2017
7781	19^62678-80	80150	Lelio R Paula	12/2015
7782	(559^29173-1)/558	80148	Serge Batalov	08/2020
7783	10^80139+32343	80140	Patrick De Geest	02/2011
7784	10^80139-9	80139	Alexander Gramolin	01/2011
7785	3^167955-106	80135	Lelio R Paula	12/2015
7786	20545^7944+7944^20545	80127	Hans Havermann	04/2020
7787	18876^17569+17569^18876	80124	Hans Havermann	03/2020
7788	(2^266137+3782)/2	80115	Stefano Morozzi	01/2020
7789	(2^266121+3846)/2	80111	Stefano Morozzi	01/2020
7790	22752^3313+3313^22752	80093	Hans Havermann	03/2020
7791	(197*10^80089-11)/3	80091	Robert Price	10/2017
7792	2^265998+75559	80074	Enzo Doria	04/2016
7793	(2^265999+3290)/2	80074	Stefano Morozzi	01/2020
7794	2^265969-109801	80065	Enzo Doria	04/2014
7795	(2^265956+3378)/2	80061	Stefano Morozzi	01/2020
7796	2^265888-112757	80041	Enzo Doria	06/2014
7797	(24847^18211-1)/24846	80038	Serge Batalov	08/2020
7798	2^265809+1701	80017	Lelio R Paula	07/2013
7799	gcd(V(957175),5F(191435)(F(191435)+1)+1)	80014	Serge Batalov	04/2015
7800	19807^10954+10954^19807	80012	Hans Havermann	04/2020
7801	3^167687-104	80008	Lelio R Paula	02/2015
7802	11^76826-5790	80007	Enzo Doria	01/2013
7803	10^80000+85731	80001	Patrick De Geest	10/2009
7804	10^80000-7169	80000	Patrick De Geest	09/2009
7805	10^79999+22399	80000	Patrick De Geest	09/2009
7806	10^79999-74873	79999	Patrick De Geest	09/2009
7807	3^167668+58	79998	Lelio R Paula	02/2015
7808	(2^265728+3742)/2	79992	Stefano Morozzi	01/2020
7809	18780^18137+18137^18780	79976	Hans Havermann	04/2020
7810	19190^14709+14709^19190	79976	Hans Havermann	04/2020
7811	155^36506-2	79961	Lelio R Paula	10/2017
7812	(2^265621+3882)/2	79960	Stefano Morozzi	01/2020
7814	2^265612+4257	79958	Lelio R Paula	07/2013
7813	(2^265613+1470)/2	79958	Stefano Morozzi	01/2020
7815	5*3^167577+4	79956	Lelio R Paula	06/2014
7816	(9179*2^265593-1)/9	79955	Lelio R Paula	04/2015
7817	6^102723-43	79935	Lelio R Paula	04/2015
7818	21052^6261+6261^21052	79927	Hans Havermann	03/2020
7819	11^76748-3360	79925	Enzo Doria	12/2012
7820	19430^12981+12981^19430	79922	Hans Havermann	03/2020
7821	(2^265490+870)/2	79921	Stefano Morozzi	01/2020
7822	(13*2^265498-1)/187119	79919	Lelio R Paula	02/2014
7823	(2^265438+3978)/2	79905	Stefano Morozzi	01/2020
7824	(2^265409+1250)/2	79896	Stefano Morozzi	01/2020
7825	2^265399-109855	79894	Enzo Doria	04/2014
7826	(2^265380+3930)/2	79888	Stefano Morozzi	01/2020
7827	(20^61403-1)/19	79886	Paul Bourdelais	03/2010
7828	(2^265368+2970)/2	79884	Stefano Morozzi	01/2020
7829	18^63635+59	79880	Lelio R Paula	02/2015
7830	(11*10^79867-107)/3	79868	Robert Price	11/2016
7831	3^167375+80	79859	Lelio R Paula	02/2015
7832	5^114240-14486	79851	Enzo Doria	02/2013
7833	49^47238+48	79842	Norbert Schneider	07/2014
7834	2^265212-3779	79837	Yves Minet	04/2017
7835	(2^265201+2790)/2	79834	Stefano Morozzi	01/2020
