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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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	(3*2^234451+1)/35	70576	Lelio R Paula	08/2012
7002	Phi(159495,10)	70560	Maksym Voznyy	09/2015
7003	2^234383-4035	70557	Lelio R Paula	05/2012
7004	2^234315-111241	70536	Enzo Doria	05/2014
7005	14^61526+97	70517	Lelio R Paula	01/2015
7006	(3*2^234170+1)/13	70492	Lelio R Paula	08/2012
7007	51^41281-50^41281	70491	Robert Price	02/2013
7008	2^234141-112123	70484	Enzo Doria	06/2014
7009	2^234139+12285	70483	Lelio R Paula	04/2012
7010	2^234133-3163	70482	Yves Minet	04/2009
7011	2^234115+83	70476	Lelio R Paula	02/2012
7012	2^234114-1595	70476	Lelio R Paula	05/2012
7013	24^51061-23^51061	70475	Robert Price	07/2012
7014	19471^16428-2	70467	Faysal YAtim	09/2005
7015	7^83381+12	70466	Robert Price	01/2014
7016	2^234067-111427	70462	Enzo Doria	05/2014
7017	(266*10^70457+1)/3	70459	Robert Price	02/2016
7018	(31*2^234041-1)/97	70453	Lelio R Paula	01/2014
7019	2^234026+12909	70449	Lelio R Paula	04/2012
7020	2^233965-19	70431	Lelio R Paula	02/2012
7021	(5*2^233932-1)/179	70419	Lelio R Paula	01/2014
7022	2^233908-17109	70414	Enzo Doria	05/2013
7023	695^24772+24772^695	70402	Norbert Schneider	09/2016
7024	3*5^100719-2	70401	Lelio R Paula	10/2014
7025	2^233829-111355	70390	Enzo Doria	05/2014
7026	(19775^16384+1)/2	70388	Henri Lifchitz	03/2007
7027	7*3^147519+8	70386	Lelio R Paula	04/2014
7028	141^32749-2	70385	Lelio R Paula	10/2017
7029	5*7^83265+2	70368	Lelio R Paula	10/2014
7030	(23*10^70363+97)/3	70364	Robert Price	02/2017
7031	(23*2^233749-1)/35325	70363	Lelio R Paula	01/2014
7033	5^100652-13916	70353	Enzo Doria	02/2013
7032	45^42555-2	70353	Lelio R Paula	08/2013
7034	2^233661-61	70339	Lelio R Paula	02/2012
7035	2^233523-112249	70298	Enzo Doria	06/2014
7036	5*3^147324-8	70293	Lelio R Paula	04/2014
7037	2^233488-13065	70287	Enzo Doria	11/2012
7038	(3^147322+8)/42851	70286	Lelio R Paula	06/2012
7039	(22*10^70259+161)/3	70260	Robert Price	02/2017
7040	2^233388+465	70257	Lelio R Paula	11/2012
7041	14^61299+59	70257	Lelio R Paula	01/2015
7042	2^233383+94065	70256	Lelio R Paula	04/2012
7043	49471!3-6561	70253	Robert Price	11/2015
7044	7^83121+6^(83121-1)	70246	Robert Price	03/2016
7045	(197*10^70241-11)/3	70243	Robert Price	10/2017
7046	23*10^70240-7	70242	Robert Price	03/2016
7047	(71*10^70227-53)/9	70228	Robert Price	10/2015
7048	(2^233247-9)/17	70214	Lelio R Paula	05/2012
7049	(11^67421-2^67421)/9	70211	Robert Price	01/2013
7050	(23*10^70209-41)/9	70210	Robert Price	03/2015
7051	(29*10^70194-11)/9	70195	Robert Price	04/2015
7052	3^147109+196	70189	Lelio R Paula	05/2014
7053	(34*10^70191-7)/9/3/40583/573047	70181	Makoto Morimoto	05/2016
7054	9^73538+8^(73538+1)	70174	Robert Price	06/2016
7055	2*5^100391+7	70171	Lelio R Paula	10/2014
7056	99^35156-2	70159	Lelio R Paula	08/2013
7057	(68*10^70148+7)/3	70150	Robert Price	03/2016
7058	11^67360-6030	70149	Enzo Doria	01/2013
7059	(35*10^70130-377)/9	70131	Robert Price	12/2017
7060	49391!3+3^49391	70128	Robert Price	09/2015
7061	(229*10^70122-1)/3	70124	Robert Price	12/2016
