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 ?
7001	15105^17054+17054^15105	71271	Norbert Schneider	08/2018
7002	(2^236738+9)/13	71265	Lelio R Paula	05/2012
7003	5^101949+42	71260	Lelio R Paula	07/2014
7004	5*10^71237+9	71238	Dmitry Domanov	11/2010
7005	2^236634-16025	71234	Enzo Doria	04/2013
7006	71^38478+70	71233	Norbert Schneider	12/2014
7007	9*7^84280+8	71226	Lelio R Paula	10/2014
7008	(10^71223+59)/3	71223	Serge Batalov	12/2014
7009	(15185*2^236569-1)/453	71216	Lelio R Paula	04/2015
7010	51829#+(216091#)/(51829#)	71208	Makoto Morimoto	03/2016
7011	2^236528-173	71203	Lelio R Paula	02/2012
7012	3*2^236511-5	71198	Lelio R Paula	04/2014
7013	2^236477-99	71187	Lelio R Paula	02/2012
7014	11^68356-2130	71186	Enzo Doria	12/2012
7015	15128^17031+17031^15128	71186	Norbert Schneider	08/2018
7016	11^68355-3120	71185	Enzo Doria	12/2012
7017	36^45737-35^45737	71181	Robert Price	10/2012
7018	(3^149183-lucasV(1,3,149183)+1)/3	71178	Paul Vanderveen	12/2017
7019	2^236432+25	71174	Lelio R Paula	02/2012
7020	5^101818-12806	71168	Enzo Doria	02/2013
7021	(7*10^71166-457)/9	71166	Robert Price	09/2017
7022	65^39253+62	71163	Lelio R Paula	01/2016
7023	39^44718+38	71150	Norbert Schneider	05/2014
7024	2^236296-407	71133	Yves Minet	02/2012
7025	2^236286-117	71130	Lelio R Paula	02/2012
7026	2^236257-111193	71121	Enzo Doria	05/2014
7027	7^84149-36	71115	Lelio R Paula	08/2014
7028	164176#-p(164176)	71108	Henri Lifchitz	12/2018
7029	2^236209-112123	71106	Enzo Doria	06/2014
7030	18^56644-4985	71104	Enzo Doria	03/2013
7031	(46*10^71077+521)/9	71078	Robert Price	08/2017
7032	21^53753+2	71074	Ray Chandler	08/2011
7033	(86*10^71068-311)/9	71069	Robert Price	10/2017
7034	2^236081-110923	71068	Enzo Doria	05/2014
7035	(293*27^49642-1736)/13	71058	Curtis Bright	05/2015
7036	65^39192+22	71052	Lelio R Paula	01/2016
7037	(439#+1)^397-439#^397	71038	Mike Oakes	11/2010
7038	7^84050-2	71031	Lelio R Paula	09/2013
7039	20^54558-23	70982	Lelio R Paula	01/2015
7040	2^235793-112555	70981	Enzo Doria	06/2014
7041	49936!3-3^49936	70981	Robert Price	08/2015
7042	2^235787-78795	70979	Lelio R Paula	05/2012
7043	Perrin(581132)	70970	Eric W. Weisstein	02/2011
7044	14^61913-97	70961	Lelio R Paula	01/2015
7045	2^235720+16321	70959	Yves Minet	03/2010
7046	2^235718+16095	70959	Lelio R Paula	05/2012
7047	163841#+349933	70957	Nicolas PALAU	11/2016
7048	2^235710+7	70956	Lelio R Paula	02/2012
7049	(175^31627+1)/176	70939	Eric Chen	10/2017
7050	2^235635-112087	70934	Enzo Doria	06/2014
7051	153^32467+152	70931	Norbert Schneider	11/2018
7053	2^235575-1965	70916	Lelio R Paula	05/2012
7052	6^91133+101	70916	Lelio R Paula	01/2015
7054	(21181*2^235505+1)/3	70898	Lelio R Paula	06/2014
7055	(14*10^70896+211)/9	70897	Robert Price	11/2017
7056	5^101425+84	70894	Lelio R Paula	07/2014
7057	177^31536+2	70893	Lelio R Paula	05/2013
7058	43*71^38292+4	70891	Serge Batalov	03/2016
7059	(29*2^235506-1)/112029785	70888	Lelio R Paula	01/2014
7060	11^68045-1530	70862	Enzo Doria	12/2012
7061	5*10^70858+21	70859	Robert Price	01/2017
7063	2^235326+3	70841	Donovan Johnson	02/2006
7062	34523!2+4	70841	Robert Price	02/2015
