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 ?
7251	2^228041+1185	68648	Lelio R Paula	04/2012
7252	2^228040-1037	68647	Yves Minet	11/2012
7253	2*F(328450)-1	68642	Henri Lifchitz	12/2009
7254	5^98201-34	68640	Lelio R Paula	06/2013
7255	9^71910+38^71910-24^71910-3*2^71910	68620	Mike Oakes	12/2010
7256	7*2^227780-3	68570	Lelio R Paula	04/2014
7257	15327^16382-16382^15327	68567	Norbert Schneider	11/2018
7258	2^227733-121	68555	Lelio R Paula	02/2012
7259	2^227702-16967	68546	Enzo Doria	05/2013
7260	2^227689-111655	68542	Enzo Doria	05/2014
7261	gcd(V(823915),5F(164783)(F(164783)-1)+1)	68536	Serge Batalov	04/2015
7262	5^98051+2	68535	Ray Chandler	07/2011
7263	5*10^68524+51	68525	Robert Price	01/2017
7264	(11*10^68520-149)/3	68521	Robert Price	01/2017
7265	19^53573-78	68507	Lelio R Paula	09/2013
7266	(68*10^68504+13)/9	68505	Ray Chandler	10/2010
7267	9*5^98003+4	68503	Lelio R Paula	09/2014
7268	2^227528+51	68493	Lelio R Paula	02/2012
7269	(146*28^47316+1)/3	68476	Karsten Bonath	06/2018
7270	3^143497+8	68466	Lelio R Paula	04/2012
7271	2^227430-95	68464	Lelio R Paula	02/2012
7272	(8*10^68455+13)/3	68456	Robert Price	11/2017
7273	3*5^97934-2	68454	Lelio R Paula	09/2014
7274	20^52613+77	68452	Lelio R Paula	09/2013
7275	2^227371+32769	68446	Lelio R Paula	04/2012
7276	(3^143465+4)/21270420067	68440	Lelio R Paula	04/2012
7277	CopelandErdos(68433)	68433	Eric W. Weisstein	08/2013
7278	2^227323+75431	68432	Enzo Doria	04/2016
7279	2^227314-1965	68429	Lelio R Paula	04/2012
7280	2^227303-110617	68426	Enzo Doria	05/2014
7281	7^80963+66	68422	Lelio R Paula	07/2013
7282	2^227290+73849	68422	Enzo Doria	04/2016
7283	(14^59693-1)/13	68415	Paul Bourdelais	06/2008
7284	2^227256-2786249	68411	Enzo Doria	03/2016
7285	8*10^68400-7	68401	Dmitry Domanov	11/2010
7286	(15*2^227228-1)/583	68401	Lelio R Paula	01/2014
7287	2^227210+1869169	68398	Enzo Doria	05/2016
7288	2^227159-1838635	68382	Enzo Doria	05/2015
7289	44*10^68368+3	68370	Robert Price	08/2017
7290	2^227115-7807	68369	Lelio R Paula	10/2009
7291	2^227078-47355	68358	Lelio R Paula	04/2012
7292	(2^227063-1017)/349	68351	Lelio R Paula	04/2012
7293	2^227057+148091	68351	Lelio R Paula	04/2012
7294	2^227046+187	68348	Lelio R Paula	02/2012
7295	9*10^68331+59	68332	Robert Price	10/2017
7296	11^65608-720	68324	Enzo Doria	11/2012
7297	(32*10^68320+319)/9	68321	Robert Price	10/2017
7298	33408!2-2^33408-1	68315	Joe McLean	05/2017
7299	2^226894-123	68302	Lelio R Paula	02/2012
7300	10^68297+141559	68298	Patrick De Geest	05/2013
7301	10^68297-93	68297	Robert Price	05/2011
7302	680^24107-679^24107	68284	Jean-Louis Charton	07/2010
7303	12^63267+59	68277	Lelio R Paula	07/2013
7304	2^226785-1159	68270	Yves Minet	11/2012
7305	7^80769+90	68258	Lelio R Paula	07/2013
7306	(88*10^68256-1)/3	68258	Robert Price	10/2017
7307	2^226741+66587	68256	Yves Minet	10/2010
7308	2^226720-112403	68250	Enzo Doria	06/2014
7309	(78557*2^226694+1)/3	68247	Lelio R Paula	06/2014
7310	(83*10^68231+7)/9	68232	Robert Price	10/2015
7311	65^37636+16	68231	Lelio R Paula	01/2016
7312	5^97615-4^(97615+1)	68230	Robert Price	04/2016
7313	12^63200-43	68205	Lelio R Paula	07/2013
