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 ?
6751	2^234890-30341	70709	Enzo Doria	11/2012
6752	17^57461+14	70703	Lelio R Paula	01/2015
6753	(9179*2^234834-1)/5	70696	Lelio R Paula	04/2015
6754	2*10^70688+51	70689	Robert Price	10/2017
6755	123^33822-122	70685	Norbert Schneider	01/2015
6756	7*10^70680-99	70681	Robert Price	11/2017
6757	(21*2^234772-1)/2095	70672	Lelio R Paula	01/2014
6758	(29*2^234686-1)/21145	70645	Lelio R Paula	01/2014
6759	(15*2^234688-1)/5278141	70643	Lelio R Paula	01/2014
6761	2^234655-67	70639	Lelio R Paula	02/2012
6760	(79*10^70638-61)/9	70639	Robert Price	10/2015
6762	2^234652-173	70638	Lelio R Paula	02/2012
6763	2^234618-3645	70628	Lelio R Paula	05/2012
6764	(2^234610-5)/19	70624	Lelio R Paula	05/2012
6765	4*5^101038+9	70624	Lelio R Paula	10/2014
6766	2^234603+71963	70623	Enzo Doria	04/2016
6767	2^234600-113129	70622	Enzo Doria	07/2014
6768	2^234586+9	70618	Lelio R Paula	02/2012
6769	3^148008+26	70618	Robert Price	11/2013
6770	(7*10^70616-151)/9	70616	Robert Price	09/2017
6771	65^38947+32	70608	Lelio R Paula	01/2016
6772	(2^234488-3)/11	70587	Lelio R Paula	05/2012
6773	(3*2^234451+1)/35	70576	Lelio R Paula	08/2012
6774	Phi(159495,10)	70560	Maksym Voznyy	09/2015
6775	2^234383-4035	70557	Lelio R Paula	05/2012
6776	2^234315-111241	70536	Enzo Doria	05/2014
6777	14^61526+97	70517	Lelio R Paula	01/2015
6778	(3*2^234170+1)/13	70492	Lelio R Paula	08/2012
6779	51^41281-50^41281	70491	Robert Price	02/2013
6780	2^234141-112123	70484	Enzo Doria	06/2014
6781	2^234139+12285	70483	Lelio R Paula	04/2012
6782	2^234133-3163	70482	Yves Minet	04/2009
6783	2^234115+83	70476	Lelio R Paula	02/2012
6784	2^234114-1595	70476	Lelio R Paula	05/2012
6785	24^51061-23^51061	70475	Robert Price	07/2012
6786	19471^16428-2	70467	Faysal YAtim	09/2005
6787	7^83381+12	70466	Robert Price	01/2014
6788	2^234067-111427	70462	Enzo Doria	05/2014
6789	(266*10^70457+1)/3	70459	Robert Price	02/2016
6790	(31*2^234041-1)/97	70453	Lelio R Paula	01/2014
6791	2^234026+12909	70449	Lelio R Paula	04/2012
6792	2^233965-19	70431	Lelio R Paula	02/2012
6793	(5*2^233932-1)/179	70419	Lelio R Paula	01/2014
6794	2^233908-17109	70414	Enzo Doria	05/2013
6795	695^24772+24772^695	70402	Norbert Schneider	09/2016
6796	3*5^100719-2	70401	Lelio R Paula	10/2014
6797	2^233829-111355	70390	Enzo Doria	05/2014
6798	(19775^16384+1)/2	70388	Henri Lifchitz	03/2007
6799	7*3^147519+8	70386	Lelio R Paula	04/2014
6800	141^32749-2	70385	Lelio R Paula	10/2017
6801	5*7^83265+2	70368	Lelio R Paula	10/2014
6802	(23*10^70363+97)/3	70364	Robert Price	02/2017
6803	(23*2^233749-1)/35325	70363	Lelio R Paula	01/2014
6804	5^100652-13916	70353	Enzo Doria	02/2013
6805	45^42555-2	70353	Lelio R Paula	08/2013
6806	2^233661-61	70339	Lelio R Paula	02/2012
6807	2^233523-112249	70298	Enzo Doria	06/2014
6808	5*3^147324-8	70293	Lelio R Paula	04/2014
6809	2^233488-13065	70287	Enzo Doria	11/2012
6810	(3^147322+8)/42851	70286	Lelio R Paula	06/2012
6811	(22*10^70259+161)/3	70260	Robert Price	02/2017
6812	2^233388+465	70257	Lelio R Paula	11/2012
6813	14^61299+59	70257	Lelio R Paula	01/2015