7062	7^82975-92	70123	Lelio R Paula	07/2014
7063	65^38670+58	70106	Lelio R Paula	01/2016
7064	105^34684+34684^105	70103	Serge Batalov	05/2014
7065	134^32955-133	70099	Norbert Schneider	03/2015
7067	2^232836-227903	70091	Enzo Doria	12/2012
7066	2^232837-1859173	70091	Enzo Doria	03/2016
7068	3*2^232820+5	70087	Lelio R Paula	04/2014
7070	2^232799+90195	70080	Lelio R Paula	02/2013
7069	2^232799-112237	70080	Enzo Doria	06/2014
7071	2^232759+262145	70068	Lelio R Paula	04/2012
7072	3*2^232750+7	70066	Lelio R Paula	04/2014
7073	12^64918-11	70059	Lelio R Paula	01/2015
7074	7^82899-12	70058	Lelio R Paula	09/2013
7075	(22*10^70051-13)/9	70052	Robert Price	03/2015
7076	(2^232685-7)/2514625	70039	Lelio R Paula	04/2012
7077	18^55786-5363	70027	Enzo Doria	03/2013
7078	(2^(77537*3+1)+243)/7	70023	Kevin Acres	11/2013
7079	2^232602+169	70021	Lelio R Paula	02/2012
7080	(137^32768+29^32768)/2	70016	Jeppe Stig Nielsen	04/2018
7081	2^232580+72133	70014	Enzo Doria	04/2016
7082	4*6^89958-7	70002	Lelio R Paula	09/2014
7083	10^70000+80487	70001	Milton L. Brown	05/2006
7084	10^69999+134857	70000	Patrick De Geest	02/2007
7089	10^70000-9273	70000	Patrick De Geest	08/2009
7088	(79*10^69999-7)/9	70000	Robert Price	01/2015
7085	((2^43112609)/10^38420)%10^70000	70000	Michael Vang	10/2016
7086	(2^756839/10^36014)%10^70000	70000	Michael Vang	12/2016
7087	(2^74207281/10^32641)%10^70000	70000	Michael Vang	12/2016
7090	10^69999-88251	69999	Patrick De Geest	08/2009
7091	2^232507+1089	69992	Lelio R Paula	04/2012
7092	(17*2^232445+1)/5	69974	Lelio R Paula	08/2012
7093	(529^25693+1)/530	69972	Richard Fischer	12/2017
7094	7^82778+48	69956	Lelio R Paula	09/2013
7095	7*2^232381+3	69955	Lelio R Paula	04/2014
7096	2^232362-110541	69948	Enzo Doria	05/2014
7097	2^232326-112391	69938	Enzo Doria	06/2014
7098	3^146575+236	69935	Lelio R Paula	09/2013
7099	30^47341-29	69929	Norbert Schneider	02/2014
7100	5^100040-68	69925	Lelio R Paula	09/2013
7101	(35*10^69866-593)/9	69867	Robert Price	08/2017
7102	2^232045-17295	69853	Lelio R Paula	04/2012
7103	(2^231987+78557)/95	69834	Lelio R Paula	05/2012
7104	2^231955+74243	69826	Yves Minet	03/2011
7105	2^231946-15873	69823	Enzo Doria	04/2013
7106	18^55618+95	69816	Lelio R Paula	09/2013
7107	6^89712+5^(89712-1)	69810	Robert Price	02/2016
7108	2^231870+135	69800	Lelio R Paula	02/2012
7109	(23*2^231827-1)/4179	69785	Lelio R Paula	01/2014
7110	2^231778+54615	69773	Lelio R Paula	04/2012
7111	(19*2^231780+1)/235	69772	Lelio R Paula	08/2012
7112	14^60866+27	69761	Lelio R Paula	09/2013
7113	13^62619-44	69755	Lelio R Paula	09/2013
7114	(2^231715-509203)/35	69752	Lelio R Paula	05/2012
7115	2^231711-110467	69752	Enzo Doria	05/2014
7116	(19^54547+18^54547)/37	69751	Robert Price	08/2013
7117	(23*2^231697-1)/45	69748	Lelio R Paula	01/2014
7118	2^231696-1861499	69748	Enzo Doria	03/2016
7119	2^231684-147	69744	Lelio R Paula	02/2012
7120	(23*2^231686-1)/1183	69743	Lelio R Paula	01/2014
7121	2^231591-477397	69716	Paul Bourdelais	03/2013
7122	11^66916-420	69686	Enzo Doria	08/2012
7123	5^99680-13706	69674	Enzo Doria	02/2013
7124	(8*10^69674-53)/9	69674	Robert Price	11/2014
