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 ?
7251	13^57733+18	64312	Lelio R Paula	07/2013
7252	2^213621+72707	64307	Enzo Doria	04/2016
7253	10^64305+136791	64306	Patrick De Geest	05/2011
7254	10^64305-9	64305	Alexander Gramolin	01/2011
7255	V(307652)	64295	Serge Batalov	03/2015
7256	4*10^64286-89	64287	Robert Price	08/2017
7257	(2^213546-5)/2221	64281	Lelio R Paula	04/2012
7258	2^213438-58695	64252	Lelio R Paula	10/2011
7259	2^213367-105	64230	Lelio R Paula	08/2011
7260	595^23148+23148^595	64225	Norbert Schneider	07/2016
7261	3^134601+8680	64221	Lelio R Paula	05/2013
7262	(26*10^64220+61)/3	64221	Robert Price	06/2017
7263	500^23793+23793^500	64217	Norbert Schneider	08/2016
7264	179^28504-2	64216	Lelio R Paula	10/2017
7266	2^213314-455	64214	Yves Minet	02/2012
7265	39^40359-38	64214	Norbert Schneider	05/2014
7267	2^213292-16085	64208	Enzo Doria	04/2013
7268	2^213274-77	64202	Lelio R Paula	08/2011
7269	19^50203+78	64198	Lelio R Paula	08/2013
7270	(44*10^64192-233)/9	64193	Robert Price	10/2017
7271	2^213240-112865	64192	Enzo Doria	06/2014
7272	2^213190-112391	64177	Enzo Doria	06/2014
7273	(9913*2^213184-1)/9657	64175	Lelio R Paula	04/2015
7274	14^55991+27	64173	Lelio R Paula	07/2013
7275	2^213158-112581	64167	Enzo Doria	06/2014
7276	2^213148+91	64164	Lelio R Paula	08/2011
7277	(96^32369+1)/97	64163	Paul Bourdelais	08/2017
7279	6^82439+125	64151	Lelio R Paula	07/2013
7278	7*2^213102+9	64151	Lelio R Paula	04/2014
7280	L(306854)+F(306855)	64129	Henri Lifchitz	01/2007
7281	610^23017+23017^610	64110	Norbert Schneider	07/2016
7282	2^212950-64875	64105	Lelio R Paula	10/2011
7283	(266*10^64102-17)/3	64104	Robert Price	06/2016
7284	p(13679)#/2+64	64097	Robert Price	03/2017
7285	19^50119+94	64090	Lelio R Paula	08/2013
7286	2^212880-147	64084	Lelio R Paula	08/2011
7287	11^61523-4590	64070	Enzo Doria	01/2013
7288	5^91663+38	64070	Lelio R Paula	05/2013
7289	5^91650+52	64061	Lelio R Paula	05/2013
7290	2^212770+69	64051	Lelio R Paula	08/2011
7291	(3^134227+1)/4	64042	Paul Bourdelais	11/2007
7292	(2*10^64041-17)/3	64041	Robert Price	08/2014
7293	(15^54449+1)/16	64036	Paul Bourdelais	03/2010
7294	(29*10^64027+91)/3	64028	Robert Price	03/2016
7295	(lucasV(1,2,425405)+2)/(17*89)	64027	Mike Oakes	03/2017
7296	16878!+16878#-1	64022	D. Gazzoni Filho & Lucas Teixeira	05/2005
7297	2^212663+53	64018	Lelio R Paula	08/2011
7298	(4*10^64014+197)/3	64015	Robert Price	03/2017
7299	10^63986+63	63987	Robert Price	01/2011
7300	10^63986-31557	63986	Patrick De Geest	05/2013
7301	31487!2-2^31487	63982	Robert Price	09/2015
7302	(21*2^212522-1)/1416323	63971	Lelio R Paula	01/2014
7303	5^91517+98	63968	Lelio R Paula	04/2013
7304	(19*10^63960-43)/3	63961	Robert Price	10/2017
7305	(62*10^63954-17)/9	63955	Robert Price	09/2015
7307	5^91493-4^91493	63951	Predrag Minovic	04/2004
7306	V(364793)	63951	Serge Batalov	03/2015
7310	19^50004+58	63943	Lelio R Paula	05/2013
7308	5*6^82172-7	63943	Lelio R Paula	09/2014
7309	(56*10^63942+223)/9	63943	Robert Price	07/2016
7311	19^50000-24	63938	Lelio R Paula	05/2013
7312	(23*2^212374-1)/27019	63928	Lelio R Paula	01/2014
7313	(9*2^212355-1)/761	63924	Lelio R Paula	01/2014