6814	2^233383+94065	70256	Lelio R Paula	04/2012
6815	49471!3-6561	70253	Robert Price	11/2015
6816	7^83121+6^(83121-1)	70246	Robert Price	03/2016
6817	(197*10^70241-11)/3	70243	Robert Price	10/2017
6818	23*10^70240-7	70242	Robert Price	03/2016
6819	(71*10^70227-53)/9	70228	Robert Price	10/2015
6820	(2^233247-9)/17	70214	Lelio R Paula	05/2012
6821	(11^67421-2^67421)/9	70211	Robert Price	01/2013
6822	(23*10^70209-41)/9	70210	Robert Price	03/2015
6823	(29*10^70194-11)/9	70195	Robert Price	04/2015
6824	3^147109+196	70189	Lelio R Paula	05/2014
6825	(34*10^70191-7)/9/3/40583/573047	70181	Makoto Morimoto	05/2016
6826	9^73538+8^(73538+1)	70174	Robert Price	06/2016
6827	2*5^100391+7	70171	Lelio R Paula	10/2014
6828	99^35156-2	70159	Lelio R Paula	08/2013
6829	(68*10^70148+7)/3	70150	Robert Price	03/2016
6830	11^67360-6030	70149	Enzo Doria	01/2013
6831	(35*10^70130-377)/9	70131	Robert Price	12/2017
6832	49391!3+3^49391	70128	Robert Price	09/2015
6833	(229*10^70122-1)/3	70124	Robert Price	12/2016
6834	7^82975-92	70123	Lelio R Paula	07/2014
6835	65^38670+58	70106	Lelio R Paula	01/2016
6836	105^34684+34684^105	70103	Serge Batalov	05/2014
6837	134^32955-133	70099	Norbert Schneider	03/2015
6838	2^232836-227903	70091	Enzo Doria	12/2012
6839	2^232837-1859173	70091	Enzo Doria	03/2016
6840	3*2^232820+5	70087	Lelio R Paula	04/2014
6842	2^232799+90195	70080	Lelio R Paula	02/2013
6841	2^232799-112237	70080	Enzo Doria	06/2014
6843	2^232759+262145	70068	Lelio R Paula	04/2012
6844	3*2^232750+7	70066	Lelio R Paula	04/2014
6845	12^64918-11	70059	Lelio R Paula	01/2015
6846	7^82899-12	70058	Lelio R Paula	09/2013
6847	(22*10^70051-13)/9	70052	Robert Price	03/2015
6848	(2^232685-7)/2514625	70039	Lelio R Paula	04/2012
6849	18^55786-5363	70027	Enzo Doria	03/2013
6850	(2^(77537*3+1)+243)/7	70023	Kevin Acres	11/2013
6851	2^232602+169	70021	Lelio R Paula	02/2012
6852	(137^32768+29^32768)/2	70016	Jeppe Stig Nielsen	04/2018
6853	2^232580+72133	70014	Enzo Doria	04/2016
6854	4*6^89958-7	70002	Lelio R Paula	09/2014
6855	10^70000+80487	70001	Milton L. Brown	05/2006
6856	10^69999+134857	70000	Patrick De Geest	02/2007
6861	10^70000-9273	70000	Patrick De Geest	08/2009
6860	(79*10^69999-7)/9	70000	Robert Price	01/2015
6859	((2^43112609)/10^38420)%10^70000	70000	Michael Vang	10/2016
6857	(2^756839/10^36014)%10^70000	70000	Michael Vang	12/2016
6858	(2^74207281/10^32641)%10^70000	70000	Michael Vang	12/2016
6862	10^69999-88251	69999	Patrick De Geest	08/2009
6863	2^232507+1089	69992	Lelio R Paula	04/2012
6864	(17*2^232445+1)/5	69974	Lelio R Paula	08/2012
6865	(529^25693+1)/530	69972	Richard Fischer	12/2017
6866	7^82778+48	69956	Lelio R Paula	09/2013
6867	7*2^232381+3	69955	Lelio R Paula	04/2014
6868	2^232362-110541	69948	Enzo Doria	05/2014
6869	2^232326-112391	69938	Enzo Doria	06/2014
6870	3^146575+236	69935	Lelio R Paula	09/2013
6871	30^47341-29	69929	Norbert Schneider	02/2014
6872	5^100040-68	69925	Lelio R Paula	09/2013
6873	(35*10^69866-593)/9	69867	Robert Price	08/2017
6874	2^232045-17295	69853	Lelio R Paula	04/2012
6875	(2^231987+78557)/95	69834	Lelio R Paula	05/2012
6876	2^231955+74243	69826	Yves Minet	03/2011
