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 ?
2251	Phi(177231,10)	118152	Maksym Voznyy	09/2015
2252	2^392413-112123	118129	Enzo Doria	06/2014
2253	(2^392342+5)/27	118106	Lelio R Paula	04/2014
2254	2^392300-1841429	118095	Enzo Doria	06/2015
2255	2^392220+75241	118070	Enzo Doria	04/2016
2256	10^118009+664447	118010	Patrick De Geest	07/2018
2257	10^118009-20001	118009	Robert Price	01/2018
2258	2^391933+5897	117984	Yves Minet	02/2011
2259	2^391912-1849259	117978	Enzo Doria	08/2015
2260	(2^391812+5)/14181	117944	Lelio R Paula	04/2014
2261	(7*2^391521+1)/285	117858	Lelio R Paula	04/2014
2262	2^391324+90901	117801	Yves Minet	02/2011
2263	2^391301-1859923	117794	Enzo Doria	03/2016
2264	2^391261-4131	117782	Yves Minet	02/2018
2265	(2^391115-7)/11791	117734	Lelio R Paula	04/2014
2266	2^390960+1880881	117691	Enzo Doria	11/2016
2267	2^390897-1860553	117672	Enzo Doria	11/2015
2268	2^390889-115003	117670	Enzo Doria	06/2015
2269	2^390779-30337	117637	Paul Bourdelais	02/2012
2270	11^112916-780	117590	Enzo Doria	12/2012
2271	(16^97613-5^97613)/11	117537	Robert Price	07/2013
2272	(17*2^390272+1)/1983	117482	Lelio R Paula	04/2014
2273	31^78759-30	117459	Theodore Burton	02/2007
2274	2^389998+37	117402	Lelio R Paula	03/2013
2275	2^389478+43	117245	Lelio R Paula	03/2013
2276	(29*2^389351-1)/9	117207	Lelio R Paula	04/2014
2277	(2^389341-7)/3865	117200	Lelio R Paula	03/2014
2278	10^117142+209223	117143	Patrick De Geest	04/2018
2280	10^117142-1000000001	117142	Robert Price	03/2018
2279	10^117142-966057	117142	Patrick De Geest	04/2018
2281	10^117135+360577	117136	Patrick De Geest	07/2018
2282	10^117135-401	117135	Robert Price	01/2018
2283	4*10^117123+79	117124	Robert Price	08/2018
2284	2^389033-12797413	117111	Enzo Doria	04/2016
2285	2^388960-109505	117089	Enzo Doria	04/2014
2286	(2^388928-5)/569	117077	Lelio R Paula	03/2014
2287	2^388888-1529	117067	Yves Minet	01/2013
2288	10^117059+28879	117060	Patrick De Geest	05/2016
2289	(10^117059-71)/1	117059	Serge Batalov	12/2014
2290	(26*10^116999-503)/9	117000	Robert Price	07/2018
2291	3^245154-6256	116969	Enzo Doria	05/2014
2292	2^388536-113495	116961	Enzo Doria	08/2014
2293	2^388469-43	116941	Lelio R Paula	03/2013
2294	(7*2^388372-1)/111	116911	Lelio R Paula	04/2014
2295	(7*2^388335-1)/25	116900	Lelio R Paula	04/2014
2296	2^388180+93	116854	Donovan Johnson	07/2008
2297	(2^388081+7)/1179	116821	Lelio R Paula	03/2014
2298	2^387946-113261	116784	Enzo Doria	07/2014
2299	2^387745+75557	116723	Enzo Doria	04/2016
2300	(7*10^116684+179)/3	116685	Robert Price	09/2018
2301	2^387554+71455	116666	Enzo Doria	04/2016
2302	(2^387447+78557)/365	116631	Lelio R Paula	12/2014
2303	(145*10^116610-1)/9	116612	Serge Batalov	12/2014
2304	(25*10^116601-331)/9	116602	Robert Price	08/2018
2305	(17*2^387284-1)/59	116584	Lelio R Paula	04/2014
2306	(31*2^386968+1)/7	116490	Lelio R Paula	03/2014
2307	2^386947+1869143	116483	Enzo Doria	05/2016
2308	(30^78857-1)/29	116480	Robert Price	12/2011
2309	(2^386903-3)/5	116469	Lelio R Paula	03/2014
2310	2^386389-1864783	116315	Enzo Doria	03/2016
2311	(31*2^386231-1)/1711	116266	Lelio R Paula	03/2014