7315	2^212344-183	63922	Lelio R Paula	08/2011
7314	(58695*2^212336-1)/379	63922	Lelio R Paula	04/2015
7316	10^63916+79	63917	Robert Price	01/2011
7317	10^63916-76823	63916	Patrick De Geest	05/2013
7318	2^212295-25	63908	Lelio R Paula	08/2011
7320	2^212285-2383	63905	Yves Minet	10/2013
7319	267^26336+26336^267	63905	Norbert Schneider	09/2014
7321	(-lucasV(1,2,424552)-2)/1601	63899	Mike Oakes	03/2017
7322	19^49962+60	63890	Lelio R Paula	05/2013
7323	3^133906-113056	63890	Enzo Doria	07/2014
7324	(lucasV(1,2,424451)+2)/3	63886	Mike Oakes	03/2017
7325	3*6^82092+5	63881	Lelio R Paula	09/2014
7326	15441^13706+13706^15441	63879	Hans Havermann	02/2017
7327	2^212154-776351	63865	Paul Bourdelais	03/2013
7328	35^41359+2	63862	Lelio R Paula	05/2013
7329	(61*10^63857-43)/9	63858	Robert Price	09/2015
7330	(2^212131-3)/485	63856	Lelio R Paula	04/2012
7331	2^212112-459995	63853	Enzo Doria	06/2015
7332	15^54290+58	63850	Lelio R Paula	05/2013
7333	3*2^212097-7	63849	Lelio R Paula	04/2014
7334	55^36683-54	63842	Norbert Schneider	08/2014
7335	(509203*2^212056-1)/3	63841	Lelio R Paula	04/2015
7336	(3^133805-7)/172	63839	Lelio R Paula	04/2012
7337	2^212049+149	63834	Lelio R Paula	08/2011
7338	5^91318-18	63829	Lelio R Paula	04/2013
7339	18468^2857+2857^18468	63824	Hans Havermann	03/2017
7340	(2^212024-5)/1111	63823	Lelio R Paula	04/2012
7341	2^211961+12915	63807	Lelio R Paula	02/2013
7342	(3^133707-7)/5780	63791	Lelio R Paula	04/2012
7343	(44*10^63790-161)/9	63791	Robert Price	11/2017
7344	747^22198+22198^747	63782	Norbert Schneider	07/2016
7345	2^211800-17169	63759	Enzo Doria	05/2013
7346	(85*10^63757-1)/3	63759	Robert Price	07/2017
7347	(14*10^63747-11)/3	63748	Erik Branger	09/2014
7348	91*19^49848+6	63746	Curtis Bright	05/2015
7349	18855^2402+2402^18855	63741	Hans Havermann	03/2017
7350	(142*10^63734-7)/9	63736	Robert Price	02/2017
7351	2^211699-111	63728	Lelio R Paula	08/2011
7352	11^61192-5550	63725	Enzo Doria	01/2013
7353	(11*10^63718+7)/9	63719	Serge Batalov	06/2011
7354	6^81872-13	63709	Lelio R Paula	04/2013
7355	3^133522+98	63707	Lelio R Paula	05/2013
7357	2^211607-61	63701	Lelio R Paula	08/2011
7356	5^91135+8	63701	Lelio R Paula	04/2013
7358	11^61157-270	63689	Enzo Doria	07/2012
7360	10^63685+1145141919	63686	Marisa Kirisame	03/2015
7359	10^63685+103837	63686	Patrick De Geest	03/2016
7361	10^63685-130797	63685	Patrick De Geest	03/2016
7362	2^211547+1155*211547	63682	Henri Lifchitz	02/2005
7363	2^211543+45	63681	Lelio R Paula	08/2011
7364	2^211534+43	63679	Lelio R Paula	08/2011
7365	11^61140-60	63671	Enzo Doria	07/2012
7366	2^211491-112321	63666	Enzo Doria	06/2014
7367	19085^2164+2164^19085	63654	Hans Havermann	03/2017
7368	(2^211430-5)/859	63644	Lelio R Paula	04/2012
7369	2^211401-91	63639	Lelio R Paula	08/2011
7370	(6883*2^211378-1)/69	63634	Lelio R Paula	04/2015
7371	(F(152232)^3-F(152231)^3)/F(152230)	63629	Wayne Halsdorf	03/2012
7372	(29*2^211384-1)/50122621	63627	Lelio R Paula	01/2014
7373	2^211333+15015	63618	Lelio R Paula	01/2013
7374	33^41889-32	63610	Norbert Schneider	03/2014
7375	13^57093+18	63599	Lelio R Paula	05/2013
7376	(5*2^211219-1)/9	63583	Lelio R Paula	01/2014