6877	2^231946-15873	69823	Enzo Doria	04/2013
6878	18^55618+95	69816	Lelio R Paula	09/2013
6879	6^89712+5^(89712-1)	69810	Robert Price	02/2016
6880	2^231870+135	69800	Lelio R Paula	02/2012
6881	(23*2^231827-1)/4179	69785	Lelio R Paula	01/2014
6882	2^231778+54615	69773	Lelio R Paula	04/2012
6883	(19*2^231780+1)/235	69772	Lelio R Paula	08/2012
6884	14^60866+27	69761	Lelio R Paula	09/2013
6885	13^62619-44	69755	Lelio R Paula	09/2013
6886	(2^231715-509203)/35	69752	Lelio R Paula	05/2012
6887	2^231711-110467	69752	Enzo Doria	05/2014
6888	(19^54547+18^54547)/37	69751	Robert Price	08/2013
6889	(23*2^231697-1)/45	69748	Lelio R Paula	01/2014
6890	2^231696-1861499	69748	Enzo Doria	03/2016
6891	2^231684-147	69744	Lelio R Paula	02/2012
6892	(23*2^231686-1)/1183	69743	Lelio R Paula	01/2014
6893	2^231591-477397	69716	Paul Bourdelais	03/2013
6894	11^66916-420	69686	Enzo Doria	08/2012
6896	5^99680-13706	69674	Enzo Doria	02/2013
6895	(8*10^69674-53)/9	69674	Robert Price	11/2014
6897	(44*10^69663-413)/9	69664	Robert Price	10/2017
6898	(77*10^69656-23)/9	69657	Robert Price	10/2015
6899	6^89509+131	69652	Lelio R Paula	09/2013
6900	(78557*2^231349+1)/35	69647	Lelio R Paula	06/2014
6901	(11*10^69645+19)/3	69646	Robert Price	03/2016
6902	11^66875-28	69644	Lelio R Paula	09/2013
6903	2^231347+71483	69643	Enzo Doria	04/2016
6904	(14^60763+3^60763)/17	69641	Robert Price	04/2013
6905	(4*10^69626+173)/3	69627	Robert Price	01/2017
6906	2^231289+255	69625	Lelio R Paula	04/2012
6907	2^231234-112913	69609	Enzo Doria	06/2014
6908	(265*10^69602-7)/3	69604	Robert Price	07/2016
6909	2^231182-112841	69593	Enzo Doria	06/2014
6910	(15*2^231129+1)/23	69577	Lelio R Paula	08/2012
6911	3^145806-28	69568	Lelio R Paula	09/2013
6912	(265*10^69554-7)/3	69556	Robert Price	07/2016
6913	2^231052-113159	69554	Enzo Doria	07/2014
6914	11^66784-8	69549	Lelio R Paula	09/2013
6915	Phi(104409,10)/2296999	69546	Maksym Voznyy	07/2015
6916	2^231016-110523	69543	Enzo Doria	05/2014
6917	2^231014+577294575	69543	Lelio R Paula	02/2016
6918	14^60658+67	69522	Lelio R Paula	09/2013
6919	5^99418+36	69491	Lelio R Paula	06/2013
6920	7^82203-30	69470	Lelio R Paula	09/2013
6921	(63^38609-1)/62	69469	Paul Bourdelais	08/2017
6922	5^99359-2^99360	69449	Mike Oakes	12/2010
6923	(29*2^230684+1)/1395	69442	Lelio R Paula	08/2012
6924	(19*10^69424+77)/3	69425	Robert Price	08/2016
6925	19^54287-96	69420	Lelio R Paula	09/2013
6926	2^230541+58905	69400	Lelio R Paula	04/2012
6927	2^230506+12705	69390	Lelio R Paula	02/2013
6928	8*6^89156-5	69378	Lelio R Paula	09/2014
6929	2^230438-111347	69369	Enzo Doria	05/2014
6930	2^230428-99	69366	Lelio R Paula	02/2012
6931	(62^38699+1)/63	69362	Paul Bourdelais	08/2017
6932	3*10^69354+17	69355	Robert Price	03/2017
6933	(493*10^69340-7)/9	69342	Robert Price	07/2016
6934	(41*10^69321+373)/9	69322	Robert Price	04/2017
6935	6^89072+53	69312	Lelio R Paula	09/2013
6936	155^31639+2	69300	Lelio R Paula	05/2013
6937	3*7^81965-4	69269	Lelio R Paula	09/2014
6938	(16*10^69265+41)/3	69266	Robert Price	10/2017
6939	(86*10^69260-77)/9	69261	Robert Price	05/2016