7064	(31*2^235307+1)/3	70836	Lelio R Paula	06/2012
7065	2^235308+135	70835	Lelio R Paula	02/2012
7066	r(35414,90)*1000+911	70831	Patrick De Geest	07/2004
7067	2^235274+159	70825	Lelio R Paula	02/2012
7068	3^148409+70	70810	Lelio R Paula	11/2014
7069	(19*10^70794+17)/9	70795	Robert Price	03/2015
7070	2^235108-232709	70775	Paul Bourdelais	03/2013
7071	(2^235099-2^117550+1)/5	70772		11/2006
7072	19^55325-6	70748	Lelio R Paula	08/2014
7073	257^29356+29356^257	70746	Norbert Schneider	10/2014
7074	22*10^70729+3	70731	Robert Price	10/2017
7075	2^234956+11715	70729	Lelio R Paula	05/2012
7076	(7*10^70727-43)/9	70727	Robert Price	10/2014
7077	2^234890-30341	70709	Enzo Doria	11/2012
7078	17^57461+14	70703	Lelio R Paula	01/2015
7079	(9179*2^234834-1)/5	70696	Lelio R Paula	04/2015
7080	2*10^70688+51	70689	Robert Price	10/2017
7081	123^33822-122	70685	Norbert Schneider	01/2015
7082	7*10^70680-99	70681	Robert Price	11/2017
7083	(21*2^234772-1)/2095	70672	Lelio R Paula	01/2014
7084	(29*2^234686-1)/21145	70645	Lelio R Paula	01/2014
7085	(15*2^234688-1)/5278141	70643	Lelio R Paula	01/2014
7087	2^234655-67	70639	Lelio R Paula	02/2012
7086	(79*10^70638-61)/9	70639	Robert Price	10/2015
7088	2^234652-173	70638	Lelio R Paula	02/2012
7089	2^234618-3645	70628	Lelio R Paula	05/2012
7090	(2^234610-5)/19	70624	Lelio R Paula	05/2012
7091	4*5^101038+9	70624	Lelio R Paula	10/2014
7092	2^234603+71963	70623	Enzo Doria	04/2016
7093	2^234600-113129	70622	Enzo Doria	07/2014
7095	2^234586+9	70618	Lelio R Paula	02/2012
7094	3^148008+26	70618	Robert Price	11/2013
7096	(7*10^70616-151)/9	70616	Robert Price	09/2017
7097	65^38947+32	70608	Lelio R Paula	01/2016
7098	(2^234488-3)/11	70587	Lelio R Paula	05/2012
7099	(3*2^234451+1)/35	70576	Lelio R Paula	08/2012
7100	Phi(159495,10)	70560	Maksym Voznyy	09/2015
7101	2^234383-4035	70557	Lelio R Paula	05/2012
7102	2^234315-111241	70536	Enzo Doria	05/2014
7103	14^61526+97	70517	Lelio R Paula	01/2015
7104	(3*2^234170+1)/13	70492	Lelio R Paula	08/2012
7105	51^41281-50^41281	70491	Robert Price	02/2013
7106	2^234141-112123	70484	Enzo Doria	06/2014
7107	2^234139+12285	70483	Lelio R Paula	04/2012
7108	2^234133-3163	70482	Yves Minet	04/2009
7109	2^234115+83	70476	Lelio R Paula	02/2012
7110	2^234114-1595	70476	Lelio R Paula	05/2012
7111	24^51061-23^51061	70475	Robert Price	07/2012
7112	19471^16428-2	70467	Faysal YAtim	09/2005
7113	7^83381+12	70466	Robert Price	01/2014
7114	2^234067-111427	70462	Enzo Doria	05/2014
7115	(266*10^70457+1)/3	70459	Robert Price	02/2016
7116	(31*2^234041-1)/97	70453	Lelio R Paula	01/2014
7117	2^234026+12909	70449	Lelio R Paula	04/2012
7118	2^233965-19	70431	Lelio R Paula	02/2012
7119	(5*2^233932-1)/179	70419	Lelio R Paula	01/2014
7120	2^233908-17109	70414	Enzo Doria	05/2013
7121	695^24772+24772^695	70402	Norbert Schneider	09/2016
7122	3*5^100719-2	70401	Lelio R Paula	10/2014
7123	2^233829-111355	70390	Enzo Doria	05/2014
7124	(19775^16384+1)/2	70388	Henri Lifchitz	03/2007
7125	7*3^147519+8	70386	Lelio R Paula	04/2014
7126	141^32749-2	70385	Lelio R Paula	10/2017
7127	5*7^83265+2	70368	Lelio R Paula	10/2014