7377	(107*10^63576-17)/9	63578	Robert Price	02/2017
7378	23^46687-1020	63575	Enzo Doria	08/2012
7379	(67607*2^211188+1)/5234319	63573	Lelio R Paula	06/2014
7380	(3^133243+7)/10726	63570	Lelio R Paula	04/2012
7381	(7*2^211181+1)/2745	63570	Lelio R Paula	06/2012
7383	(20^48859-1)/19	63566	Paul Bourdelais	03/2010
7382	2*3^133227+5	63566	Lelio R Paula	04/2014
7384	2^211155+113	63564	Lelio R Paula	08/2011
7385	2^211134+345	63558	Lelio R Paula	09/2011
7386	2^211121+16385	63554	Lelio R Paula	09/2011
7387	16996^5483+5483^16996	63549	Hans Havermann	02/2017
7388	(2^211079+9)/364283	63536	Lelio R Paula	03/2012
7389	3*10^63522+13	63523	Robert Price	08/2017
7390	15852^10157+10157^15852	63516	Hans Havermann	02/2017
7391	2^210948-15873	63502	Enzo Doria	04/2013
7392	7^75136+6	63498	Lelio R Paula	04/2013
7393	2^210928+12915	63496	Lelio R Paula	02/2013
7394	7*10^63493+39	63494	Robert Price	07/2016
7395	2^210909+135	63490	Lelio R Paula	08/2011
7396	(3*2^210832+1)/7	63467	Lelio R Paula	07/2012
7397	8*7^75098-3	63467	Lelio R Paula	09/2014
7398	17683^3882+3882^17683	63466	Hans Havermann	03/2017
7400	Pell-LucasQ(165799)/2	63464	Eric W. Weisstein	11/2006
7399	2^210820-16905	63464	Enzo Doria	05/2013
7401	5^90795-36	63463	Lelio R Paula	04/2013
7402	2^210816-13197	63462	Enzo Doria	10/2012
7403	2^210750+133	63443	Lelio R Paula	08/2011
7404	291^25742+25742^291	63426	Norbert Schneider	09/2014
7405	(3^132908+8)/279859	63408	Lelio R Paula	04/2012
7406	6^81480-139	63404	Lelio R Paula	04/2013
7407	2^210576-173	63390	Lelio R Paula	08/2011
7408	18^50497+55	63388	Lelio R Paula	05/2013
7409	2^210545+11	63381	Lelio R Paula	08/2011
7410	2^210543+63	63380	Lelio R Paula	08/2011
7411	83^33016+82	63361	Norbert Schneider	04/2015
7412	2^210464+98765331	63356	Jason Earls	12/2008
7413	7*10^63351+9	63352	Dmitry Domanov	11/2010
7414	p(13534)#/2+512	63348	Robert Price	05/2017
7415	1741^19546+19546^1741	63345	Serge Batalov	05/2014
7416	10^63336+19819	63337	Patrick De Geest	12/2013
7417	10^63336-122883	63336	Patrick De Geest	12/2013
7418	(19^49523-2^49523)/17	63327	Robert Price	09/2013
7419	(2^210378+47)/95516931	63323	Lelio R Paula	03/2012
7420	31191!2+256	63316	Robert Price	01/2015
7421	16458^7031+7031^16458	63315	Hans Havermann	01/2017
7422	(lucasV(1,2,420636)-2)/(731^2210319)	63303	Mike Oakes	03/2017
7423	(2^210283+7)/1691145	63296	Lelio R Paula	03/2012
7424	2^210217+1299	63282	Lelio R Paula	09/2011
7425	(2^210221-3)/269	63281	Lelio R Paula	04/2012
7426	Phi(193404,10)/386809/8122969	63268	Maksym Voznyy	10/2011
7427	96^31913-95	63261	Norbert Schneider	04/2016
7428	3^132572+280	63253	Lelio R Paula	04/2013
7429	3^132570-2^(132570-1)	63252	Robert Price	01/2016
7430	11^60734-4920	63248	Enzo Doria	01/2013
7432	2^210061+21	63235	Donovan Johnson	06/2006
7431	18^50375+95	63235	Lelio R Paula	05/2013
7433	85^32773-2	63233	Lelio R Paula	08/2013
7434	(-lucasV(1,2,420115)-2)/(3*5^3)	63232	Mike Oakes	02/2017
7435	(2^210054-1017)/671	63230	Lelio R Paula	04/2012
7436	3*2^210022+5	63224	Lelio R Paula	04/2014
7437	15^53756+32	63222	Lelio R Paula	05/2013
7439	17^51380+22	63221	Lelio R Paula	05/2013
7438	(lucasV(1,2,420045)+2)/257	63221	Mike Oakes	02/2017