7836	91^40746+40746^91	79824	Norbert Schneider	12/2014
7837	(68*10^79813-257)/9	79814	Robert Price	06/2017
7838	(13063^19391-1)/13062	79811	Serge Batalov	08/2020
7839	(5*2^265118-1)/61	79808	Lelio R Paula	02/2014
7840	(2^265102+1462)/2	79804	Stefano Morozzi	01/2020
7841	2^265074+28425	79796	Lelio R Paula	07/2013
7842	2^265072+1185	79795	Lelio R Paula	07/2013
7844	p(16682)#/2-128	79771	Robert Price	05/2017
7843	(2^264994+1714)/2	79771	Stefano Morozzi	01/2020
7846	3^167167-34	79759	Robert Price	11/2013
7845	(2^264952+3258)/2	79759	Stefano Morozzi	01/2020
7847	12^73906+29	79758	Lelio R Paula	02/2015
7848	2^264934+255	79754	Lelio R Paula	07/2013
7849	4*10^79729-87	79730	Robert Price	03/2017
7850	2^264846-111701	79727	Enzo Doria	05/2014
7851	2^264831-112041	79723	Enzo Doria	06/2014
7852	2^264816-455	79718	Yves Minet	03/2012
7853	(55*10^79711+89)/9	79712	Robert Price	09/2017
7854	47^47667-46	79704	Theodore Burton	02/2007
7855	13^71547+96	79700	Lelio R Paula	03/2015
7856	2^264752-112883	79699	Enzo Doria	06/2014
7857	(2^264748+1978)/2	79697	Stefano Morozzi	01/2020
7858	2^264732+133	79693	Lelio R Paula	05/2012
7859	8*3^167010+7	79685	Lelio R Paula	06/2014
7860	42^49087-41	79681	Norbert Schneider	06/2014
7861	(26*10^79678-119)/3	79679	Robert Price	07/2016
7862	2^264683-21	79678	Lelio R Paula	05/2012
7863	7^94279+18	79675	Lelio R Paula	02/2015
7865	2^264655-127	79670	Lelio R Paula	02/2012
7864	(2^264658+3102)/2	79670	Stefano Morozzi	01/2020
7866	(2^264637+1682)/2	79664	Stefano Morozzi	01/2020
7867	2^264597-459043	79652	Enzo Doria	05/2015
7868	(21*2^264566+1)/5	79643	Lelio R Paula	10/2012
7869	2^264536+1870021	79634	Enzo Doria	05/2016
7870	(17*2^264512-1)/359	79625	Lelio R Paula	02/2014
7871	19957^9762+9762^19957	79620	Hans Havermann	03/2020
7872	2^264477-109783	79616	Enzo Doria	04/2014
7873	18^63419-1333	79609	Enzo Doria	03/2013
7874	13^71451-36	79593	Lelio R Paula	03/2015
7875	23314^2593+2593^23314	79590	Hans Havermann	03/2020
7876	(2^264410-5)/128002609121	79585	Lelio R Paula	10/2012
7877	19^62234+90	79582	Lelio R Paula	03/2015
7878	(2^264276+2866)/2	79555	Stefano Morozzi	01/2020
7879	12^73714+49	79551	Lelio R Paula	02/2015
7880	(2^264213+1442)/2	79536	Stefano Morozzi	01/2020
7881	(3*2^264184-1)/1433339	79522	Lelio R Paula	02/2014
7882	(2^264160+1590)/2	79520	Stefano Morozzi	01/2020
7883	(29*10^79510-107)/3	79511	Robert Price	08/2020
7884	(9363^20021-1)/9362	79508	Serge Batalov	08/2020
7885	2^264103-112531	79503	Enzo Doria	06/2014
7886	19^62170+78	79501	Lelio R Paula	03/2015
7887	11^76340-2580	79500	Enzo Doria	12/2012
7888	(2^264084+858)/2	79497	Stefano Morozzi	01/2020
7889	(5652^21187-1)/5651	79495	Serge Batalov	08/2020
7890	(23*10^79492-11)/3	79493	Robert Price	10/2015
7891	((2^132049+13650)^2+(2^132049+13650)+41)/2003/23841473	79491	Makoto Morimoto	05/2016
7892	2^264060-112133	79490	Enzo Doria	06/2014