7314	-330*Bern(21940)/223790620733	68201	Serge Batalov	04/2015
7315	3^142925+8680	68193	Lelio R Paula	06/2013
7316	3*2^226512-7	68188	Lelio R Paula	04/2014
7317	14^59484+57	68177	Lelio R Paula	08/2013
7318	11^65438-2190	68147	Enzo Doria	12/2012
7319	91^34784-2	68144	Lelio R Paula	09/2013
7320	(2^226336-3)*6-7	68135	Gilbert Mozzo	06/2016
7321	(22*10^68133-37)/3	68134	Robert Price	05/2017
7322	5^97476+36	68133	Lelio R Paula	06/2013
7323	3*5^97474-2	68132	Lelio R Paula	09/2014
7324	12^63130+49	68129	Lelio R Paula	07/2013
7325	2^226281+5385	68118	Lelio R Paula	04/2012
7326	2^226257-3049	68111	Yves Minet	10/2014
7327	(28*10^68107-43)/3	68108	Robert Price	04/2016
7328	2^226243-2587	68106	Yves Minet	07/2014
7329	20^52346-11	68104	Lelio R Paula	09/2013
7330	2^226205-99	68095	Lelio R Paula	02/2012
7331	2^226187-49	68090	Lelio R Paula	02/2012
7332	3^142708+76	68090	Lelio R Paula	06/2013
7333	7*10^68088-89	68089	Robert Price	01/2017
7334	2^226154+71839	68080	Enzo Doria	04/2016
7335	(10^68078+59)/3	68078	Serge Batalov	12/2014
7337	14^59387+69	68066	Lelio R Paula	08/2013
7336	2^226108-113429	68066	Enzo Doria	07/2014
7338	(62*10^68059-197)/9	68060	Robert Price	10/2017
7339	(24^49307-1)/23	68053	Robert Price	04/2012
7340	15^57859-28	68048	Lelio R Paula	08/2013
7341	(509203*2^226003-1)/13	68039	Lelio R Paula	04/2015
7342	2^226015-111361	68038	Enzo Doria	05/2014
7343	(10^(234016+1)+7210^34016-1)/9	68033	Robert Price	09/2017
7344	4*10^68020+91	68021	Robert Price	11/2017
7345	156(10^(417000)-1)/101-1	68001	Robert Price	05/2014
7346	2^225878-1017	67997	Lelio R Paula	04/2012
7347	38^75289+5^75289-34^75289+3*2^75289	67994	Mike Oakes	11/2010
7348	3*2^225865+5	67993	Lelio R Paula	04/2014
7350	11^65284-5820	67987	Enzo Doria	01/2013
7349	19^53166+70	67987	Lelio R Paula	08/2013
7351	2^225837+75407	67984	Enzo Doria	04/2016
7352	3^142464-112654	67973	Enzo Doria	06/2014
7353	2^225777+95	67966	Lelio R Paula	02/2012
7354	(2^225641-1017)/138815	67920	Lelio R Paula	04/2012
7355	2^225609-18445	67916	Enzo Doria	05/2013
7356	2^225542-177	67895	Lelio R Paula	02/2012
7357	2^225536-29	67894	Henri Lifchitz	05/2005
7358	11^65190-3390	67889	Enzo Doria	12/2012
7359	3^142249-2^(142249-1)	67871	Robert Price	01/2016
7360	11^65168-4830	67866	Enzo Doria	01/2013
7361	10^67863+58627	67864	Patrick De Geest	01/2016
7362	10^67863-11	67863	Robert Price	05/2011
7363	(1!)^2+(2!)^2+(3!)^2+...+(9566!)^2	67856	T. D. Noe	02/2006
7364	(19*2^225357-1)/11	67840	Lelio R Paula	01/2014
7365	9*6^87164-7	67828	Lelio R Paula	09/2014
7366	131^32034+130	67825	Norbert Schneider	03/2015
7367	(29*2^225314+1)/10881	67824	Lelio R Paula	08/2012
7368	(134*10^67816+7)/3	67818	Robert Price	02/2017
7369	2^225261+855	67811	Lelio R Paula	04/2012
7370	(29*2^225252-1)/2933	67806	Lelio R Paula	01/2014
7371	(4*10^67796+23)/9	67796	Robert Price	11/2014
7372	15477^16180-16180^15477	67790	Norbert Schneider	09/2018
7373	(23*2^225177+1)/31	67785	Lelio R Paula	08/2012
7374	(4*10^67784+149)/9	67784	Robert Price	03/2017
7375	8177^17322+17322^8177	67774	Norbert Schneider	03/2019
7376	2^225120+151	67768	Lelio R Paula	02/2012