7128	(23*10^70363+97)/3	70364	Robert Price	02/2017
7129	(23*2^233749-1)/35325	70363	Lelio R Paula	01/2014
7131	5^100652-13916	70353	Enzo Doria	02/2013
7130	45^42555-2	70353	Lelio R Paula	08/2013
7132	2^233661-61	70339	Lelio R Paula	02/2012
7133	2^233523-112249	70298	Enzo Doria	06/2014
7134	5*3^147324-8	70293	Lelio R Paula	04/2014
7135	2^233488-13065	70287	Enzo Doria	11/2012
7136	(3^147322+8)/42851	70286	Lelio R Paula	06/2012
7137	(22*10^70259+161)/3	70260	Robert Price	02/2017
7139	2^233388+465	70257	Lelio R Paula	11/2012
7138	14^61299+59	70257	Lelio R Paula	01/2015
7140	2^233383+94065	70256	Lelio R Paula	04/2012
7141	49471!3-6561	70253	Robert Price	11/2015
7142	7^83121+6^(83121-1)	70246	Robert Price	03/2016
7143	(197*10^70241-11)/3	70243	Robert Price	10/2017
7144	23*10^70240-7	70242	Robert Price	03/2016
7145	(71*10^70227-53)/9	70228	Robert Price	10/2015
7146	10815^17408+17408^10815	70225	Norbert Schneider	05/2019
7147	(2^233247-9)/17	70214	Lelio R Paula	05/2012
7148	(11^67421-2^67421)/9	70211	Robert Price	01/2013
7149	(23*10^70209-41)/9	70210	Robert Price	03/2015
7150	(29*10^70194-11)/9	70195	Robert Price	04/2015
7151	3^147109+196	70189	Lelio R Paula	05/2014
7152	(34*10^70191-7)/9/3/40583/573047	70181	Makoto Morimoto	05/2016
7153	9^73538+8^(73538+1)	70174	Robert Price	06/2016
7154	2*5^100391+7	70171	Lelio R Paula	10/2014
7155	99^35156-2	70159	Lelio R Paula	08/2013
7156	(68*10^70148+7)/3	70150	Robert Price	03/2016
7157	11^67360-6030	70149	Enzo Doria	01/2013
7158	(35*10^70130-377)/9	70131	Robert Price	12/2017
7159	49391!3+3^49391	70128	Robert Price	09/2015
7160	(229*10^70122-1)/3	70124	Robert Price	12/2016
7161	7^82975-92	70123	Lelio R Paula	07/2014
7162	65^38670+58	70106	Lelio R Paula	01/2016
7163	105^34684+34684^105	70103	Serge Batalov	05/2014
7164	134^32955-133	70099	Norbert Schneider	03/2015
7166	2^232836-227903	70091	Enzo Doria	12/2012
7165	2^232837-1859173	70091	Enzo Doria	03/2016
7167	3*2^232820+5	70087	Lelio R Paula	04/2014
7169	2^232799+90195	70080	Lelio R Paula	02/2013
7168	2^232799-112237	70080	Enzo Doria	06/2014
7170	2^232759+262145	70068	Lelio R Paula	04/2012
7171	3*2^232750+7	70066	Lelio R Paula	04/2014
7172	12^64918-11	70059	Lelio R Paula	01/2015
7173	7^82899-12	70058	Lelio R Paula	09/2013
7174	(22*10^70051-13)/9	70052	Robert Price	03/2015
7175	(2^232685-7)/2514625	70039	Lelio R Paula	04/2012
7176	18^55786-5363	70027	Enzo Doria	03/2013
7177	(2^(77537*3+1)+243)/7	70023	Kevin Acres	11/2013
7178	2^232602+169	70021	Lelio R Paula	02/2012
7179	(137^32768+29^32768)/2	70016	Jeppe Stig Nielsen	04/2018
7180	2^232580+72133	70014	Enzo Doria	04/2016
7181	4*6^89958-7	70002	Lelio R Paula	09/2014
7182	10^70000+80487	70001	Milton L. Brown	05/2006
7183	10^69999+134857	70000	Patrick De Geest	02/2007
7188	10^70000-9273	70000	Patrick De Geest	08/2009
7187	(79*10^69999-7)/9	70000	Robert Price	01/2015
7184	((2^43112609)/10^38420)%10^70000	70000	Michael Vang	10/2016
7185	(2^756839/10^36014)%10^70000	70000	Michael Vang	12/2016
7186	(2^74207281/10^32641)%10^70000	70000	Michael Vang	12/2016
7189	10^69999-88251	69999	Patrick De Geest	08/2009
7190	2^232507+1089	69992	Lelio R Paula	04/2012
