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 ?
2251	(9*2^398145+1)/73	119853	Lelio R Paula	04/2014
2252	(10^119836+77)/3	119836	Robert Price	01/2018
2253	2^398029+1872527	119819	Enzo Doria	05/2016
2254	2^397897-113541	119779	Enzo Doria	08/2014
2255	(21*2^397661-1)/27593	119705	Lelio R Paula	04/2014
2256	(58^67853-1)/57	119653	Paul Bourdelais	09/2017
2257	2^397426+73849	119638	Enzo Doria	04/2016
2258	2^396933-112723	119489	Enzo Doria	06/2014
2259	11^114738-150	119488	Enzo Doria	10/2012
2260	(4*10^119474+149)/9	119474	Robert Price	04/2018
2261	2^396790-21	119446	Lelio R Paula	04/2013
2262	(2^396633-7)/5	119398	Lelio R Paula	04/2014
2263	105^59050+104	119352	Norbert Schneider	11/2016
2264	2^396374+73729	119321	Enzo Doria	04/2016
2265	2^396258-459491	119286	Enzo Doria	05/2015
2266	2^396128-396128-1	119247	Karsten Bonath	06/2018
2267	(2^395986+5)/76881	119199	Lelio R Paula	04/2014
2268	(23*2^395942-1)/91	119190	Lelio R Paula	04/2014
2269	(11*2^395548+1)/3	119073	Lelio R Paula	04/2014
2270	(30^80599+1)/31	119054	Robert Price	07/2013
2271	2^395062-109121	118926	Enzo Doria	04/2014
2272	(2^394918+78557)/3	118882	Lelio R Paula	01/2015
2273	(2^394739+3)/1883	118826	Lelio R Paula	04/2014
2274	2^394266+71389	118686	Enzo Doria	04/2016
2275	2^394215-51261	118671	Tony Prest / Never Odd Or Even	04/2018
2276	(2^394215-48793)/5/5	118670	Tony Prest / Never Odd Or Even	04/2018
2277	(2^394215-17063)/3/3/5	118669	Tony Prest / Never Odd Or Even	04/2018
2278	(2^394215-24393)/5/5/5/5/5	118668	Tony Prest / Never Odd Or Even	04/2018
2279	(2^394215-35885)/3/71/173	118666	Tony Prest / Never Odd Or Even	04/2018
2280	(2^394215-47925)/353/2269	118665	Tony Prest / Never Odd Or Even	04/2018
2281	(2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673	118650	Tony Prest / Never Odd Or Even	04/2018
2282	5^169727+2	118635	Lelio R Paula	08/2013
2283	2^394034-3	118617	M. Frind & P. Underwood	09/2002
2284	(7*10^118607+179)/3	118608	Robert Price	09/2018
2285	3^248572-6242	118599	Enzo Doria	05/2014
2286	(3*2^393964-1)/181	118594	Lelio R Paula	04/2014
2287	7^140303-6	118570	Robert Price	11/2014
2288	2^393427+75683	118434	Enzo Doria	04/2016
2289	2^393376-114749	118418	Enzo Doria	04/2015
2290	2^393180+73	118359	Lelio R Paula	04/2013
2291	p(23881)#/2+256	118328	Robert Price	05/2017
2292	(10^118324+359)/9	118324	Serge Batalov	12/2014
2293	p(23879)#/2+64	118317	Robert Price	03/2017
2294	(53*10^118216+1)/9	118217	Serge Batalov	11/2010
2295	(7*2^392697+1)/15	118214	Renaud Lifchitz	03/2011
2296	(157^53819-1)/156	118179	Alexander Zhirkov	06/2016
2297	(19*2^392551+1)/3	118171	Lelio R Paula	04/2014
2298	2^392516-29219	118160	Enzo Doria	07/2015
2299	Phi(177231,10)	118152	Maksym Voznyy	09/2015
2300	2^392413-112123	118129	Enzo Doria	06/2014
2301	(2^392342+5)/27	118106	Lelio R Paula	04/2014
2302	2^392300-1841429	118095	Enzo Doria	06/2015
2303	2^392220+75241	118070	Enzo Doria	04/2016
2304	10^118009+664447	118010	Patrick De Geest	07/2018
2305	10^118009-20001	118009	Robert Price	01/2018
2306	(14*10^117991+61)/3	117992	Robert Price	12/2018
2307	2^391933+5897	117984	Yves Minet	02/2011
2308	2^391912-1849259	117978	Enzo Doria	08/2015
2309	(2^391812+5)/14181	117944	Lelio R Paula	04/2014