7377	(44^41233+1)/45	67763	Robert Price	11/2013
7378	89933!6-16	67747	Robert Price	08/2018
7379	8*10^67742+9	67743	Dmitry Domanov	11/2010
7380	2^224977+1089	67725	Lelio R Paula	04/2012
7381	(2^224950+5)/19509	67713	Lelio R Paula	04/2012
7382	11^65011-5970	67702	Enzo Doria	01/2013
7383	88*10^67691+7	67693	Robert Price	11/2016
7384	11^65000-7140	67691	Enzo Doria	01/2013
7386	2^224841+59	67684	Lelio R Paula	02/2012
7385	33129!2+2^33129	67684	Robert Price	09/2015
7387	2^224827+8415	67680	Lelio R Paula	02/2013
7388	(9913*2^224821-1)/19825	67678	Lelio R Paula	04/2015
7389	2^224815-49789	67677	Henri Lifchitz	04/2005
7390	(43*10^67664+11)/9	67665	Robert Price	06/2015
7391	(292*10^67659-1)/3	67661	Robert Price	01/2017
7392	(17*2^224766+1)/29007	67659	Lelio R Paula	06/2012
7393	2^224744+577294575	67655	Lelio R Paula	02/2016
7394	((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
7395	(2^224721+78557)/1739	67645	Lelio R Paula	05/2012
7396	2^224700+1915	67642	Lelio R Paula	04/2012
7397	(29*2^224694-1)/198905	67636	Lelio R Paula	01/2014
7398	2^224658-93	67629	Lelio R Paula	02/2012
7399	2^224624-13077	67619	Enzo Doria	10/2012
7400	18^53860-3319	67609	Enzo Doria	03/2013
7401	(21181*2^224570+1)/5	67606	Lelio R Paula	06/2014
7402	89762!6-3	67606	Robert Price	08/2018
7403	2^224578-111041	67605	Enzo Doria	05/2014
7404	2^224569-113233	67603	Enzo Doria	07/2014
7405	2^224562-113171	67600	Enzo Doria	07/2014
7406	2^224556-113129	67599	Enzo Doria	07/2014
7407	6*7^79980-5	67592	Lelio R Paula	09/2014
7408	(6883*2^224523-1)/16031	67588	Lelio R Paula	04/2015
7409	10^67579+164779	67580	Patrick De Geest	07/2017
7411	(52*10^67578-61)/9	67579	Robert Price	09/2015
7410	10^67579-401	67579	Robert Price	06/2017
7412	(17^54919-1)/16	67574	Paul Bourdelais	03/2010
7413	(2^224363-9)/1951	67537	Lelio R Paula	04/2012
7414	(709*10^67517-7)/9	67519	Robert Price	09/2017
7415	47719!3-59049	67516	Robert Price	12/2015
7416	(22^50287+1)/23	67506	Robert Price	06/2013
7417	3*10^67499+67	67500	Robert Price	11/2017
7418	11^64811-5820	67494	Enzo Doria	01/2013
7419	131^31870+31870^131	67478	Serge Batalov	05/2014
7420	9*10^67468+7	67469	Dmitry Domanov	11/2010
7421	(31*2^224115-1)/47723	67463	Lelio R Paula	01/2014
7422	128^32001+32001^128	67433	Serge Batalov	05/2014
7423	(89*10^67431-17)/9	67432	Robert Price	11/2015
7424	2^223912-111059	67405	Enzo Doria	05/2014
7425	2^223913+73697	67405	Enzo Doria	04/2016
7426	(2*10^67405-23)/3	67405	Robert Price	09/2017
7427	(10^67404+179)/9	67404	Serge Batalov	12/2014
7428	18738^3955+3955^18738	67404	Hans Havermann	09/2016
7429	9*7^79728-2	67379	Lelio R Paula	09/2014
7430	(28*10^67378-43)/3	67379	Robert Price	04/2016
7431	(3^141234-7)/430241282	67378	Lelio R Paula	04/2012
7432	211^28988-2	67377	Lelio R Paula	09/2013
7433	4*10^67375+91	67376	Robert Price	11/2017
7434	2^223793-18069	67369	Enzo Doria	05/2013
7435	2^223777-2521	67364	Yves Minet	07/2014
7436	(15185*2^223775-1)/15183	67363	Lelio R Paula	04/2015
7437	(2^223759-lucasV(1,2,223759)+1)/2	67358	Mike Oakes	11/2016
7438	V(340138)	67336	Serge Batalov	03/2015
7439	43125^14528-106	67334	Enzo Doria	07/2012
7440	15275^16086-16086^15275	67304	Norbert Schneider	09/2018
