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	2^215351-111925	64828	Enzo Doria	05/2014
7252	2^215310-117	64815	Lelio R Paula	08/2011
7253	124^30958-123	64809	Norbert Schneider	02/2015
7254	(7*10^64807+17)/3	64808	Erik Branger	03/2014
7255	(710^(232400+1)-27*10^32400-7)/9	64801	Robert Price	11/2015
7256	2^215243-15949	64795	Enzo Doria	04/2013
7257	23^47581-22^47581	64793	Robert Price	08/2012
7258	(62*10^64783-17)/9	64784	Robert Price	09/2015
7259	5*3^135747-4	64769	Lelio R Paula	04/2014
7260	(59*10^64767-41)/9	64768	Robert Price	09/2015
7262	(2^215140+3)/19	64763	Lelio R Paula	04/2012
7261	2^215135-17169	64763	Enzo Doria	05/2013
7263	2^215115-111277	64757	Enzo Doria	05/2014
7264	9*5^92641+2	64755	Lelio R Paula	09/2014
7265	(lucasV(1,2,430086)-2)/(7*1033)	64731	Mike Oakes	03/2017
7266	(5*10^64715-23)/9	64715	Robert Price	11/2014
7267	2^214938-1781	64703	Yves Minet	03/2013
7268	11^62111-420	64682	Enzo Doria	08/2012
7269	5^92525+42	64673	Lelio R Paula	06/2013
7270	2^214824+71893	64669	Enzo Doria	04/2016
7271	2^214799-2221	64661	Yves Minet	08/2013
7272	(21*2^214688+1)/293	64627	Lelio R Paula	08/2012
7273	92^32907+32907^92	64623	Serge Batalov	05/2014
7274	(89*10^64608-539)/9	64609	Robert Price	11/2017
7275	6^83013+101	64597	Lelio R Paula	07/2013
7276	p(13775)#/2+8	64594	Robert Price	01/2017
7277	(7*10^64568-43)/9	64568	Robert Price	10/2014
7278	Pell-LucasQ(168677)/2	64566	Eric W. Weisstein	11/2006
7279	(24737*2^214476+1)/2877	64565	Lelio R Paula	06/2014
7280	(47*2^214463+1)/7	64561	Lelio R Paula	04/2015
7281	2^214458+54615	64559	Lelio R Paula	10/2011
7282	(3^135322+7)/122911408	64557	Lelio R Paula	04/2012
7283	2^214389-683113	64538	Paul Bourdelais	03/2013
7284	(76*10^64534+113)/9	64535	Robert Price	11/2017
7285	2^214369-111241	64532	Enzo Doria	05/2014
7286	(19^50461+3^50461)/22	64526	Robert Price	07/2013
7287	11^61954-3660	64519	Enzo Doria	12/2012
7288	(23*2^214319-1)/21	64517	Lelio R Paula	01/2014
7289	(58695*2^214310-1)/571	64516	Lelio R Paula	04/2015
7290	35^41779-34	64510	Norbert Schneider	04/2014
7291	(159^29303+1)/160	64506	Eric Chen	12/2017
7292	(89*10^64504-179)/9	64505	Robert Price	11/2017
7293	11^61939-5220	64503	Enzo Doria	01/2013
7294	(2^214271+78557)/35	64501	Lelio R Paula	05/2012
7295	L(308604)+P(308604)	64495	Robert Price	12/2017
7296	126^30706-125	64494	Norbert Schneider	02/2015
7297	gcd(V(1157265),5F(231453)(F(231453)-1)+1)	64492	Serge Batalov	04/2015
7298	2^214215+12909	64486	Lelio R Paula	10/2011
7299	5^92225+66	64463	Lelio R Paula	06/2013
7300	2^214126-240551	64459	Paul Bourdelais	03/2013
7301	8*6^82827+5	64453	Lelio R Paula	09/2014
7302	(31*2^214120-1)/2170485	64452	Lelio R Paula	01/2014
7303	(31*2^214088-1)/5955	64445	Lelio R Paula	01/2014
7304	14^56227+89	64444	Lelio R Paula	08/2013
7307	2^214055-159	64437	Lelio R Paula	08/2011
7305	10^64436+2667	64437	Patrick De Geest	05/2013
7306	65^35543-64^35543	64437	Robert Price	08/2013
7308	10^64436-53	64436	Robert Price	05/2011
7309	(3^135043-lucasV(1,3,135043)+1)/3	64432	Paul Vanderveen	11/2017
7310	Phi(128878,10)/39503297927	64428	Maksym Voznyy	11/2015
7311	3^135027+100	64425	Lelio R Paula	05/2013
