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	10^117059+28879	117060	Patrick De Geest	05/2016
2252	(10^117059-71)/1	117059	Serge Batalov	12/2014
2253	(26*10^116999-503)/9	117000	Robert Price	07/2018
2254	3^245154-6256	116969	Enzo Doria	05/2014
2255	2^388536-113495	116961	Enzo Doria	08/2014
2256	2^388469-43	116941	Lelio R Paula	03/2013
2257	(7*2^388372-1)/111	116911	Lelio R Paula	04/2014
2258	(7*2^388335-1)/25	116900	Lelio R Paula	04/2014
2259	2^388180+93	116854	Donovan Johnson	07/2008
2260	(2^388081+7)/1179	116821	Lelio R Paula	03/2014
2261	2^387946-113261	116784	Enzo Doria	07/2014
2262	2^387745+75557	116723	Enzo Doria	04/2016
2263	2^387554+71455	116666	Enzo Doria	04/2016
2264	(2^387447+78557)/365	116631	Lelio R Paula	12/2014
2265	(145*10^116610-1)/9	116612	Serge Batalov	12/2014
2266	(17*2^387284-1)/59	116584	Lelio R Paula	04/2014
2267	(31*2^386968+1)/7	116490	Lelio R Paula	03/2014
2268	2^386947+1869143	116483	Enzo Doria	05/2016
2269	(30^78857-1)/29	116480	Robert Price	12/2011
2270	(2^386903-3)/5	116469	Lelio R Paula	03/2014
2271	2^386389-1864783	116315	Enzo Doria	03/2016
2272	(31*2^386231-1)/1711	116266	Lelio R Paula	03/2014
2273	297^47012+47012^297	116250	Norbert Schneider	07/2018
2274	(2^386087-5)/40959	116220	Lelio R Paula	03/2014
2275	2^385969-823	116189	Yves Minet	05/2012
2276	57^66162+2	116173	Lelio R Paula	08/2013
2277	2^385854+75049	116154	Enzo Doria	04/2016
2278	2^385775-109587	116130	Enzo Doria	04/2014
2279	2^385622+71839	116084	Enzo Doria	04/2016
2280	2^385564+781	116067	Lelio R Paula	01/2012
2281	2^385410+71893	116020	Enzo Doria	04/2016
2282	(25*2^385091+1)/27	115924	Lelio R Paula	04/2014
2283	2^384953-111943	115883	Paul Bourdelais	02/2012
2284	43^70942-2	115882	Lelio R Paula	04/2014
2285	7*10^115863+3	115864	Robert Price	08/2015
2286	2^384834+93	115847	Donovan Johnson	07/2008
2287	2^384809+71297	115840	Enzo Doria	04/2016
2288	(7*2^384759-1)/5	115825	Lelio R Paula	04/2014
2289	(71*10^115810-17)/9	115811	Ray Chandler	08/2011
2290	(97*10^115794-1)/3	115796	Serge Batalov	12/2014
2291	2*10^115784-27	115785	Robert Price	05/2018
2292	10^115773+126739	115774	Patrick De Geest	04/2018
2294	10^115773-1000000001	115773	Robert Price	03/2018
2293	10^115773-396221	115773	Patrick De Geest	04/2018
2295	2^384530+1874305	115756	Enzo Doria	06/2016
2296	(3*2^384524-1)/7631	115750	Lelio R Paula	03/2014
2297	2^384312+81091	115690	Yves Minet	02/2010
2298	(4*10^115668-79)/3	115669	Robert Price	02/2018
2299	(266947#+273808)/(2109157)	115646	Makoto Morimoto	10/2017
2300	3^242337-4042	115625	Enzo Doria	05/2014
2301	(11*2^383859-13)/15	115553	Renaud Lifchitz	03/2011
2302	2^383780-3149	115530	Yves Minet	10/2014
2303	2^383560-455	115464	Yves Minet	03/2012
2304	(2^383544+5)/3	115458	Lelio R Paula	03/2014
2305	89^59221-88^59221	115445	Robert Price	06/2015
2306	2^383347+1869413	115399	Enzo Doria	05/2016
2307	(2^383130-7)/131793	115329	Lelio R Paula	03/2014
2308	(12^106859+1)/13	115320	Paul Bourdelais	02/2010
2309	2^383039+1869509	115307	Enzo Doria	05/2016
2310	(13*2^382968+1)/7	115286	Lelio R Paula	04/2014
2311	2^382633+73697	115185	Enzo Doria	04/2016
