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 ?
7001	2^225609-18445	67916	Enzo Doria	05/2013
7002	2^225542-177	67895	Lelio R Paula	02/2012
7003	2^225536-29	67894	Henri Lifchitz	05/2005
7004	11^65190-3390	67889	Enzo Doria	12/2012
7005	3^142249-2^(142249-1)	67871	Robert Price	01/2016
7006	11^65168-4830	67866	Enzo Doria	01/2013
7007	10^67863+58627	67864	Patrick De Geest	01/2016
7008	10^67863-11	67863	Robert Price	05/2011
7009	(1!)^2+(2!)^2+(3!)^2+...+(9566!)^2	67856	T. D. Noe	02/2006
7010	(19*2^225357-1)/11	67840	Lelio R Paula	01/2014
7011	9*6^87164-7	67828	Lelio R Paula	09/2014
7012	131^32034+130	67825	Norbert Schneider	03/2015
7013	(29*2^225314+1)/10881	67824	Lelio R Paula	08/2012
7014	(134*10^67816+7)/3	67818	Robert Price	02/2017
7015	2^225261+855	67811	Lelio R Paula	04/2012
7016	(29*2^225252-1)/2933	67806	Lelio R Paula	01/2014
7017	(4*10^67796+23)/9	67796	Robert Price	11/2014
7018	15477^16180-16180^15477	67790	Norbert Schneider	09/2018
7019	(23*2^225177+1)/31	67785	Lelio R Paula	08/2012
7020	(4*10^67784+149)/9	67784	Robert Price	03/2017
7021	2^225120+151	67768	Lelio R Paula	02/2012
7022	(44^41233+1)/45	67763	Robert Price	11/2013
7023	89933!6-16	67747	Robert Price	08/2018
7024	8*10^67742+9	67743	Dmitry Domanov	11/2010
7025	2^224977+1089	67725	Lelio R Paula	04/2012
7026	(2^224950+5)/19509	67713	Lelio R Paula	04/2012
7027	11^65011-5970	67702	Enzo Doria	01/2013
7028	88*10^67691+7	67693	Robert Price	11/2016
7029	11^65000-7140	67691	Enzo Doria	01/2013
7030	2^224841+59	67684	Lelio R Paula	02/2012
7031	33129!2+2^33129	67684	Robert Price	09/2015
7032	2^224827+8415	67680	Lelio R Paula	02/2013
7033	(9913*2^224821-1)/19825	67678	Lelio R Paula	04/2015
7034	2^224815-49789	67677	Henri Lifchitz	04/2005
7035	(43*10^67664+11)/9	67665	Robert Price	06/2015
7036	(292*10^67659-1)/3	67661	Robert Price	01/2017
7037	(17*2^224766+1)/29007	67659	Lelio R Paula	06/2012
7038	2^224744+577294575	67655	Lelio R Paula	02/2016
7039	((1+sqrt(7)+sqrt(6))^45863-1)((1+sqrt(7)-sqrt(6))^45863-1)((1-sqrt(7)+sqrt(6))^45863-1)*((1-sqrt(7	67653	Mike Oakes	05/2009
7040	(2^224721+78557)/1739	67645	Lelio R Paula	05/2012
7041	2^224700+1915	67642	Lelio R Paula	04/2012
7042	(29*2^224694-1)/198905	67636	Lelio R Paula	01/2014
7043	2^224658-93	67629	Lelio R Paula	02/2012
7044	2^224624-13077	67619	Enzo Doria	10/2012
7045	18^53860-3319	67609	Enzo Doria	03/2013
7047	(21181*2^224570+1)/5	67606	Lelio R Paula	06/2014
7046	89762!6-3	67606	Robert Price	08/2018
7048	2^224578-111041	67605	Enzo Doria	05/2014
7049	2^224569-113233	67603	Enzo Doria	07/2014
7050	2^224562-113171	67600	Enzo Doria	07/2014
7051	2^224556-113129	67599	Enzo Doria	07/2014
7052	6*7^79980-5	67592	Lelio R Paula	09/2014
7053	(6883*2^224523-1)/16031	67588	Lelio R Paula	04/2015
7054	10^67579+164779	67580	Patrick De Geest	07/2017
7056	(52*10^67578-61)/9	67579	Robert Price	09/2015
7055	10^67579-401	67579	Robert Price	06/2017
7057	(17^54919-1)/16	67574	Paul Bourdelais	03/2010
7058	(2^224363-9)/1951	67537	Lelio R Paula	04/2012
7059	(709*10^67517-7)/9	67519	Robert Price	09/2017
7060	47719!3-59049	67516	Robert Price	12/2015
7061	(22^50287+1)/23	67506	Robert Price	06/2013
7062	3*10^67499+67	67500	Robert Price	11/2017