6940	9*5^99087+4	69260	Lelio R Paula	09/2014
6941	3^145145+2660	69252	Lelio R Paula	09/2013
6943	11^66492-1140	69245	Enzo Doria	11/2012
6942	5*3^145129-4	69245	Lelio R Paula	04/2014
6944	7*3^145126+8	69244	Lelio R Paula	04/2014
6945	11^66480-2370	69232	Enzo Doria	12/2012
6946	2^229962-65	69226	Lelio R Paula	02/2012
6947	2^229958-110733	69225	Enzo Doria	05/2014
6948	V(332407)	69225	Serge Batalov	03/2015
6949	6^88959+7	69224	Lelio R Paula	09/2013
6950	15^58855-94	69219	Lelio R Paula	09/2013
6951	(2^229838+47)/12081	69185	Lelio R Paula	04/2012
6952	3^144952+98	69160	Lelio R Paula	09/2013
6953	5^98941-72	69157	Lelio R Paula	06/2013
6954	(17*2^229604-1)/229	69117	Lelio R Paula	01/2014
6955	2^229585-1063	69112	Yves Minet	11/2012
6956	(13*2^229567-1)/19	69107	Lelio R Paula	01/2014
6957	(13*2^229393-1)/5	69055	Lelio R Paula	01/2014
6958	(53*10^69050-17)/9	69051	Robert Price	09/2015
6959	(43*10^69048+47)/9	69049	Robert Price	12/2017
6960	2^229305-1868533	69028	Enzo Doria	04/2016
6961	2^229297+1385	69026	Lelio R Paula	04/2012
6962	18^54986-2441	69023	Enzo Doria	03/2013
6963	(34*10^69021-7)/9/3/67	69020	Makoto Morimoto	04/2016
6964	5^98736-14636	69014	Enzo Doria	02/2013
6965	(13^61949-5^61949)/8	69007	Robert Price	03/2013
6966	(2^229227+5)/611	69002	Lelio R Paula	04/2012
6967	2^229216-113279	69001	Enzo Doria	07/2014
6968	10^68994+51913	68995	Patrick De Geest	03/2016
6970	10^68994-10^5814-1	68994	Serge Batalov	01/2011
6969	10^68994-82947	68994	Patrick De Geest	03/2016
6971	(17*2^229136-1)/2381	68975	Lelio R Paula	01/2014
6972	2^229113+107	68970	Lelio R Paula	02/2012
6973	11^66202-4410	68943	Enzo Doria	01/2013
6974	12^63883+5	68942	Lelio R Paula	07/2013
6975	(9913*2^229002-1)/399903	68935	Lelio R Paula	04/2015
6976	2^228962-111581	68925	Enzo Doria	05/2014
6977	2^228944+81	68920	Henri Lifchitz	01/2007
6978	11^66174-54	68914	Lelio R Paula	09/2013
6979	2^228913-111265	68910	Enzo Doria	05/2014
6980	2^228902+73519	68907	Enzo Doria	04/2016
6981	(47*2^228884+1)/63	68901	Lelio R Paula	04/2015
6982	2^228821+76427	68882	Enzo Doria	05/2016
6983	3^144340+50	68868	Lelio R Paula	09/2013
6984	2^228758-112967	68864	Enzo Doria	06/2014
6985	2^228743-111379	68859	Enzo Doria	05/2014
6986	2^228741-110911	68858	Enzo Doria	05/2014
6988	lucasU(1926,1,20964)-lucasU(1926,1,20963)	68857	Mike Oakes	05/2009
6987	3*5^98511-8	68857	Lelio R Paula	09/2014
6989	2^228717+467	68851	Lelio R Paula	02/2011
6990	Phi(153218,10)/2211855049/23592660859/497714117291	68849	Maksym Voznyy	10/2011
6991	(509203*2^228665-1)/35	68840	Lelio R Paula	04/2015
6992	8^76213-7^76213	68828	Ananda Tallur & Jean-Louis Charton	11/2003
6993	11^66074-1050	68809	Enzo Doria	11/2012
6994	(68*10^68798-11)/3	68800	Robert Price	10/2017
6995	2^228484+181	68781	Lelio R Paula	02/2012
6996	2^228479-58695	68780	Lelio R Paula	04/2012
6997	2^228465-15853	68775	Enzo Doria	04/2013
6998	11^66040-5400	68774	Enzo Doria	01/2013
6999	(13*2^228441-1)/575	68766	Lelio R Paula	01/2014
7000	(17*2^228393+1)/295	68752	Lelio R Paula	08/2012

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Probable Primes Top 10000

(247113 PRPs in the top)