7894	((2^132049+4641)^2+(2^132049+4641)+41)/487/8537/10426147	79488	Makoto Morimoto	05/2016
7893	20158^8775+8775^20158	79488	Hans Havermann	02/2020
7895	9^83298+6^83298-2^83298	79487	Mike Oakes	08/2010
7896	18^63319+35	79483	Lelio R Paula	02/2015
7897	(10011^19867-1)/10010	79474	Serge Batalov	08/2020
7898	2*10^79468+77	79469	Robert Price	08/2020
7899	22479^3428+3428^22479	79465	Hans Havermann	04/2020
7900	38303!2+256	79461	Robert Price	01/2015
7901	(29*10^79445+61)/9	79446	Robert Price	04/2015
7902	2^263902-195	79443	Lelio R Paula	05/2012
7903	3^166499-112696	79441	Enzo Doria	06/2014
7904	11^76279-2760	79437	Enzo Doria	12/2012
7905	18907^15894+15894^18907	79433	Hans Havermann	03/2020
7906	6^102077-25	79432	Lelio R Paula	03/2015
7907	2^263852-1017	79428	Lelio R Paula	07/2013
7908	2^263842-33	79425	Lelio R Paula	05/2012
7909	(2^263814+3582)/2	79416	Stefano Morozzi	01/2020
7910	12^73584-55	79411	Lelio R Paula	02/2015
7911	(2^263783+3558)/2	79407	Stefano Morozzi	01/2020
7912	2^263772-185	79404	Lelio R Paula	05/2012
7913	(15^67489+1)/16	79373	Paul Bourdelais	03/2010
7914	2^263664+15015	79371	Lelio R Paula	07/2013
7915	(2^263643+1206)/2	79365	Stefano Morozzi	01/2020
7916	(2^263642+3082)/2	79364	Stefano Morozzi	01/2020
7917	(3319^22541-1)/3318	79364	Serge Batalov	08/2020
7918	10^79362+3^79363	79363	Mike Oakes	06/2010
7919	(2^263591+2910)/2	79349	Stefano Morozzi	01/2020
7920	(2^263589+1922)/2	79348	Stefano Morozzi	01/2020
7921	Phi(163244,10)/2448661/6856249	79331	Maksym Voznyy	11/2015
7922	3^166262+44	79328	Lelio R Paula	02/2015
7923	4*10^79327-63	79328	Robert Price	12/2016
7924	2^263486+513	79318	Lelio R Paula	07/2013
7925	(2^263458+1282)/2	79309	Stefano Morozzi	01/2020
7926	(2^263456+1558)/2	79308	Stefano Morozzi	01/2020
7927	2^263448-519509	79306	Paul Bourdelais	03/2013
7928	(18926^18541-1)/18925	79297	Serge Batalov	08/2020
7929	69153^16384+2	79296	Matt Stath	01/2019
7930	21^59971-20^59971	79295	Robert Price	05/2012
7931	2^263372+123	79283	Lelio R Paula	05/2012
7932	(2^263366+1974)/2	79281	Stefano Morozzi	01/2020
7933	17^64429+84	79277	Lelio R Paula	03/2015
7934	11^76124-11430	79275	Enzo Doria	12/2012
7935	19294^12845+12845^19294	79274	Hans Havermann	03/2020
7936	(206*10^79268-17)/9	79270	Robert Price	03/2017
7937	13^71157+18	79265	Lelio R Paula	03/2015
7938	2^263297+65835	79261	Lelio R Paula	07/2013
7939	19^61980-18	79258	Theodore Burton	12/2005
7940	(2^263259+2970)/2	79249	Stefano Morozzi	01/2020
7941	2*10^79242+93	79243	Robert Price	07/2016
7942	(2^263226+1074)/2	79239	Stefano Morozzi	01/2020
7943	(88^40751-1)/87	79238	Paul Bourdelais	08/2017
7944	(103*29^54179-39)/4	79233	Curtis Bright	05/2015
7945	9^83024-83024^9	79226	Norbert Schneider	08/2017
7946	17^64382-26	79219	Lelio R Paula	03/2015
7947	7^93733-74	79214	Lelio R Paula	02/2015
7948	15^67352+38	79213	Lelio R Paula	02/2015