2312	297^47012+47012^297	116250	Norbert Schneider	07/2018
2313	(2^386087-5)/40959	116220	Lelio R Paula	03/2014
2314	2^385969-823	116189	Yves Minet	05/2012
2315	57^66162+2	116173	Lelio R Paula	08/2013
2316	2^385854+75049	116154	Enzo Doria	04/2016
2317	2^385775-109587	116130	Enzo Doria	04/2014
2318	2^385622+71839	116084	Enzo Doria	04/2016
2319	2^385564+781	116067	Lelio R Paula	01/2012
2320	2^385410+71893	116020	Enzo Doria	04/2016
2321	(25*2^385091+1)/27	115924	Lelio R Paula	04/2014
2322	(11*10^115910-131)/3	115911	Robert Price	09/2018
2323	2^384953-111943	115883	Paul Bourdelais	02/2012
2324	43^70942-2	115882	Lelio R Paula	04/2014
2325	7*10^115863+3	115864	Robert Price	08/2015
2326	2^384834+93	115847	Donovan Johnson	07/2008
2327	2^384809+71297	115840	Enzo Doria	04/2016
2328	(7*2^384759-1)/5	115825	Lelio R Paula	04/2014
2329	(71*10^115810-17)/9	115811	Ray Chandler	08/2011
2330	(97*10^115794-1)/3	115796	Serge Batalov	12/2014
2331	2*10^115784-27	115785	Robert Price	05/2018
2332	10^115773+126739	115774	Patrick De Geest	04/2018
2334	10^115773-1000000001	115773	Robert Price	03/2018
2333	10^115773-396221	115773	Patrick De Geest	04/2018
2335	2^384530+1874305	115756	Enzo Doria	06/2016
2336	(3*2^384524-1)/7631	115750	Lelio R Paula	03/2014
2337	2^384312+81091	115690	Yves Minet	02/2010
2338	(4*10^115668-79)/3	115669	Robert Price	02/2018
2339	(266947#+273808)/(2109157)	115646	Makoto Morimoto	10/2017
2340	3^242337-4042	115625	Enzo Doria	05/2014
2341	(11*2^383859-13)/15	115553	Renaud Lifchitz	03/2011
2342	2^383780-3149	115530	Yves Minet	10/2014
2343	2^383560-455	115464	Yves Minet	03/2012
2344	(2^383544+5)/3	115458	Lelio R Paula	03/2014
2345	89^59221-88^59221	115445	Robert Price	06/2015
2346	2^383347+1869413	115399	Enzo Doria	05/2016
2347	(2^383130-7)/131793	115329	Lelio R Paula	03/2014
2348	(12^106859+1)/13	115320	Paul Bourdelais	02/2010
2349	2^383039+1869509	115307	Enzo Doria	05/2016
2350	(13*2^382968+1)/7	115286	Lelio R Paula	04/2014
2351	2^382633+73697	115185	Enzo Doria	04/2016
2352	2^382509-113593	115147	Enzo Doria	08/2014
2353	2^382502-2791721	115145	Enzo Doria	03/2016
2354	9^120590-120590	115073	Robert Price	03/2014
2355	2^382198+9	115054	Lelio R Paula	03/2013
2356	2^381883-59197	114959	Enzo Doria	10/2015
2358	2^381806-4481	114936	Yves Minet	07/2011
2357	2^381808-1851507	114936	Enzo Doria	08/2015
2359	2^381774-112373	114926	Enzo Doria	06/2014
2360	2^381555-109051	114860	Enzo Doria	04/2014
2361	2^381546-113501	114857	Enzo Doria	08/2014
2362	2^381360-110429	114801	Enzo Doria	05/2014
2363	(66^63079+1)/67	114774	Paul Bourdelais	09/2017
2364	2^381252-115079	114769	Enzo Doria	06/2015
2365	2^381209-29323	114756	Enzo Doria	07/2015
2366	569^41651-568^41651	114754	Jean-Louis Charton	11/2009
2367	2^381201+1873205	114753	Enzo Doria	06/2016
2368	2^380974-112991	114685	Enzo Doria	07/2014
2369	88^58949-87	114626	Norbert Schneider	11/2015
2370	2^380700+91	114603	Lelio R Paula	03/2013
2372	10^114575+3^114576	114576	Mike Oakes	09/2010
2371	10^114575+66561	114576	Patrick De Geest	02/2017
2373	10^114575-581081	114575	Patrick De Geest	02/2017
2374	2^380587-115315	114569	Enzo Doria	06/2015