2312	2^382509-113593	115147	Enzo Doria	08/2014
2313	2^382502-2791721	115145	Enzo Doria	03/2016
2314	9^120590-120590	115073	Robert Price	03/2014
2315	2^382198+9	115054	Lelio R Paula	03/2013
2316	2^381883-59197	114959	Enzo Doria	10/2015
2318	2^381806-4481	114936	Yves Minet	07/2011
2317	2^381808-1851507	114936	Enzo Doria	08/2015
2319	2^381774-112373	114926	Enzo Doria	06/2014
2320	2^381555-109051	114860	Enzo Doria	04/2014
2321	2^381546-113501	114857	Enzo Doria	08/2014
2322	2^381360-110429	114801	Enzo Doria	05/2014
2323	(66^63079+1)/67	114774	Paul Bourdelais	09/2017
2324	2^381252-115079	114769	Enzo Doria	06/2015
2325	2^381209-29323	114756	Enzo Doria	07/2015
2326	569^41651-568^41651	114754	Jean-Louis Charton	11/2009
2327	2^381201+1873205	114753	Enzo Doria	06/2016
2328	2^380974-112991	114685	Enzo Doria	07/2014
2329	88^58949-87	114626	Norbert Schneider	11/2015
2330	2^380700+91	114603	Lelio R Paula	03/2013
2332	10^114575+3^114576	114576	Mike Oakes	09/2010
2331	10^114575+66561	114576	Patrick De Geest	02/2017
2333	10^114575-581081	114575	Patrick De Geest	02/2017
2334	2^380587-115315	114569	Enzo Doria	06/2015
2335	2^380513-216925	114546	Enzo Doria	05/2014
2336	2^380451-1840087	114528	Enzo Doria	06/2015
2337	(15*2^380388-1)/539	114507	Lelio R Paula	04/2014
2338	2^380279-461347	114476	Enzo Doria	07/2015
2339	2^380021+1871147	114398	Enzo Doria	05/2016
2340	2^380005+1869707	114393	Enzo Doria	05/2016
2341	2^379958-113297	114379	Enzo Doria	07/2014
2342	2^379881-109105	114356	Enzo Doria	04/2014
2343	(21*2^379857-1)/13	114349	Lelio R Paula	03/2014
2344	(4*10^114340+83)/3	114341	Robert Price	02/2018
2345	(4*10^114296+149)/9	114296	Robert Price	04/2018
2346	88^58773-87	114284	Norbert Schneider	11/2015
2347	2^379529-2790283	114250	Enzo Doria	03/2016
2348	2^379522+1869115	114248	Enzo Doria	05/2016
2349	(145*10^114226-1)/9	114228	Serge Batalov	12/2014
2350	2^379317-115033	114186	Enzo Doria	06/2015
2351	(17*2^379246-1)/17407	114162	Lelio R Paula	03/2014
2352	(4*10^114076+143)/3	114077	Robert Price	03/2018
2353	2*10^113941+9	113942	Dmitry Domanov	11/2010
2354	2^378272-16565	113872	Enzo Doria	04/2013
2355	2^378217-109075	113855	Enzo Doria	04/2014
2356	2^378198+67	113849	Lelio R Paula	03/2013
2357	2^378173-3249	113842	Yves Minet	12/2014
2358	(2^378155-5)/6597	113833	Lelio R Paula	03/2014
2359	92941#+(355049#)/(92941#)	113830	Makoto Morimoto	10/2017
2360	2^378128-262977	113828	Enzo Doria	05/2014
2361	2^378123-113215	113827	Enzo Doria	07/2014
2362	6^146274-18893	113824	Enzo Doria	03/2013
2363	2^378078+75	113813	Lelio R Paula	03/2013
2364	2^377940+63	113772	Lelio R Paula	03/2013
2365	2^377941-2785843	113772	Enzo Doria	04/2016
2366	2^377810+1875109	113733	Enzo Doria	09/2016
2367	2^377803-1838635	113731	Enzo Doria	05/2015
2368	2^377799+52223	113729	Yves Minet	08/2010
2369	11^109190-270	113710	Enzo Doria	12/2012
2370	7*10^113693+9	113694	Robert Price	09/2015
2371	(2*10^113631+529)/9	113631	Robert Price	01/2018
2372	2^377408-2798279	113612	Enzo Doria	04/2016
2373	2^377222+93679	113556	Yves Minet	02/2011
2374	262147#+316847	113552	Makoto Morimoto	02/2016
2375	2^377026-458903	113497	Enzo Doria	04/2015