7312	(3^134972-7)/2	64398	Lelio R Paula	04/2012
7313	6*10^64387+7	64388	Dmitry Domanov	11/2010
7314	2^213864-18377	64380	Enzo Doria	05/2013
7315	(2^213821+9)/209	64365	Lelio R Paula	04/2012
7316	2^213788+135	64357	Lelio R Paula	08/2011
7317	(3^134883+2)/48313	64351	Lelio R Paula	04/2012
7318	(49^38069-46^38069)/3	64344	Serge Batalov	12/2016
7319	(11^61781+2^61781)/13	64338	Robert Price	02/2013
7320	6^82670+37	64330	Lelio R Paula	07/2013
7321	(3^134839+4)/32312959	64328	Lelio R Paula	04/2012
7322	(22*10^64326+161)/3	64327	Robert Price	02/2017
7323	11^61767-4050	64324	Enzo Doria	12/2012
7324	2^213645-114853	64314	Enzo Doria	05/2015
7325	13^57733+18	64312	Lelio R Paula	07/2013
7326	2^213621+72707	64307	Enzo Doria	04/2016
7327	10^64305+136791	64306	Patrick De Geest	05/2011
7328	10^64305-9	64305	Alexander Gramolin	01/2011
7329	V(307652)	64295	Serge Batalov	03/2015
7330	4*10^64286-89	64287	Robert Price	08/2017
7331	(2^213546-5)/2221	64281	Lelio R Paula	04/2012
7332	2^213438-58695	64252	Lelio R Paula	10/2011
7333	2^213367-105	64230	Lelio R Paula	08/2011
7334	595^23148+23148^595	64225	Norbert Schneider	07/2016
7335	3^134601+8680	64221	Lelio R Paula	05/2013
7336	(26*10^64220+61)/3	64221	Robert Price	06/2017
7337	500^23793+23793^500	64217	Norbert Schneider	08/2016
7338	179^28504-2	64216	Lelio R Paula	10/2017
7340	2^213314-455	64214	Yves Minet	02/2012
7339	39^40359-38	64214	Norbert Schneider	05/2014
7341	2^213292-16085	64208	Enzo Doria	04/2013
7342	2^213274-77	64202	Lelio R Paula	08/2011
7343	19^50203+78	64198	Lelio R Paula	08/2013
7344	(44*10^64192-233)/9	64193	Robert Price	10/2017
7345	2^213240-112865	64192	Enzo Doria	06/2014
7346	2^213190-112391	64177	Enzo Doria	06/2014
7347	(9913*2^213184-1)/9657	64175	Lelio R Paula	04/2015
7348	14^55991+27	64173	Lelio R Paula	07/2013
7349	2^213158-112581	64167	Enzo Doria	06/2014
7350	2^213148+91	64164	Lelio R Paula	08/2011
7351	(96^32369+1)/97	64163	Paul Bourdelais	08/2017
7353	6^82439+125	64151	Lelio R Paula	07/2013
7352	7*2^213102+9	64151	Lelio R Paula	04/2014
7354	L(306854)+F(306855)	64129	Henri Lifchitz	01/2007
7355	610^23017+23017^610	64110	Norbert Schneider	07/2016
7356	2^212950-64875	64105	Lelio R Paula	10/2011
7357	(266*10^64102-17)/3	64104	Robert Price	06/2016
7358	p(13679)#/2+64	64097	Robert Price	03/2017
7359	19^50119+94	64090	Lelio R Paula	08/2013
7360	2^212880-147	64084	Lelio R Paula	08/2011
7361	11^61523-4590	64070	Enzo Doria	01/2013
7362	5^91663+38	64070	Lelio R Paula	05/2013
7363	5^91650+52	64061	Lelio R Paula	05/2013
7364	2^212770+69	64051	Lelio R Paula	08/2011
7365	(3^134227+1)/4	64042	Paul Bourdelais	11/2007
7366	(2*10^64041-17)/3	64041	Robert Price	08/2014
7367	(15^54449+1)/16	64036	Paul Bourdelais	03/2010
7368	(29*10^64027+91)/3	64028	Robert Price	03/2016
7369	(lucasV(1,2,425405)+2)/(17*89)	64027	Mike Oakes	03/2017
7370	16878!+16878#-1	64022	D. Gazzoni Filho & Lucas Teixeira	05/2005
7371	2^212663+53	64018	Lelio R Paula	08/2011
7372	(4*10^64014+197)/3	64015	Robert Price	03/2017
7373	(140^29819+1)/141	63994	Richard Fischer	05/2018
7374	10^63986+63	63987	Robert Price	01/2011
7375	10^63986-31557	63986	Patrick De Geest	05/2013
7376	31487!2-2^31487	63982	Robert Price	09/2015