2310	(7*2^391521+1)/285	117858	Lelio R Paula	04/2014
2311	2^391324+90901	117801	Yves Minet	02/2011
2312	2^391301-1859923	117794	Enzo Doria	03/2016
2313	2^391261-4131	117782	Yves Minet	02/2018
2314	(2^391115-7)/11791	117734	Lelio R Paula	04/2014
2315	2^390960+1880881	117691	Enzo Doria	11/2016
2316	2^390897-1860553	117672	Enzo Doria	11/2015
2317	2^390889-115003	117670	Enzo Doria	06/2015
2318	2^390779-30337	117637	Paul Bourdelais	02/2012
2319	11^112916-780	117590	Enzo Doria	12/2012
2320	(16^97613-5^97613)/11	117537	Robert Price	07/2013
2321	(17*2^390272+1)/1983	117482	Lelio R Paula	04/2014
2322	31^78759-30	117459	Theodore Burton	02/2007
2323	2^389998+37	117402	Lelio R Paula	03/2013
2324	(13*10^117249+161)/3	117250	Robert Price	11/2018
2325	2^389478+43	117245	Lelio R Paula	03/2013
2326	(29*2^389351-1)/9	117207	Lelio R Paula	04/2014
2327	(2^389341-7)/3865	117200	Lelio R Paula	03/2014
2328	10^117142+209223	117143	Patrick De Geest	04/2018
2330	10^117142-1000000001	117142	Robert Price	03/2018
2329	10^117142-966057	117142	Patrick De Geest	04/2018
2331	10^117135+360577	117136	Patrick De Geest	07/2018
2332	10^117135-401	117135	Robert Price	01/2018
2333	4*10^117123+79	117124	Robert Price	08/2018
2334	2^389033-12797413	117111	Enzo Doria	04/2016
2335	2^388960-109505	117089	Enzo Doria	04/2014
2336	(2^388928-5)/569	117077	Lelio R Paula	03/2014
2337	2^388888-1529	117067	Yves Minet	01/2013
2338	10^117059+28879	117060	Patrick De Geest	05/2016
2339	(10^117059-71)/1	117059	Serge Batalov	12/2014
2340	(26*10^116999-503)/9	117000	Robert Price	07/2018
2341	3^245154-6256	116969	Enzo Doria	05/2014
2342	2^388536-113495	116961	Enzo Doria	08/2014
2343	2^388469-43	116941	Lelio R Paula	03/2013
2344	(7*2^388372-1)/111	116911	Lelio R Paula	04/2014
2345	(7*2^388335-1)/25	116900	Lelio R Paula	04/2014
2346	2^388180+93	116854	Donovan Johnson	07/2008
2347	(2^388081+7)/1179	116821	Lelio R Paula	03/2014
2348	2^387946-113261	116784	Enzo Doria	07/2014
2349	2^387745+75557	116723	Enzo Doria	04/2016
2350	(7*10^116684+179)/3	116685	Robert Price	09/2018
2351	2^387554+71455	116666	Enzo Doria	04/2016
2352	(2^387447+78557)/365	116631	Lelio R Paula	12/2014
2353	(145*10^116610-1)/9	116612	Serge Batalov	12/2014
2354	(25*10^116601-331)/9	116602	Robert Price	08/2018
2355	(17*2^387284-1)/59	116584	Lelio R Paula	04/2014
2356	(31*2^386968+1)/7	116490	Lelio R Paula	03/2014
2357	2^386947+1869143	116483	Enzo Doria	05/2016
2358	(30^78857-1)/29	116480	Robert Price	12/2011
2359	(2^386903-3)/5	116469	Lelio R Paula	03/2014
2360	2^386389-1864783	116315	Enzo Doria	03/2016
2361	(31*2^386231-1)/1711	116266	Lelio R Paula	03/2014
2362	297^47012+47012^297	116250	Norbert Schneider	07/2018
2363	(2^386087-5)/40959	116220	Lelio R Paula	03/2014
2364	2^385969-823	116189	Yves Minet	05/2012
2365	57^66162+2	116173	Lelio R Paula	08/2013
2366	2^385854+75049	116154	Enzo Doria	04/2016
2367	2^385775-109587	116130	Enzo Doria	04/2014
2368	2^385622+71839	116084	Enzo Doria	04/2016
2369	2^385564+781	116067	Lelio R Paula	01/2012
2370	2^385410+71893	116020	Enzo Doria	04/2016
2371	(25*2^385091+1)/27	115924	Lelio R Paula	04/2014
2372	(11*10^115910-131)/3	115911	Robert Price	09/2018
2373	2^384953-111943	115883	Paul Bourdelais	02/2012