2376	35^73477-34^73477	113454	Robert Price	05/2012
2377	2^376790+27	113426	Lelio R Paula	03/2013
2378	2^376786-112701	113424	Enzo Doria	06/2014
2379	2^376731+21	113408	Lelio R Paula	03/2013
2380	2^376634+1871245	113379	Enzo Doria	05/2016
2381	(4^188318+17)/3	113379	Robert Price	02/2017
2382	2^376576-344369	113361	Enzo Doria	07/2015
2383	(17*2^376526-1)/223	113345	Lelio R Paula	03/2014
2384	(27*2^376441-1)/811	113319	Lelio R Paula	03/2014
2385	2^376128-21237	113226	Enzo Doria	06/2013
2386	2^375638-1787171	113079	Enzo Doria	03/2016
2387	2^375537+4847	113048	Yves Minet	02/2011
2388	(17^91837+16^91837)/33	113000	Robert Price	08/2013
2389	5F(270343)(F(270343)+1)+1	112997	Serge Batalov	04/2015
2390	2^375350-3221	112992	Yves Minet	07/2011
2392	(13*2^375306+1)/7	112979	Lelio R Paula	03/2014
2391	2^375305+76757	112979	Enzo Doria	05/2016
2393	2^375258+1874989	112964	Enzo Doria	07/2016
2394	(29^77237-1)/28	112950	Robert Price	04/2012
2395	2^375154+74959	112933	Enzo Doria	04/2016
2396	2^374993-2787163	112885	Enzo Doria	11/2015
2397	123^53970+2	112793	Lelio R Paula	06/2013
2398	p(22852)#/2+512	112745	Robert Price	05/2017
2399	2^374441-21049	112718	Enzo Doria	06/2013
2400	(2^374321+1)/3	112682	H.&R. Lifchitz	12/2000
2401	(13^101089-1)/12	112607	Paul Bourdelais	03/2010
2402	3^236011-8828	112606	Enzo Doria	05/2014
2403	39^70666+2	112435	Lelio R Paula	11/2013
2404	(2^373350-7)/3	112390	Lelio R Paula	03/2014
2405	2^373306-1840931	112377	Enzo Doria	06/2015
2406	2^373117+1872107	112320	Enzo Doria	05/2016
2407	2^373040+2792761	112297	Enzo Doria	03/2016
2408	EPrime(112280)	112280	Eric W. Weisstein	10/2010
2409	2^372950+7	112270	Lelio R Paula	03/2013
2410	2^372945+1872167	112268	Enzo Doria	05/2016
2411	2^372695+72113	112193	Enzo Doria	04/2016
2412	2^372689-2563	112191	Yves Minet	07/2014
2413	2^372638-1859441	112176	Enzo Doria	03/2016
2414	3^235074-113056	112159	Enzo Doria	07/2014
2415	(91*10^112098-1)/9	112100	Robert Price	04/2015
2416	2^372310-85061	112077	Paul Bourdelais	02/2012
2417	(10^112067+53)/9	112067	Serge Batalov	07/2015
2418	75^59760+2	112054	Lelio R Paula	08/2013
2419	2^372108+74221	112016	Enzo Doria	04/2016
2420	2^371970-459491	111975	Enzo Doria	05/2015
2421	41^69427-40^69427	111971	Robert Price	07/2012
2422	(10^111902+71)/9	111902	Serge Batalov	07/2015
2423	2^371440-112865	111815	Enzo Doria	06/2014
2424	2^371426-459161	111811	Enzo Doria	05/2015
2425	2^371276-461267	111766	Enzo Doria	07/2015
2426	2^371098-113261	111712	Enzo Doria	07/2014
2427	(7*10^111706-61)/9	111706	Erik Branger	01/2011
2428	2^371044+1869391	111696	Enzo Doria	05/2016
2429	88^57416+87	111645	Norbert Schneider	11/2015
2430	2^370829-109693	111631	Enzo Doria	04/2014
2431	15^94906-2	111619	Lelio R Paula	11/2013
2433	2^370643-37	111575	Yves Minet	01/2012
2432	(2^370655-5)/2439	111575	Lelio R Paula	03/2014
2434	2^370610-3911	111565	Yves Minet	04/2017
2435	286^45405+45405^286	111532	Norbert Schneider	04/2015
2436	4*5^159563-9	111531	Lelio R Paula	11/2014
2437	2^370393-2797093	111500	Enzo Doria	03/2016
2438	(21*2^370382-1)/629	111495	Lelio R Paula	03/2014
2439	2^370292-2791979	111469	Enzo Doria	03/2016