2375	2^380513-216925	114546	Enzo Doria	05/2014
2376	2^380451-1840087	114528	Enzo Doria	06/2015
2377	(15*2^380388-1)/539	114507	Lelio R Paula	04/2014
2378	2^380279-461347	114476	Enzo Doria	07/2015
2379	2^380021+1871147	114398	Enzo Doria	05/2016
2380	2^380005+1869707	114393	Enzo Doria	05/2016
2381	2^379958-113297	114379	Enzo Doria	07/2014
2382	2^379881-109105	114356	Enzo Doria	04/2014
2383	(21*2^379857-1)/13	114349	Lelio R Paula	03/2014
2384	(4*10^114340+83)/3	114341	Robert Price	02/2018
2385	(4*10^114296+149)/9	114296	Robert Price	04/2018
2386	88^58773-87	114284	Norbert Schneider	11/2015
2387	2^379529-2790283	114250	Enzo Doria	03/2016
2388	2^379522+1869115	114248	Enzo Doria	05/2016
2389	(145*10^114226-1)/9	114228	Serge Batalov	12/2014
2390	2^379317-115033	114186	Enzo Doria	06/2015
2391	(17*2^379246-1)/17407	114162	Lelio R Paula	03/2014
2392	(4*10^114076+143)/3	114077	Robert Price	03/2018
2393	2*10^113941+9	113942	Dmitry Domanov	11/2010
2394	4*10^113905+91	113906	Robert Price	08/2018
2395	4*10^113874-21	113875	Robert Price	09/2018
2396	2^378272-16565	113872	Enzo Doria	04/2013
2397	2^378217-109075	113855	Enzo Doria	04/2014
2398	2^378198+67	113849	Lelio R Paula	03/2013
2399	2^378173-3249	113842	Yves Minet	12/2014
2400	(2^378155-5)/6597	113833	Lelio R Paula	03/2014
2401	92941#+(355049#)/(92941#)	113830	Makoto Morimoto	10/2017
2402	2^378128-262977	113828	Enzo Doria	05/2014
2403	2^378123-113215	113827	Enzo Doria	07/2014
2404	6^146274-18893	113824	Enzo Doria	03/2013
2405	2^378078+75	113813	Lelio R Paula	03/2013
2406	2^377940+63	113772	Lelio R Paula	03/2013
2407	2^377941-2785843	113772	Enzo Doria	04/2016
2408	2^377810+1875109	113733	Enzo Doria	09/2016
2409	2^377803-1838635	113731	Enzo Doria	05/2015
2410	2^377799+52223	113729	Yves Minet	08/2010
2411	11^109190-270	113710	Enzo Doria	12/2012
2412	7*10^113693+9	113694	Robert Price	09/2015
2413	(2*10^113631+529)/9	113631	Robert Price	01/2018
2414	2^377408-2798279	113612	Enzo Doria	04/2016
2415	2^377222+93679	113556	Yves Minet	02/2011
2416	262147#+316847	113552	Makoto Morimoto	02/2016
2417	2^377026-458903	113497	Enzo Doria	04/2015
2418	35^73477-34^73477	113454	Robert Price	05/2012
2419	2^376790+27	113426	Lelio R Paula	03/2013
2420	2^376786-112701	113424	Enzo Doria	06/2014
2421	2^376731+21	113408	Lelio R Paula	03/2013
2422	2^376634+1871245	113379	Enzo Doria	05/2016
2423	(4^188318+17)/3	113379	Robert Price	02/2017
2424	2^376576-344369	113361	Enzo Doria	07/2015
2425	(17*2^376526-1)/223	113345	Lelio R Paula	03/2014
2426	(27*2^376441-1)/811	113319	Lelio R Paula	03/2014
2427	2^376128-21237	113226	Enzo Doria	06/2013
2428	2^375638-1787171	113079	Enzo Doria	03/2016
2429	2^375537+4847	113048	Yves Minet	02/2011
2430	(17^91837+16^91837)/33	113000	Robert Price	08/2013
2431	5F(270343)(F(270343)+1)+1	112997	Serge Batalov	04/2015
2432	2^375350-3221	112992	Yves Minet	07/2011
2434	(13*2^375306+1)/7	112979	Lelio R Paula	03/2014
2433	2^375305+76757	112979	Enzo Doria	05/2016
2435	2^375258+1874989	112964	Enzo Doria	07/2016
2436	(29^77237-1)/28	112950	Robert Price	04/2012
2437	2^375154+74959	112933	Enzo Doria	04/2016
2438	2^374993-2787163	112885	Enzo Doria	11/2015