2374	43^70942-2	115882	Lelio R Paula	04/2014
2375	7*10^115863+3	115864	Robert Price	08/2015
2376	2^384834+93	115847	Donovan Johnson	07/2008
2377	2^384809+71297	115840	Enzo Doria	04/2016
2378	(7*2^384759-1)/5	115825	Lelio R Paula	04/2014
2379	(71*10^115810-17)/9	115811	Ray Chandler	08/2011
2380	(97*10^115794-1)/3	115796	Serge Batalov	12/2014
2381	2*10^115784-27	115785	Robert Price	05/2018
2382	10^115773+126739	115774	Patrick De Geest	04/2018
2384	10^115773-1000000001	115773	Robert Price	03/2018
2383	10^115773-396221	115773	Patrick De Geest	04/2018
2385	2^384530+1874305	115756	Enzo Doria	06/2016
2386	(3*2^384524-1)/7631	115750	Lelio R Paula	03/2014
2387	2^384312+81091	115690	Yves Minet	02/2010
2388	(4*10^115668-79)/3	115669	Robert Price	02/2018
2389	(266947#+273808)/(2109157)	115646	Makoto Morimoto	10/2017
2390	3^242337-4042	115625	Enzo Doria	05/2014
2391	(11*2^383859-13)/15	115553	Renaud Lifchitz	03/2011
2392	2^383780-3149	115530	Yves Minet	10/2014
2393	(41*10^115523-383)/9	115524	Robert Price	11/2018
2394	2^383560-455	115464	Yves Minet	03/2012
2395	(2^383544+5)/3	115458	Lelio R Paula	03/2014
2396	89^59221-88^59221	115445	Robert Price	06/2015
2397	2^383347+1869413	115399	Enzo Doria	05/2016
2398	(2^383130-7)/131793	115329	Lelio R Paula	03/2014
2399	(12^106859+1)/13	115320	Paul Bourdelais	02/2010
2400	2^383039+1869509	115307	Enzo Doria	05/2016
2401	(13*2^382968+1)/7	115286	Lelio R Paula	04/2014
2402	2^382633+73697	115185	Enzo Doria	04/2016
2403	2^382509-113593	115147	Enzo Doria	08/2014
2404	2^382502-2791721	115145	Enzo Doria	03/2016
2405	9^120590-120590	115073	Robert Price	03/2014
2406	2^382198+9	115054	Lelio R Paula	03/2013
2407	2^381883-59197	114959	Enzo Doria	10/2015
2409	2^381806-4481	114936	Yves Minet	07/2011
2408	2^381808-1851507	114936	Enzo Doria	08/2015
2410	2^381774-112373	114926	Enzo Doria	06/2014
2411	2^381555-109051	114860	Enzo Doria	04/2014
2412	2^381546-113501	114857	Enzo Doria	08/2014
2413	2^381360-110429	114801	Enzo Doria	05/2014
2414	(66^63079+1)/67	114774	Paul Bourdelais	09/2017
2415	2^381252-115079	114769	Enzo Doria	06/2015
2416	2^381209-29323	114756	Enzo Doria	07/2015
2417	569^41651-568^41651	114754	Jean-Louis Charton	11/2009
2418	2^381201+1873205	114753	Enzo Doria	06/2016
2419	2^380974-112991	114685	Enzo Doria	07/2014
2420	88^58949-87	114626	Norbert Schneider	11/2015
2421	2^380700+91	114603	Lelio R Paula	03/2013
2423	10^114575+3^114576	114576	Mike Oakes	09/2010
2422	10^114575+66561	114576	Patrick De Geest	02/2017
2424	10^114575-581081	114575	Patrick De Geest	02/2017
2425	2^380587-115315	114569	Enzo Doria	06/2015
2426	2^380513-216925	114546	Enzo Doria	05/2014
2427	2^380451-1840087	114528	Enzo Doria	06/2015
2428	(15*2^380388-1)/539	114507	Lelio R Paula	04/2014
2429	2^380279-461347	114476	Enzo Doria	07/2015
2430	2^380021+1871147	114398	Enzo Doria	05/2016
2431	2^380005+1869707	114393	Enzo Doria	05/2016
2432	2^379958-113297	114379	Enzo Doria	07/2014
2433	2^379881-109105	114356	Enzo Doria	04/2014
2434	(21*2^379857-1)/13	114349	Lelio R Paula	03/2014
2435	(4*10^114340+83)/3	114341	Robert Price	02/2018
2436	(4*10^114296+149)/9	114296	Robert Price	04/2018
2437	88^58773-87	114284	Norbert Schneider	11/2015