7191	(17*2^232445+1)/5	69974	Lelio R Paula	08/2012
7192	(529^25693+1)/530	69972	Richard Fischer	12/2017
7193	7^82778+48	69956	Lelio R Paula	09/2013
7194	7*2^232381+3	69955	Lelio R Paula	04/2014
7195	2^232362-110541	69948	Enzo Doria	05/2014
7196	2^232326-112391	69938	Enzo Doria	06/2014
7197	3^146575+236	69935	Lelio R Paula	09/2013
7198	30^47341-29	69929	Norbert Schneider	02/2014
7199	5^100040-68	69925	Lelio R Paula	09/2013
7200	(35*10^69866-593)/9	69867	Robert Price	08/2017
7201	2^232045-17295	69853	Lelio R Paula	04/2012
7202	(2^231987+78557)/95	69834	Lelio R Paula	05/2012
7203	2^231955+74243	69826	Yves Minet	03/2011
7204	2^231946-15873	69823	Enzo Doria	04/2013
7205	18^55618+95	69816	Lelio R Paula	09/2013
7206	6^89712+5^(89712-1)	69810	Robert Price	02/2016
7207	2^231870+135	69800	Lelio R Paula	02/2012
7208	(23*2^231827-1)/4179	69785	Lelio R Paula	01/2014
7209	2^231778+54615	69773	Lelio R Paula	04/2012
7210	(19*2^231780+1)/235	69772	Lelio R Paula	08/2012
7211	14^60866+27	69761	Lelio R Paula	09/2013
7212	13^62619-44	69755	Lelio R Paula	09/2013
7213	(2^231715-509203)/35	69752	Lelio R Paula	05/2012
7214	2^231711-110467	69752	Enzo Doria	05/2014
7215	(19^54547+18^54547)/37	69751	Robert Price	08/2013
7216	(23*2^231697-1)/45	69748	Lelio R Paula	01/2014
7217	2^231696-1861499	69748	Enzo Doria	03/2016
7218	2^231684-147	69744	Lelio R Paula	02/2012
7219	(23*2^231686-1)/1183	69743	Lelio R Paula	01/2014
7220	2^231591-477397	69716	Paul Bourdelais	03/2013
7221	11^66916-420	69686	Enzo Doria	08/2012
7222	5^99680-13706	69674	Enzo Doria	02/2013
7223	(8*10^69674-53)/9	69674	Robert Price	11/2014
7224	(44*10^69663-413)/9	69664	Robert Price	10/2017
7225	(77*10^69656-23)/9	69657	Robert Price	10/2015
7226	6^89509+131	69652	Lelio R Paula	09/2013
7227	(78557*2^231349+1)/35	69647	Lelio R Paula	06/2014
7228	(11*10^69645+19)/3	69646	Robert Price	03/2016
7229	11^66875-28	69644	Lelio R Paula	09/2013
7230	2^231347+71483	69643	Enzo Doria	04/2016
7231	(14^60763+3^60763)/17	69641	Robert Price	04/2013
7232	(4*10^69626+173)/3	69627	Robert Price	01/2017
7233	2^231289+255	69625	Lelio R Paula	04/2012
7234	2^231234-112913	69609	Enzo Doria	06/2014
7235	(265*10^69602-7)/3	69604	Robert Price	07/2016
7236	2^231182-112841	69593	Enzo Doria	06/2014
7237	(15*2^231129+1)/23	69577	Lelio R Paula	08/2012
7238	3^145806-28	69568	Lelio R Paula	09/2013
7239	(265*10^69554-7)/3	69556	Robert Price	07/2016
7240	2^231052-113159	69554	Enzo Doria	07/2014
7241	(10^9+1)(10^129+1)(10^831+1)*(10^107199+1)/1001/(10^387+1)/(10^2493+1)/(10^35733+1)	69552	Makoto Kamada	03/2019
7242	11^66784-8	69549	Lelio R Paula	09/2013
7243	Phi(104409,10)/2296999	69546	Maksym Voznyy	07/2015
7244	2^231016-110523	69543	Enzo Doria	05/2014
7245	2^231014+577294575	69543	Lelio R Paula	02/2016
7246	14^60658+67	69522	Lelio R Paula	09/2013
7247	5^99418+36	69491	Lelio R Paula	06/2013
7248	7^82203-30	69470	Lelio R Paula	09/2013
7249	(63^38609-1)/62	69469	Paul Bourdelais	08/2017
7250	5^99359-2^99360	69449	Mike Oakes	12/2010

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PRP Records

Probable Primes Top 10000

(252932 PRPs in the top)