7063	11^64811-5820	67494	Enzo Doria	01/2013
7064	131^31870+31870^131	67478	Serge Batalov	05/2014
7065	9*10^67468+7	67469	Dmitry Domanov	11/2010
7066	(31*2^224115-1)/47723	67463	Lelio R Paula	01/2014
7067	128^32001+32001^128	67433	Serge Batalov	05/2014
7068	(89*10^67431-17)/9	67432	Robert Price	11/2015
7069	2^223912-111059	67405	Enzo Doria	05/2014
7071	2^223913+73697	67405	Enzo Doria	04/2016
7070	(2*10^67405-23)/3	67405	Robert Price	09/2017
7072	(10^67404+179)/9	67404	Serge Batalov	12/2014
7073	18738^3955+3955^18738	67404	Hans Havermann	09/2016
7074	9*7^79728-2	67379	Lelio R Paula	09/2014
7075	(28*10^67378-43)/3	67379	Robert Price	04/2016
7076	(3^141234-7)/430241282	67378	Lelio R Paula	04/2012
7077	211^28988-2	67377	Lelio R Paula	09/2013
7078	4*10^67375+91	67376	Robert Price	11/2017
7079	2^223793-18069	67369	Enzo Doria	05/2013
7080	2^223777-2521	67364	Yves Minet	07/2014
7081	(15185*2^223775-1)/15183	67363	Lelio R Paula	04/2015
7082	(2^223759-lucasV(1,2,223759)+1)/2	67358	Mike Oakes	11/2016
7083	V(340138)	67336	Serge Batalov	03/2015
7084	43125^14528-106	67334	Enzo Doria	07/2012
7085	15275^16086-16086^15275	67304	Norbert Schneider	09/2018
7086	8*10^67302-51	67303	Robert Price	10/2017
7087	17458^7153+7153^17458	67292	Hans Havermann	08/2016
7088	16366^12925+12925^16366	67288	Hans Havermann	08/2016
7089	37^42906-2	67286	Lelio R Paula	08/2013
7090	18^53592-13	67273	Lelio R Paula	08/2013
7091	V(396221)	67256	Serge Batalov	03/2015
7093	(34*10^67245-7)/9/3^4/193/1381537	67236	Makoto Morimoto	04/2016
7092	(14*10^67235-101)/3	67236	Robert Price	04/2017
7094	53^38993-52^38993	67235	Robert Price	01/2013
7095	(2^223349-7)/6485	67231	Lelio R Paula	04/2012
7096	2^223333+315	67230	Lelio R Paula	04/2012
7097	2^223278-111041	67214	Enzo Doria	05/2014
7098	(23472^223281+1)/(351971213*1783)	67208	Jens K. Andersen	09/2007
7099	2^223256-45	67207	Lelio R Paula	02/2012
7100	2^223253-112111	67206	Enzo Doria	06/2014
7101	18407^4474+4474^18407	67199	Hans Havermann	08/2016
7102	47^40182+40182^47	67189	Norbert Schneider	11/2014
7103	13^60309+94	67181	Lelio R Paula	07/2013
7104	11^64503-84	67173	Lelio R Paula	07/2013
7105	3^140781+236	67170	Lelio R Paula	06/2013
7106	2^223107-865057	67162	Paul Bourdelais	03/2013
7107	2^223100-59	67160	Lelio R Paula	02/2012
7108	2^223087+71963	67156	Enzo Doria	04/2016
7109	18^53481-3779	67134	Enzo Doria	03/2013
7110	(326^26713-1)/325	67134	Eric Chen	09/2017
7111	4^111473-62573	67114	Mike Oakes	02/2011
7112	2^222943+29	67113	Henri Lifchitz	08/2005
7113	(2^222939-9)/103	67110	Lelio R Paula	04/2012
7114	2^222862-459161	67089	Enzo Doria	05/2015
7115	2^222828+8193	67078	Lelio R Paula	04/2012
7116	3^140570+2660	67069	Lelio R Paula	06/2013
7117	2^222744+855	67053	Lelio R Paula	04/2012
7118	13^60189+84	67048	Lelio R Paula	07/2013
7119	2*10^67043-51	67044	Robert Price	11/2017
7120	2^222701+577294575	67040	Lelio R Paula	02/2016
7121	(13*10^67038-31)/9	67039	Serge Batalov	11/2008
7122	(151*10^67027-7)/9	67029	Robert Price	07/2017
7123	(58695*2^222620-1)/61	67019	Lelio R Paula	04/2015
7124	2^222614-111041	67014	Enzo Doria	05/2014
7125	118^32333-117	66991	Norbert Schneider	08/2018
7126	2^222520-1907	66986	Yves Minet	03/2013
7127	(4^111231+23)/3	66968	Robert Price	02/2017