7377	(21*2^212522-1)/1416323	63971	Lelio R Paula	01/2014
7378	5^91517+98	63968	Lelio R Paula	04/2013
7379	(19*10^63960-43)/3	63961	Robert Price	10/2017
7380	(62*10^63954-17)/9	63955	Robert Price	09/2015
7382	5^91493-4^91493	63951	Predrag Minovic	04/2004
7381	V(364793)	63951	Serge Batalov	03/2015
7384	19^50004+58	63943	Lelio R Paula	05/2013
7383	5*6^82172-7	63943	Lelio R Paula	09/2014
7385	(56*10^63942+223)/9	63943	Robert Price	07/2016
7386	19^50000-24	63938	Lelio R Paula	05/2013
7387	(23*2^212374-1)/27019	63928	Lelio R Paula	01/2014
7388	(9*2^212355-1)/761	63924	Lelio R Paula	01/2014
7390	2^212344-183	63922	Lelio R Paula	08/2011
7389	(58695*2^212336-1)/379	63922	Lelio R Paula	04/2015
7391	10^63916+79	63917	Robert Price	01/2011
7392	10^63916-76823	63916	Patrick De Geest	05/2013
7393	2^212295-25	63908	Lelio R Paula	08/2011
7395	2^212285-2383	63905	Yves Minet	10/2013
7394	267^26336+26336^267	63905	Norbert Schneider	09/2014
7396	(-lucasV(1,2,424552)-2)/1601	63899	Mike Oakes	03/2017
7397	19^49962+60	63890	Lelio R Paula	05/2013
7398	3^133906-113056	63890	Enzo Doria	07/2014
7399	(lucasV(1,2,424451)+2)/3	63886	Mike Oakes	03/2017
7400	3*6^82092+5	63881	Lelio R Paula	09/2014
7401	15441^13706+13706^15441	63879	Hans Havermann	02/2017
7402	2^212154-776351	63865	Paul Bourdelais	03/2013
7403	35^41359+2	63862	Lelio R Paula	05/2013
7404	(61*10^63857-43)/9	63858	Robert Price	09/2015
7405	(2^212131-3)/485	63856	Lelio R Paula	04/2012
7406	2^212112-459995	63853	Enzo Doria	06/2015
7407	15^54290+58	63850	Lelio R Paula	05/2013
7408	3*2^212097-7	63849	Lelio R Paula	04/2014
7409	55^36683-54	63842	Norbert Schneider	08/2014
7410	(509203*2^212056-1)/3	63841	Lelio R Paula	04/2015
7411	(3^133805-7)/172	63839	Lelio R Paula	04/2012
7412	2^212049+149	63834	Lelio R Paula	08/2011
7413	5^91318-18	63829	Lelio R Paula	04/2013
7414	18468^2857+2857^18468	63824	Hans Havermann	03/2017
7415	(2^212024-5)/1111	63823	Lelio R Paula	04/2012
7416	2^211961+12915	63807	Lelio R Paula	02/2013
7417	(3^133707-7)/5780	63791	Lelio R Paula	04/2012
7418	(44*10^63790-161)/9	63791	Robert Price	11/2017
7419	747^22198+22198^747	63782	Norbert Schneider	07/2016
7420	2^211800-17169	63759	Enzo Doria	05/2013
7421	(85*10^63757-1)/3	63759	Robert Price	07/2017
7422	(14*10^63747-11)/3	63748	Erik Branger	09/2014
7423	91*19^49848+6	63746	Curtis Bright	05/2015
7424	18855^2402+2402^18855	63741	Hans Havermann	03/2017
7425	(142*10^63734-7)/9	63736	Robert Price	02/2017
7426	2^211699-111	63728	Lelio R Paula	08/2011
7427	11^61192-5550	63725	Enzo Doria	01/2013
7428	(11*10^63718+7)/9	63719	Serge Batalov	06/2011
7429	6^81872-13	63709	Lelio R Paula	04/2013
7430	3^133522+98	63707	Lelio R Paula	05/2013
7432	2^211607-61	63701	Lelio R Paula	08/2011
7431	5^91135+8	63701	Lelio R Paula	04/2013
7433	11^61157-270	63689	Enzo Doria	07/2012
7435	10^63685+1145141919	63686	Marisa Kirisame	03/2015
7434	10^63685+103837	63686	Patrick De Geest	03/2016
7436	10^63685-130797	63685	Patrick De Geest	03/2016
7437	2^211547+1155*211547	63682	Henri Lifchitz	02/2005
7438	2^211543+45	63681	Lelio R Paula	08/2011
7439	2^211534+43	63679	Lelio R Paula	08/2011
7440	11^61140-60	63671	Enzo Doria	07/2012