2439	123^53970+2	112793	Lelio R Paula	06/2013
2440	p(22852)#/2+512	112745	Robert Price	05/2017
2441	(11*10^112742-131)/3	112743	Robert Price	09/2018
2442	2^374441-21049	112718	Enzo Doria	06/2013
2443	(2^374321+1)/3	112682	H.&R. Lifchitz	12/2000
2444	(13^101089-1)/12	112607	Paul Bourdelais	03/2010
2445	3^236011-8828	112606	Enzo Doria	05/2014
2446	39^70666+2	112435	Lelio R Paula	11/2013
2447	(2^373350-7)/3	112390	Lelio R Paula	03/2014
2448	2^373306-1840931	112377	Enzo Doria	06/2015
2449	2^373117+1872107	112320	Enzo Doria	05/2016
2450	2^373040+2792761	112297	Enzo Doria	03/2016
2451	EPrime(112280)	112280	Eric W. Weisstein	10/2010
2452	2^372950+7	112270	Lelio R Paula	03/2013
2453	2^372945+1872167	112268	Enzo Doria	05/2016
2454	2^372695+72113	112193	Enzo Doria	04/2016
2455	2^372689-2563	112191	Yves Minet	07/2014
2456	2^372638-1859441	112176	Enzo Doria	03/2016
2457	3^235074-113056	112159	Enzo Doria	07/2014
2458	(91*10^112098-1)/9	112100	Robert Price	04/2015
2459	2^372310-85061	112077	Paul Bourdelais	02/2012
2460	(10^112067+53)/9	112067	Serge Batalov	07/2015
2461	75^59760+2	112054	Lelio R Paula	08/2013
2462	2^372108+74221	112016	Enzo Doria	04/2016
2463	2^371970-459491	111975	Enzo Doria	05/2015
2464	41^69427-40^69427	111971	Robert Price	07/2012
2465	(10^111902+71)/9	111902	Serge Batalov	07/2015
2466	2^371440-112865	111815	Enzo Doria	06/2014
2467	2^371426-459161	111811	Enzo Doria	05/2015
2468	2^371276-461267	111766	Enzo Doria	07/2015
2469	2^371098-113261	111712	Enzo Doria	07/2014
2470	(7*10^111706-61)/9	111706	Erik Branger	01/2011
2471	2^371044+1869391	111696	Enzo Doria	05/2016
2472	88^57416+87	111645	Norbert Schneider	11/2015
2473	2^370829-109693	111631	Enzo Doria	04/2014
2474	15^94906-2	111619	Lelio R Paula	11/2013
2476	2^370643-37	111575	Yves Minet	01/2012
2475	(2^370655-5)/2439	111575	Lelio R Paula	03/2014
2477	2^370610-3911	111565	Yves Minet	04/2017
2478	286^45405+45405^286	111532	Norbert Schneider	04/2015
2479	4*5^159563-9	111531	Lelio R Paula	11/2014
2480	(4^185225+23)/3	111517	Robert Price	10/2018
2481	2^370393-2797093	111500	Enzo Doria	03/2016
2482	(21*2^370382-1)/629	111495	Lelio R Paula	03/2014
2483	2^370292-2791979	111469	Enzo Doria	03/2016
2484	2^370177-461551	111435	Enzo Doria	07/2015
2485	109^54683-108	111413	Norbert Schneider	02/2017
2486	numbpart(10^10+76282)	111391	Serge Batalov	04/2015
2487	2^369974+733	111374	Lelio R Paula	05/2013
2488	2^369915-286267	111356	Enzo Doria	07/2015
2489	2^369855-1615	111338	Lelio R Paula	05/2017
2490	7*10^111325+3	111326	Robert Price	08/2015
2491	51^65176+2	111293	Lelio R Paula	08/2013
2492	2^369643-1865767	111274	Enzo Doria	03/2016
2493	2^369603+885	111262	Lelio R Paula	05/2017
2494	L(532277)	111240	Renaud Lifchitz	03/2004
2495	105^55033-2	111233	Lelio R Paula	10/2017
2496	(35*10^111232-737)/9	111233	Robert Price	07/2018
2497	2^369392+29835	111199	Lelio R Paula	05/2017
2498	2^369354-3413	111187	Yves Minet	12/2016
2499	2^369296-27	111170	Lelio R Paula	02/2013
2500	2^369239-109837	111153	Enzo Doria	05/2014

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Probable Primes Top 10000

(224926 PRPs in the top)