7128	2^222408-111275	66952	Enzo Doria	05/2014
7129	10^66949-9^66949	66949	Jean-Louis Charton	12/2005
7130	2^222378-1005	66943	Lelio R Paula	04/2012
7131	(9*2^222366+1)/73	66938	Lelio R Paula	08/2012
7132	7^79202-6^(79202+1)	66934	Robert Price	06/2016
7133	2^222325-112255	66927	Enzo Doria	06/2014
7134	20^51428+33	66910	Lelio R Paula	08/2013
7135	2^222224-18509	66897	Enzo Doria	05/2013
7136	(38*10^66896+187)/9	66897	Robert Price	11/2017
7137	2^222192-869688105	66887	Lelio R Paula	02/2016
7138	(19*10^66878-43)/3	66879	Robert Price	10/2017
7139	11^64219-64	66878	Lelio R Paula	07/2013
7140	2^222151-17295	66875	Lelio R Paula	04/2012
7141	gcd(V(799885),5F(159977)(F(159977)+1)+1)	66867	Serge Batalov	04/2015
7142	2^222085-111031	66855	Enzo Doria	05/2014
7143	8*10^66848-13	66849	Robert Price	05/2017
7144	(3^140087+4)/13	66838	Lelio R Paula	04/2012
7145	(3^140102+4)/8843609437	66836	Lelio R Paula	04/2012
7146	19^52265+52	66835	Lelio R Paula	08/2013
7147	2*10^66826-27	66827	Robert Price	02/2017
7148	4*6^85867+5	66819	Lelio R Paula	09/2014
7149	15^56800+8	66802	Lelio R Paula	08/2013
7150	(2^221891-2^110946+1)/5	66796		11/2006
7151	10^66793+69441	66794	Patrick De Geest	05/2013
7152	10^66793-63	66793	Robert Price	05/2011
7153	35^43256-1704	66791	Enzo Doria	03/2013
7154	3^139976+2^(139976-1)	66786	Robert Price	05/2016
7155	88769!6-48	66786	Robert Price	08/2018
7156	7^79023-54	66783	Lelio R Paula	06/2013
7157	104^33109-103	66782	Norbert Schneider	11/2016
7158	(34*10^66778-7)/9/37/358901	66772	Makoto Morimoto	04/2016
7159	(-lucasV(1,2,443622)+2)/(7281487)	66766	Mike Oakes	04/2017
7161	2^221768+183	66759	Lelio R Paula	02/2012
7160	gcd(V(1197915),5F(239583)(F(239583)+1)+1)	66759	Serge Batalov	04/2015
7162	(154*10^66755-1)/9	66757	Serge Batalov	12/2014
7163	11^64097+48	66751	Lelio R Paula	07/2013
7164	(lucasV(1,2,443547)-2)/(713791327221773)	66749	Mike Oakes	04/2017
7165	(19*10^66748+413)/9	66749	Robert Price	10/2017
7166	(3*2^221696-1)/13	66737	Lelio R Paula	01/2014
7167	8*6^85758-7	66734	Lelio R Paula	09/2014
7168	135^31325+2	66733	Lelio R Paula	05/2013
7169	(49*10^66729+41)/9	66730	Robert Price	07/2015
7170	(349*10^66720-7)/9	66722	Robert Price	03/2017
7171	(-lucasV(1,2,443285)+2)/(3^2*307)	66718	Mike Oakes	04/2017
7172	(25*10^66714+71)/3	66715	Robert Price	01/2017
7173	11^64061-780	66713	Enzo Doria	11/2012
7174	7^78929+4	66703	Lelio R Paula	06/2013
7175	11^64048-930	66700	Enzo Doria	11/2012
7176	120^32079-119	66699	Norbert Schneider	09/2018
7177	2*7^78921+5	66697	Lelio R Paula	09/2014
7178	(25*2^221526+1)/409	66685	Lelio R Paula	08/2012
7179	(2^221509-1)/292391881	66673	Jens K. Andersen	02/2009
7180	2^221479+72953	66672	Enzo Doria	04/2016
7181	10^66666+275403	66667	Patrick De Geest	03/2010
7182	10^66666-115521	66666	Patrick De Geest	03/2010
7183	(18*10^66657-81)/99	66657	Ray Chandler	01/2011
7184	4*10^66653+21	66654	Robert Price	08/2016
7185	(10^66650+149)/3	66650	Serge Batalov	12/2014
7186	9^69842+38^69842-24^69842-3*2^69842	66647	Mike Oakes	12/2010
7187	2^221391-2145	66646	Lelio R Paula	04/2012
7188	(5*10^66613-119)/3	66614	Robert Price	04/2016
7189	2^221273-113233	66610	Enzo Doria	07/2014
7190	3^139571-46	66593	Lelio R Paula	06/2013