7441	8*10^67302-51	67303	Robert Price	10/2017
7442	17458^7153+7153^17458	67292	Hans Havermann	08/2016
7443	16366^12925+12925^16366	67288	Hans Havermann	08/2016
7444	37^42906-2	67286	Lelio R Paula	08/2013
7445	18^53592-13	67273	Lelio R Paula	08/2013
7446	V(396221)	67256	Serge Batalov	03/2015
7448	(34*10^67245-7)/9/3^4/193/1381537	67236	Makoto Morimoto	04/2016
7447	(14*10^67235-101)/3	67236	Robert Price	04/2017
7449	53^38993-52^38993	67235	Robert Price	01/2013
7450	(2^223349-7)/6485	67231	Lelio R Paula	04/2012
7451	2^223333+315	67230	Lelio R Paula	04/2012
7452	2^223278-111041	67214	Enzo Doria	05/2014
7453	(23472^223281+1)/(351971213*1783)	67208	Jens K. Andersen	09/2007
7454	2^223256-45	67207	Lelio R Paula	02/2012
7455	2^223253-112111	67206	Enzo Doria	06/2014
7456	18407^4474+4474^18407	67199	Hans Havermann	08/2016
7457	47^40182+40182^47	67189	Norbert Schneider	11/2014
7458	13^60309+94	67181	Lelio R Paula	07/2013
7459	11^64503-84	67173	Lelio R Paula	07/2013
7460	3^140781+236	67170	Lelio R Paula	06/2013
7461	2^223107-865057	67162	Paul Bourdelais	03/2013
7462	2^223100-59	67160	Lelio R Paula	02/2012
7463	2^223087+71963	67156	Enzo Doria	04/2016
7464	18^53481-3779	67134	Enzo Doria	03/2013
7465	(326^26713-1)/325	67134	Eric Chen	09/2017
7466	4^111473-62573	67114	Mike Oakes	02/2011
7467	2^222943+29	67113	Henri Lifchitz	08/2005
7468	(2^222939-9)/103	67110	Lelio R Paula	04/2012
7469	2^222862-459161	67089	Enzo Doria	05/2015
7470	2^222828+8193	67078	Lelio R Paula	04/2012
7471	3^140570+2660	67069	Lelio R Paula	06/2013
7472	2^222744+855	67053	Lelio R Paula	04/2012
7473	13^60189+84	67048	Lelio R Paula	07/2013
7474	2*10^67043-51	67044	Robert Price	11/2017
7475	2^222701+577294575	67040	Lelio R Paula	02/2016
7476	(13*10^67038-31)/9	67039	Serge Batalov	11/2008
7477	(151*10^67027-7)/9	67029	Robert Price	07/2017
7478	(58695*2^222620-1)/61	67019	Lelio R Paula	04/2015
7479	2^222614-111041	67014	Enzo Doria	05/2014
7480	118^32333-117	66991	Norbert Schneider	08/2018
7481	2^222520-1907	66986	Yves Minet	03/2013
7482	(4^111231+23)/3	66968	Robert Price	02/2017
7483	2^222408-111275	66952	Enzo Doria	05/2014
7484	10^66949-9^66949	66949	Jean-Louis Charton	12/2005
7485	2^222378-1005	66943	Lelio R Paula	04/2012
7486	(9*2^222366+1)/73	66938	Lelio R Paula	08/2012
7487	7^79202-6^(79202+1)	66934	Robert Price	06/2016
7488	2^222325-112255	66927	Enzo Doria	06/2014
7489	20^51428+33	66910	Lelio R Paula	08/2013
7491	2^222224-18509	66897	Enzo Doria	05/2013
7490	(38*10^66896+187)/9	66897	Robert Price	11/2017
7492	2^222192-869688105	66887	Lelio R Paula	02/2016
7493	(19*10^66878-43)/3	66879	Robert Price	10/2017
7494	11^64219-64	66878	Lelio R Paula	07/2013
7495	2^222151-17295	66875	Lelio R Paula	04/2012
7496	gcd(V(799885),5F(159977)(F(159977)+1)+1)	66867	Serge Batalov	04/2015
7497	2^222085-111031	66855	Enzo Doria	05/2014
7498	8*10^66848-13	66849	Robert Price	05/2017
7499	(3^140087+4)/13	66838	Lelio R Paula	04/2012
7500	(3^140102+4)/8843609437	66836	Lelio R Paula	04/2012

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PRP Records

Probable Primes Top 10000

(252675 PRPs in the top)