2438	2^379529-2790283	114250	Enzo Doria	03/2016
2439	2^379522+1869115	114248	Enzo Doria	05/2016
2440	(145*10^114226-1)/9	114228	Serge Batalov	12/2014
2441	2^379317-115033	114186	Enzo Doria	06/2015
2442	(17*2^379246-1)/17407	114162	Lelio R Paula	03/2014
2443	(4*10^114076+143)/3	114077	Robert Price	03/2018
2444	2*10^113941+9	113942	Dmitry Domanov	11/2010
2445	4*10^113905+91	113906	Robert Price	08/2018
2446	4*10^113874-21	113875	Robert Price	09/2018
2447	2^378272-16565	113872	Enzo Doria	04/2013
2448	2^378217-109075	113855	Enzo Doria	04/2014
2449	2^378198+67	113849	Lelio R Paula	03/2013
2450	2^378173-3249	113842	Yves Minet	12/2014
2451	(2^378155-5)/6597	113833	Lelio R Paula	03/2014
2452	92941#+(355049#)/(92941#)	113830	Makoto Morimoto	10/2017
2453	2^378128-262977	113828	Enzo Doria	05/2014
2454	2^378123-113215	113827	Enzo Doria	07/2014
2455	6^146274-18893	113824	Enzo Doria	03/2013
2456	2^378078+75	113813	Lelio R Paula	03/2013
2457	2^377940+63	113772	Lelio R Paula	03/2013
2458	2^377941-2785843	113772	Enzo Doria	04/2016
2459	2^377810+1875109	113733	Enzo Doria	09/2016
2460	2^377803-1838635	113731	Enzo Doria	05/2015
2461	2^377799+52223	113729	Yves Minet	08/2010
2462	11^109190-270	113710	Enzo Doria	12/2012
2463	7*10^113693+9	113694	Robert Price	09/2015
2464	(2*10^113631+529)/9	113631	Robert Price	01/2018
2465	2^377408-2798279	113612	Enzo Doria	04/2016
2466	2^377222+93679	113556	Yves Minet	02/2011
2467	262147#+316847	113552	Makoto Morimoto	02/2016
2468	2^377026-458903	113497	Enzo Doria	04/2015
2469	35^73477-34^73477	113454	Robert Price	05/2012
2470	2^376790+27	113426	Lelio R Paula	03/2013
2471	2^376786-112701	113424	Enzo Doria	06/2014
2472	2^376731+21	113408	Lelio R Paula	03/2013
2474	2^376634+1871245	113379	Enzo Doria	05/2016
2473	(4^188318+17)/3	113379	Robert Price	02/2017
2475	2^376576-344369	113361	Enzo Doria	07/2015
2476	(17*2^376526-1)/223	113345	Lelio R Paula	03/2014
2477	(27*2^376441-1)/811	113319	Lelio R Paula	03/2014
2478	2^376128-21237	113226	Enzo Doria	06/2013
2479	2^375638-1787171	113079	Enzo Doria	03/2016
2480	2^375537+4847	113048	Yves Minet	02/2011
2481	(17^91837+16^91837)/33	113000	Robert Price	08/2013
2482	5F(270343)(F(270343)+1)+1	112997	Serge Batalov	04/2015
2483	2^375350-3221	112992	Yves Minet	07/2011
2485	(13*2^375306+1)/7	112979	Lelio R Paula	03/2014
2484	2^375305+76757	112979	Enzo Doria	05/2016
2486	2^375258+1874989	112964	Enzo Doria	07/2016
2487	(29^77237-1)/28	112950	Robert Price	04/2012
2488	2^375154+74959	112933	Enzo Doria	04/2016
2489	2^374993-2787163	112885	Enzo Doria	11/2015
2490	123^53970+2	112793	Lelio R Paula	06/2013
2491	p(22852)#/2+512	112745	Robert Price	05/2017
2492	(11*10^112742-131)/3	112743	Robert Price	09/2018
2493	2^374441-21049	112718	Enzo Doria	06/2013
2494	(2^374321+1)/3	112682	H.&R. Lifchitz	12/2000
2495	(13^101089-1)/12	112607	Paul Bourdelais	03/2010
2496	3^236011-8828	112606	Enzo Doria	05/2014
2497	39^70666+2	112435	Lelio R Paula	11/2013
2498	(2^373350-7)/3	112390	Lelio R Paula	03/2014
2499	2^373306-1840931	112377	Enzo Doria	06/2015
2500	2^373117+1872107	112320	Enzo Doria	05/2016

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Probable Primes Top 10000

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