7949	2^263135-110235	79212	Enzo Doria	05/2014
7950	(2^263080+3658)/2	79195	Stefano Morozzi	01/2020
7951	2^263044+4257	79185	Lelio R Paula	07/2013
7952	(2^263039+3554)/2	79183	Stefano Morozzi	01/2020
7954	2^263032+87517	79181	Yves Minet	11/2010
7953	6^101755+95	79181	Lelio R Paula	03/2015
7955	(2^263010+1738)/2	79174	Stefano Morozzi	01/2020
7956	4^131497-3^131497	79170	Jean-Louis Charton	05/2004
7957	5*7^93674+8	79165	Lelio R Paula	10/2014
7958	(2^262939+1326)/2	79153	Stefano Morozzi	01/2020
7959	(2^262941+926)/2	79153	Stefano Morozzi	01/2020
7960	lucasU(486,25,29457)-5*lucasU(486,25,29456)	79137	Mike Oakes	05/2009
7961	260^32768+179^32768	79134	Serge Batalov	03/2018
7962	11^75978-42	79123	Lelio R Paula	02/2015
7963	8*5^113180+9	79111	Lelio R Paula	10/2014
7964	(2^262757+3222)/2	79098	Stefano Morozzi	01/2020
7965	(6883*2^262741-1)/4835	79094	Lelio R Paula	04/2015
7966	(9*2^262745+1)/137	79093	Lelio R Paula	10/2012
7967	12^73285+85	79088	Lelio R Paula	02/2015
7968	19^61840+52	79079	Lelio R Paula	03/2015
7970	(10^79067+77)/3	79067	Robert Price	01/2017
7969	(2^262655+678)/2	79067	Stefano Morozzi	01/2020
7971	(1017*2^262640-1)/11557	79062	Lelio R Paula	04/2015
7972	(2^262634+1674)/2	79061	Stefano Morozzi	01/2020
7973	10^79040+137949	79041	Patrick De Geest	02/2016
7975	10^79040-1007297	79040	Robert Price	02/2015
7974	10^79040-77427	79040	Patrick De Geest	02/2016
7976	2^262551-17295	79036	Lelio R Paula	07/2013
7977	(22973^18121-1)/22972	79026	Serge Batalov	08/2020
7978	3^165597+340	79010	Lelio R Paula	02/2015
7979	19620^10633+10633^19620	79003	Hans Havermann	02/2020
7980	(23*2^262435+1)/55	79001	Lelio R Paula	10/2012
7981	11^75860-2100	79001	Enzo Doria	12/2012
7982	8*7^93463+9	78987	Lelio R Paula	10/2014
7983	(2^262376+3942)/2	78983	Stefano Morozzi	01/2020
7984	67^43240-2	78960	Lelio R Paula	09/2013
7985	1000001^13159-1000000^13159	78953	Jean-Louis Charton	10/2003
7986	(2^262263+3410)/2	78949	Stefano Morozzi	01/2020
7987	2^262199-110287	78930	Enzo Doria	05/2014
7988	(19*2^262180-1)/177	78924	Lelio R Paula	02/2014
7989	(3^165403+4)/7	78917	Lelio R Paula	10/2012
7990	2^21068*(2^241076+1)-1	78914	Makoto Morimoto	03/2014
7991	2^29258*(2^232886+1)-1	78914	Makoto Morimoto	03/2014
7993	2^262144+18531	78914	Makoto Morimoto	12/2015
7992	2^262144-231425	78914	Matthias Baur	03/2020
7994	(2^262137+1730)/2	78911	Stefano Morozzi	01/2020
7995	(2^(2^18)+2450)/(23^2137*577)	78908	Makoto Morimoto	08/2017
7996	(2^(2^18)-5719)/(35993623)	78907	Makoto Morimoto	08/2017
7997	14^68837+75	78897	Lelio R Paula	02/2015
7998	(2^262055+1806)/2	78887	Stefano Morozzi	01/2020
7999	(20450^18301-1)/20449	78886	Serge Batalov	08/2020
8000	(2^262049+1406)/2	78885	Stefano Morozzi	01/2020

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Probable Primes Top 10000

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