7125	(44*10^69663-413)/9	69664	Robert Price	10/2017
7126	(77*10^69656-23)/9	69657	Robert Price	10/2015
7127	6^89509+131	69652	Lelio R Paula	09/2013
7128	(78557*2^231349+1)/35	69647	Lelio R Paula	06/2014
7129	(11*10^69645+19)/3	69646	Robert Price	03/2016
7130	11^66875-28	69644	Lelio R Paula	09/2013
7131	2^231347+71483	69643	Enzo Doria	04/2016
7132	(14^60763+3^60763)/17	69641	Robert Price	04/2013
7133	(4*10^69626+173)/3	69627	Robert Price	01/2017
7134	2^231289+255	69625	Lelio R Paula	04/2012
7135	2^231234-112913	69609	Enzo Doria	06/2014
7136	(265*10^69602-7)/3	69604	Robert Price	07/2016
7137	2^231182-112841	69593	Enzo Doria	06/2014
7138	(15*2^231129+1)/23	69577	Lelio R Paula	08/2012
7139	3^145806-28	69568	Lelio R Paula	09/2013
7140	(265*10^69554-7)/3	69556	Robert Price	07/2016
7141	2^231052-113159	69554	Enzo Doria	07/2014
7142	(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
7143	11^66784-8	69549	Lelio R Paula	09/2013
7144	Phi(104409,10)/2296999	69546	Maksym Voznyy	07/2015
7145	2^231016-110523	69543	Enzo Doria	05/2014
7146	2^231014+577294575	69543	Lelio R Paula	02/2016
7147	14^60658+67	69522	Lelio R Paula	09/2013
7148	5^99418+36	69491	Lelio R Paula	06/2013
7149	7^82203-30	69470	Lelio R Paula	09/2013
7150	(63^38609-1)/62	69469	Paul Bourdelais	08/2017
7151	5^99359-2^99360	69449	Mike Oakes	12/2010
7152	(29*2^230684+1)/1395	69442	Lelio R Paula	08/2012
7153	(19*10^69424+77)/3	69425	Robert Price	08/2016
7154	19^54287-96	69420	Lelio R Paula	09/2013
7155	2^230541+58905	69400	Lelio R Paula	04/2012
7156	2^230506+12705	69390	Lelio R Paula	02/2013
7157	8*6^89156-5	69378	Lelio R Paula	09/2014
7158	2^230438-111347	69369	Enzo Doria	05/2014
7159	2^230428-99	69366	Lelio R Paula	02/2012
7160	(62^38699+1)/63	69362	Paul Bourdelais	08/2017
7161	3*10^69354+17	69355	Robert Price	03/2017
7162	(493*10^69340-7)/9	69342	Robert Price	07/2016
7163	(41*10^69321+373)/9	69322	Robert Price	04/2017
7164	6^89072+53	69312	Lelio R Paula	09/2013
7165	155^31639+2	69300	Lelio R Paula	05/2013
7166	3*7^81965-4	69269	Lelio R Paula	09/2014
7167	(16*10^69265+41)/3	69266	Robert Price	10/2017
7168	(86*10^69260-77)/9	69261	Robert Price	05/2016
7169	9*5^99087+4	69260	Lelio R Paula	09/2014
7170	3^145145+2660	69252	Lelio R Paula	09/2013
7172	11^66492-1140	69245	Enzo Doria	11/2012
7171	5*3^145129-4	69245	Lelio R Paula	04/2014
7173	7*3^145126+8	69244	Lelio R Paula	04/2014
7174	11^66480-2370	69232	Enzo Doria	12/2012
7175	2^229962-65	69226	Lelio R Paula	02/2012
7176	2^229958-110733	69225	Enzo Doria	05/2014
7177	V(332407)	69225	Serge Batalov	03/2015
7178	6^88959+7	69224	Lelio R Paula	09/2013
7179	15^58855-94	69219	Lelio R Paula	09/2013
7180	159773#-p(159773)	69212	Henri Lifchitz	12/2018
7181	(2^229838+47)/12081	69185	Lelio R Paula	04/2012
7182	3^144952+98	69160	Lelio R Paula	09/2013
7183	5^98941-72	69157	Lelio R Paula	06/2013
7184	(17*2^229604-1)/229	69117	Lelio R Paula	01/2014
7185	2^229585-1063	69112	Yves Minet	11/2012
7186	(13*2^229567-1)/19	69107	Lelio R Paula	01/2014
7187	(13*2^229393-1)/5	69055	Lelio R Paula	01/2014
7188	(53*10^69050-17)/9	69051	Robert Price	09/2015
7189	(43*10^69048+47)/9	69049	Robert Price	12/2017