7441	2^211491-112321	63666	Enzo Doria	06/2014
7442	19085^2164+2164^19085	63654	Hans Havermann	03/2017
7443	(2^211430-5)/859	63644	Lelio R Paula	04/2012
7444	2^211401-91	63639	Lelio R Paula	08/2011
7445	(6883*2^211378-1)/69	63634	Lelio R Paula	04/2015
7446	(F(152232)^3-F(152231)^3)/F(152230)	63629	Wayne Halsdorf	03/2012
7447	(29*2^211384-1)/50122621	63627	Lelio R Paula	01/2014
7448	2^211333+15015	63618	Lelio R Paula	01/2013
7449	33^41889-32	63610	Norbert Schneider	03/2014
7450	13^57093+18	63599	Lelio R Paula	05/2013
7451	(5*2^211219-1)/9	63583	Lelio R Paula	01/2014
7452	(107*10^63576-17)/9	63578	Robert Price	02/2017
7453	23^46687-1020	63575	Enzo Doria	08/2012
7454	(67607*2^211188+1)/5234319	63573	Lelio R Paula	06/2014
7455	(3^133243+7)/10726	63570	Lelio R Paula	04/2012
7456	(7*2^211181+1)/2745	63570	Lelio R Paula	06/2012
7458	(20^48859-1)/19	63566	Paul Bourdelais	03/2010
7457	2*3^133227+5	63566	Lelio R Paula	04/2014
7459	2^211155+113	63564	Lelio R Paula	08/2011
7460	2^211134+345	63558	Lelio R Paula	09/2011
7461	2^211121+16385	63554	Lelio R Paula	09/2011
7462	16996^5483+5483^16996	63549	Hans Havermann	02/2017
7463	(2^211079+9)/364283	63536	Lelio R Paula	03/2012
7464	3*10^63522+13	63523	Robert Price	08/2017
7465	15852^10157+10157^15852	63516	Hans Havermann	02/2017
7466	2^210948-15873	63502	Enzo Doria	04/2013
7467	7^75136+6	63498	Lelio R Paula	04/2013
7468	2^210928+12915	63496	Lelio R Paula	02/2013
7469	7*10^63493+39	63494	Robert Price	07/2016
7470	2^210909+135	63490	Lelio R Paula	08/2011
7471	(3*2^210832+1)/7	63467	Lelio R Paula	07/2012
7472	8*7^75098-3	63467	Lelio R Paula	09/2014
7473	17683^3882+3882^17683	63466	Hans Havermann	03/2017
7474	Pell-LucasQ(165799)/2	63464	Eric W. Weisstein	11/2006
7475	2^210820-16905	63464	Enzo Doria	05/2013
7476	5^90795-36	63463	Lelio R Paula	04/2013
7477	2^210816-13197	63462	Enzo Doria	10/2012
7478	2^210750+133	63443	Lelio R Paula	08/2011
7479	291^25742+25742^291	63426	Norbert Schneider	09/2014
7480	(3^132908+8)/279859	63408	Lelio R Paula	04/2012
7481	6^81480-139	63404	Lelio R Paula	04/2013
7482	2^210576-173	63390	Lelio R Paula	08/2011
7483	18^50497+55	63388	Lelio R Paula	05/2013
7484	2^210545+11	63381	Lelio R Paula	08/2011
7485	2^210543+63	63380	Lelio R Paula	08/2011
7486	83^33016+82	63361	Norbert Schneider	04/2015
7487	2^210464+98765331	63356	Jason Earls	12/2008
7488	7*10^63351+9	63352	Dmitry Domanov	11/2010
7489	p(13534)#/2+512	63348	Robert Price	05/2017
7490	1741^19546+19546^1741	63345	Serge Batalov	05/2014
7491	10^63336+19819	63337	Patrick De Geest	12/2013
7492	10^63336-122883	63336	Patrick De Geest	12/2013
7493	(19^49523-2^49523)/17	63327	Robert Price	09/2013
7494	(2^210378+47)/95516931	63323	Lelio R Paula	03/2012
7495	31191!2+256	63316	Robert Price	01/2015
7496	16458^7031+7031^16458	63315	Hans Havermann	01/2017
7497	(lucasV(1,2,420636)-2)/(731^2210319)	63303	Mike Oakes	03/2017
7498	(2^210283+7)/1691145	63296	Lelio R Paula	03/2012
7499	2^210217+1299	63282	Lelio R Paula	09/2011
7500	(2^210221-3)/269	63281	Lelio R Paula	04/2012

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Probable Primes Top 10000

(211563 PRPs in the top)