7191	(410^(233295)-2*(10^33295)+1)/3	66591	Robert Price	04/2018
7192	2^221181-869688105	66583	Lelio R Paula	02/2016
7193	(61*10^66575-7)/9	66576	Ray Chandler	02/2012
7194	2^221126+133	66566	Lelio R Paula	02/2012
7196	12^61680+91	66564	Lelio R Paula	07/2013
7195	(lucasV(1,2,442258)+2)/103	66564	Mike Oakes	04/2017
7197	(13*10^66551-73)/3	66552	Robert Price	12/2016
7198	11^63901-1590	66547	Enzo Doria	12/2012
7199	11^63901-1500	66547	Enzo Doria	12/2012
7200	6^85517+23	66546	Lelio R Paula	07/2013
7201	17^54069-40	66530	Lelio R Paula	08/2013
7202	(2^110503+4725)^2+(2^110503+4725)+41	66530	Makoto Morimoto	05/2016
7203	(2^110503+8099)^2+(2^110503+8099)+41	66530	Makoto Morimoto	05/2016
7205	(2^221008-1017)/78533	66526	Lelio R Paula	04/2012
7204	3^139432+26	66526	Lelio R Paula	06/2013
7206	((2^110503+5139)^2+(2^110503+5139)+41)/20865797	66523	Makoto Morimoto	05/2016
7207	((2^110503+6647)^2+(2^110503+6647)+41)/197/17327	66523	Makoto Morimoto	05/2016
7208	6^85481+85481	66518	Henri Lifchitz	08/2014
7209	(9179*2^220913-1)/399	66503	Lelio R Paula	04/2015
7210	13^59687+66	66488	Lelio R Paula	07/2013
7211	(49*10^66485-31)/9	66486	Robert Price	07/2015
7212	(46*10^66469+17)/9	66470	Robert Price	06/2015
7213	2^220790+97	66465	Lelio R Paula	02/2012
7214	(23*2^220790+1)/807	66463	Lelio R Paula	06/2012
7215	40009^14441-102	66460	Enzo Doria	07/2012
7216	2^220736-143	66449	Lelio R Paula	02/2012
7217	(79*10^66447-97)/99	66447	Ray Chandler	01/2011
7218	2^220675+69	66430	Lelio R Paula	02/2012
7219	88323!6-16	66419	Robert Price	08/2018
7220	2^220633-111381	66418	Enzo Doria	05/2014
7221	(2^220625-509203)/4000321	66409	Lelio R Paula	05/2012
7222	2^220596-15813	66407	Enzo Doria	04/2013
7223	(5*10^66394-17)/3	66395	Serge Batalov	05/2009
7224	2^220549-1859173	66392	Enzo Doria	04/2016
7225	2^220478-161	66371	Lelio R Paula	02/2012
7226	5^94938-14636	66359	Enzo Doria	02/2013
7227	(F(67)^4861-F(66)^4861)/F(65)	66353	Wayne Halsdorf	03/2012
7228	15444^15839-15839^15444	66346	Norbert Schneider	08/2018
7229	2^220253-114871	66303	Enzo Doria	05/2015
7230	12^61432+95	66297	Lelio R Paula	07/2013
7231	2^220192-111563	66285	Enzo Doria	05/2014
7232	2^220188-111449	66284	Enzo Doria	05/2014
7233	(4*10^66284+23)/9	66284	Robert Price	11/2014
7234	32501!2+2	66266	Robert Price	01/2015
7235	(8*10^66261-101)/3	66262	Robert Price	10/2017
7236	1530*10^66254+R(66254)	66258	Patrick De Geest	05/2016
7237	(47^39623-1)/46	66252	Robert Price	06/2014
7238	2^220044-97305	66240	Lelio R Paula	04/2012
7239	(77*10^66237-257)/9	66238	Robert Price	10/2017
7240	29^45285+2	66225	Ray Chandler	08/2011
7241	15^56289+38	66202	Lelio R Paula	08/2013
7242	3^138749+98	66201	Lelio R Paula	06/2013
7243	(21*2^219912-1)/5	66201	Lelio R Paula	01/2014
7244	2^219904-16995	66198	Lelio R Paula	10/2011
7245	(3^138712-2)/5297	66179	Lelio R Paula	04/2012
7246	Phi(198552,10)	66177	Ray Chandler	07/2010
7247	4*6^85041+7	66176	Lelio R Paula	09/2014
7248	2^219812-3149	66171	Yves Minet	10/2009
7249	2^219795-611167	66165	Paul Bourdelais	03/2013
7250	32455!2+512	66162	Robert Price	02/2015

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Probable Primes Top 10000

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