7190	2^229305-1868533	69028	Enzo Doria	04/2016
7191	2^229297+1385	69026	Lelio R Paula	04/2012
7192	18^54986-2441	69023	Enzo Doria	03/2013
7193	(34*10^69021-7)/9/3/67	69020	Makoto Morimoto	04/2016
7194	5^98736-14636	69014	Enzo Doria	02/2013
7195	(13^61949-5^61949)/8	69007	Robert Price	03/2013
7196	(2^229227+5)/611	69002	Lelio R Paula	04/2012
7197	2^229216-113279	69001	Enzo Doria	07/2014
7198	10^68994+51913	68995	Patrick De Geest	03/2016
7200	10^68994-10^5814-1	68994	Serge Batalov	01/2011
7199	10^68994-82947	68994	Patrick De Geest	03/2016
7201	(17*2^229136-1)/2381	68975	Lelio R Paula	01/2014
7202	2^229113+107	68970	Lelio R Paula	02/2012
7203	11^66202-4410	68943	Enzo Doria	01/2013
7204	12^63883+5	68942	Lelio R Paula	07/2013
7205	(9913*2^229002-1)/399903	68935	Lelio R Paula	04/2015
7206	2^228962-111581	68925	Enzo Doria	05/2014
7207	2^228944+81	68920	Henri Lifchitz	01/2007
7208	11^66174-54	68914	Lelio R Paula	09/2013
7209	2^228913-111265	68910	Enzo Doria	05/2014
7210	2^228902+73519	68907	Enzo Doria	04/2016
7211	(47*2^228884+1)/63	68901	Lelio R Paula	04/2015
7212	2^228821+76427	68882	Enzo Doria	05/2016
7213	3^144340+50	68868	Lelio R Paula	09/2013
7214	2^228758-112967	68864	Enzo Doria	06/2014
7215	2^228743-111379	68859	Enzo Doria	05/2014
7216	2^228741-110911	68858	Enzo Doria	05/2014
7218	lucasU(1926,1,20964)-lucasU(1926,1,20963)	68857	Mike Oakes	05/2009
7217	3*5^98511-8	68857	Lelio R Paula	09/2014
7219	2^228717+467	68851	Lelio R Paula	02/2011
7220	Phi(153218,10)/2211855049/23592660859/497714117291	68849	Maksym Voznyy	10/2011
7221	(509203*2^228665-1)/35	68840	Lelio R Paula	04/2015
7222	8^76213-7^76213	68828	Ananda Tallur & Jean-Louis Charton	11/2003
7223	11^66074-1050	68809	Enzo Doria	11/2012
7224	(68*10^68798-11)/3	68800	Robert Price	10/2017
7225	2^228484+181	68781	Lelio R Paula	02/2012
7226	2^228479-58695	68780	Lelio R Paula	04/2012
7227	2^228465-15853	68775	Enzo Doria	04/2013
7228	11^66040-5400	68774	Enzo Doria	01/2013
7229	(13*2^228441-1)/575	68766	Lelio R Paula	01/2014
7230	(17*2^228393+1)/295	68752	Lelio R Paula	08/2012
7231	2*10^68744+41	68745	Robert Price	01/2017
7232	11^66011-150	68744	Enzo Doria	08/2012
7233	(13*2^228304-1)/81	68726	Lelio R Paula	01/2014
7234	2^228295-111079	68724	Enzo Doria	05/2014
7236	(3^144039+7)/22	68723	Lelio R Paula	04/2012
7235	(8*10^68722+49)/3	68723	Robert Price	03/2016
7237	(35*10^68718+1)/9	68719	Serge Batalov	11/2010
7238	2^228271-228271	68717	Henri Lifchitz	11/2004
7239	2^228257+82875	68713	Lelio R Paula	02/2013
7240	3^144013+40	68712	Lelio R Paula	09/2013
7241	13^61671-86	68699	Lelio R Paula	09/2013
7242	(46*10^68698+683)/9	68699	Robert Price	12/2017
7243	17^55828-72	68694	Lelio R Paula	09/2013
7244	6^88259+61	68679	Lelio R Paula	09/2013
7245	18^54699-5	68663	Lelio R Paula	09/2013
7246	33^45216+2	68662	Lelio R Paula	05/2013
7248	(2^228073-5)/3	68657	Lelio R Paula	04/2012
7247	(2^(6*38012+1)-5)/3	68657	Kevin Acres	11/2013
7249	2^228055-111607	68652	Enzo Doria	05/2014
7250	2^228054-114761	68652	Enzo Doria	05/2015

Find by discoverer :

PRP Records

Probable Primes Top 10000

(252675 PRPs in the top)