2440	2^370177-461551	111435	Enzo Doria	07/2015
2441	109^54683-108	111413	Norbert Schneider	02/2017
2442	numbpart(10^10+76282)	111391	Serge Batalov	04/2015
2443	2^369974+733	111374	Lelio R Paula	05/2013
2444	2^369915-286267	111356	Enzo Doria	07/2015
2445	2^369855-1615	111338	Lelio R Paula	05/2017
2446	7*10^111325+3	111326	Robert Price	08/2015
2447	51^65176+2	111293	Lelio R Paula	08/2013
2448	2^369643-1865767	111274	Enzo Doria	03/2016
2449	2^369603+885	111262	Lelio R Paula	05/2017
2450	L(532277)	111240	Renaud Lifchitz	03/2004
2451	105^55033-2	111233	Lelio R Paula	10/2017
2452	(35*10^111232-737)/9	111233	Robert Price	07/2018
2453	2^369392+29835	111199	Lelio R Paula	05/2017
2454	2^369354-3413	111187	Yves Minet	12/2016
2455	2^369296-27	111170	Lelio R Paula	02/2013
2456	2^369239-109837	111153	Enzo Doria	05/2014
2457	2^369224-291839	111148	Enzo Doria	07/2015
2458	2^369216+2798881	111146	Enzo Doria	04/2016
2459	10^111111+163849	111112	Patrick De Geest	03/2017
2460	10^111111-312911	111111	Patrick De Geest	03/2017
2461	2^369092-216923	111108	Enzo Doria	05/2014
2462	2^369081-55	111105	Lelio R Paula	02/2013
2463	88^57124-87	111077	Norbert Schneider	11/2015
2464	2^368980+753	111075	Lelio R Paula	05/2013
2465	2^368946-3623	111064	Yves Minet	03/2017
2466	2^368929+29835	111059	Lelio R Paula	05/2017
2467	4^184463-3^184463	111058	Jean-Louis Charton	12/2004
2468	111^54298+110	111057	Norbert Schneider	04/2017
2469	(4*10^111032-7)/3	111033	Ray Chandler	04/2011
2470	2^368641-460303	110972	Enzo Doria	06/2015
2471	2^368619-109087	110966	Enzo Doria	04/2014
2472	3*2^368489+7	110927	Lelio R Paula	09/2014
2473	97411!4-2	110913	Robert Price	07/2017
2474	(9179*2^368330-1)/35	110881	Lelio R Paula	05/2015
2475	(34*10^110882-7)/9/13/29/1019374319	110871	Makoto Morimoto	05/2016
2476	2^368050-64875	110795	Lelio R Paula	05/2017
2477	2^368048+25	110794	Lelio R Paula	02/2013
2478	69^60239-2	110771	Lelio R Paula	10/2013
2479	(23*2^367952+1)/15717	110762	Lelio R Paula	03/2014
2480	2^367924-69	110757	Lelio R Paula	02/2013
2481	2^367709-109723	110692	Enzo Doria	04/2014
2482	(3*2^367644-1)/107	110671	Lelio R Paula	03/2014
2483	(23*2^367398+1)/57963	110595	Lelio R Paula	03/2014
2484	2^367215+1879223	110543	Enzo Doria	09/2016
2485	2^367141+41	110521	Lelio R Paula	02/2013
2486	2^367126+29835	110516	Lelio R Paula	05/2017
2487	(11*10^110496+49)/3	110497	Robert Price	07/2018
2488	(31*2^366976+1)/7	110472	Lelio R Paula	03/2014
2489	2^366853+5711	110434	Lelio R Paula	05/2017
2490	(21181*2^366833+1)/3	110432	Lelio R Paula	07/2014
2491	2^366816+315	110423	Lelio R Paula	05/2017
2492	2^366775-2787037	110411	Enzo Doria	03/2016
2493	(112*10^110405-1)/3	110407	Serge Batalov	12/2014
2494	2^366751+2797553	110404	Enzo Doria	03/2016
2495	2^366748+255	110403	Lelio R Paula	05/2017
2496	2^366738-2985	110400	Yves Minet	09/2014
2497	(23*2^366739+1)/74575	110396	Lelio R Paula	03/2014
2498	2^366716+1871791	110393	Enzo Doria	05/2016
2499	2^366649+1871687	110373	Enzo Doria	05/2016
2500	2^366629-351205	110367	Enzo Doria	06/2015

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PRP Records

Probable Primes Top 10000

(218736 PRPs in the top)