7440	43^38700+42	63216	Norbert Schneider	06/2014
7441	5^90431-96	63209	Lelio R Paula	04/2013
7442	(172*10^63202-1)/9	63204	Serge Batalov	12/2014
7443	(43*10^63200+83)/9	63201	Robert Price	08/2017
7444	2^209914-16005	63191	Enzo Doria	04/2013
7445	3*6^81190-5	63179	Lelio R Paula	09/2014
7446	2^209820+4257	63163	Lelio R Paula	10/2011
7448	99^31648+2	63158	Lelio R Paula	05/2013
7447	16976^5253+5253^16976	63158	Hans Havermann	01/2017
7449	2^209790+67	63154	Lelio R Paula	08/2011
7450	2^209759+90195	63144	Lelio R Paula	02/2013
7451	145823#+211507	63142	Arkadiusz Wesolowski	03/2013
7453	2^209707+513	63129	Lelio R Paula	10/2011
7452	(3^132314-8)/17	63129	Lelio R Paula	04/2012
7454	(2*10^63117+7)/9	63117	Erik Branger	03/2011
7455	9*2^209654-7	63114	Lelio R Paula	04/2014
7456	11^60598-14	63107	Lelio R Paula	05/2013
7457	15103^15078+15078^15103	63106	Hans Havermann	01/2017
7458	15346^12941+12941^15346	63103	Hans Havermann	01/2017
7460	3^132253+76	63101	Lelio R Paula	04/2013
7459	(56*10^63100+403)/9	63101	Robert Price	10/2017
7461	17549^3936+3936^17549	63090	Hans Havermann	01/2017
7462	(55459*2^209553+1)/423	63084	Lelio R Paula	06/2014
7463	(331^25033-1)/330	63077	Eric Chen	09/2017
7464	20^48480+31	63074	Lelio R Paula	06/2013
7465	(26*10^63073-23)/3	63074	Robert Price	08/2016
7466	2^209499+76253	63066	Enzo Doria	04/2016
7467	11^60546-11340	63053	Enzo Doria	12/2012
7468	2^209426+57889	63044	Yves Minet	02/2010
7469	(22699*2^209405+1)/21	63041	Lelio R Paula	06/2014
7470	5^90189+54	63040	Lelio R Paula	04/2013
7471	(22*10^63034-73)/3	63035	Robert Price	09/2017
7472	(314021^11467+1)/314022	63029	Faysal YAtim	05/2008
7473	V(301486)	63007	Henri Lifchitz	05/2003
7474	(31*2^209298+1)/95	63005	Lelio R Paula	08/2012
7475	(27*2^209245+1)/5	62990	Lelio R Paula	08/2012
7476	6^80946-5^(80946-1)	62989	Robert Price	05/2016
7477	467^23596+23596^467	62986	Norbert Schneider	08/2016
7478	(7*2^209212-1)/3	62980	Lelio R Paula	01/2014
7479	(27*2^209206-1)/11	62978	Lelio R Paula	01/2014
7480	1456^19909+19909^1456	62976	Serge Batalov	05/2014
7482	(3^131964-5)/185212396	62955	Lelio R Paula	04/2012
7481	35^40772-1466	62955	Enzo Doria	03/2013
7483	5^90064-13706	62953	Enzo Doria	02/2013
7484	(22*10^62926+257)/9	62927	Robert Price	11/2017
7485	(13*10^62914+401)/9	62915	Robert Price	10/2017
7486	2^208993+107	62914	Lelio R Paula	08/2011
7487	2^208993+77	62914	Lelio R Paula	08/2011
7488	189^27636-2	62913	Lelio R Paula	10/2017
7489	(2^208948-7)/261	62898	Lelio R Paula	03/2012
7490	(151*10^62879-1)/3	62881	Robert Price	04/2017
7491	15^53464-82	62879	Lelio R Paula	05/2013
7492	2^208843-112921	62869	Enzo Doria	06/2014
7493	2^208779+81	62849	Henri Lifchitz	01/2007
7494	(21181*2^208780+1)/8993838841	62844	Lelio R Paula	06/2014
7495	(73*10^62824+17)/9	62825	Robert Price	10/2015
7496	3^131670-82	62823	Lelio R Paula	04/2013
7497	19^49128-90	62823	Lelio R Paula	05/2013
7498	11^60314-4410	62811	Enzo Doria	01/2013
7499	(17*2^208614-1)/53	62799	Lelio R Paula	01/2014
7500	2^208594+93	62794	Donovan Johnson	06/2008

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PRP Records

Probable Primes Top 10000

(205869 PRPs in the top)