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	2^383560-455	115464	Yves Minet	03/2012
2252	(2^383544+5)/3	115458	Lelio R Paula	03/2014
2253	89^59221-88^59221	115445	Robert Price	06/2015
2254	2^383347+1869413	115399	Enzo Doria	05/2016
2255	(2^383130-7)/131793	115329	Lelio R Paula	03/2014
2256	(12^106859+1)/13	115320	Paul Bourdelais	02/2010
2257	2^383039+1869509	115307	Enzo Doria	05/2016
2258	(13*2^382968+1)/7	115286	Lelio R Paula	04/2014
2259	2^382633+73697	115185	Enzo Doria	04/2016
2260	2^382509-113593	115147	Enzo Doria	08/2014
2261	2^382502-2791721	115145	Enzo Doria	03/2016
2262	9^120590-120590	115073	Robert Price	03/2014
2263	2^382198+9	115054	Lelio R Paula	03/2013
2264	2^381883-59197	114959	Enzo Doria	10/2015
2266	2^381806-4481	114936	Yves Minet	07/2011
2265	2^381808-1851507	114936	Enzo Doria	08/2015
2267	2^381774-112373	114926	Enzo Doria	06/2014
2268	2^381555-109051	114860	Enzo Doria	04/2014
2269	2^381546-113501	114857	Enzo Doria	08/2014
2270	2^381360-110429	114801	Enzo Doria	05/2014
2271	(66^63079+1)/67	114774	Paul Bourdelais	09/2017
2272	2^381252-115079	114769	Enzo Doria	06/2015
2273	2^381209-29323	114756	Enzo Doria	07/2015
2274	569^41651-568^41651	114754	Jean-Louis Charton	11/2009
2275	2^381201+1873205	114753	Enzo Doria	06/2016
2276	2^380974-112991	114685	Enzo Doria	07/2014
2277	88^58949-87	114626	Norbert Schneider	11/2015
2278	2^380700+91	114603	Lelio R Paula	03/2013
2280	10^114575+3^114576	114576	Mike Oakes	09/2010
2279	10^114575+66561	114576	Patrick De Geest	02/2017
2281	10^114575-581081	114575	Patrick De Geest	02/2017
2282	2^380587-115315	114569	Enzo Doria	06/2015
2283	2^380513-216925	114546	Enzo Doria	05/2014
2284	2^380451-1840087	114528	Enzo Doria	06/2015
2285	(15*2^380388-1)/539	114507	Lelio R Paula	04/2014
2286	2^380279-461347	114476	Enzo Doria	07/2015
2287	2^380021+1871147	114398	Enzo Doria	05/2016
2288	2^380005+1869707	114393	Enzo Doria	05/2016
2289	2^379958-113297	114379	Enzo Doria	07/2014
2290	2^379881-109105	114356	Enzo Doria	04/2014
2291	(21*2^379857-1)/13	114349	Lelio R Paula	03/2014
2292	(4*10^114340+83)/3	114341	Robert Price	02/2018
2293	(4*10^114296+149)/9	114296	Robert Price	04/2018
2294	88^58773-87	114284	Norbert Schneider	11/2015
2295	2^379529-2790283	114250	Enzo Doria	03/2016
2296	2^379522+1869115	114248	Enzo Doria	05/2016
2297	(145*10^114226-1)/9	114228	Serge Batalov	12/2014
2298	2^379317-115033	114186	Enzo Doria	06/2015
2299	(17*2^379246-1)/17407	114162	Lelio R Paula	03/2014
2300	(4*10^114076+143)/3	114077	Robert Price	03/2018
2301	2*10^113941+9	113942	Dmitry Domanov	11/2010
2302	2^378272-16565	113872	Enzo Doria	04/2013
2303	2^378217-109075	113855	Enzo Doria	04/2014
2304	2^378198+67	113849	Lelio R Paula	03/2013
2305	2^378173-3249	113842	Yves Minet	12/2014
2306	(2^378155-5)/6597	113833	Lelio R Paula	03/2014
2307	92941#+(355049#)/(92941#)	113830	Makoto Morimoto	10/2017
2308	2^378128-262977	113828	Enzo Doria	05/2014
2309	2^378123-113215	113827	Enzo Doria	07/2014
2310	6^146274-18893	113824	Enzo Doria	03/2013
2311	2^378078+75	113813	Lelio R Paula	03/2013
2312	2^377940+63	113772	Lelio R Paula	03/2013
2313	2^377941-2785843	113772	Enzo Doria	04/2016
2314	2^377810+1875109	113733	Enzo Doria	09/2016
2315	2^377803-1838635	113731	Enzo Doria	05/2015
2316	2^377799+52223	113729	Yves Minet	08/2010
2317	11^109190-270	113710	Enzo Doria	12/2012
2318	7*10^113693+9	113694	Robert Price	09/2015
2319	(2*10^113631+529)/9	113631	Robert Price	01/2018
2320	2^377408-2798279	113612	Enzo Doria	04/2016
2321	2^377222+93679	113556	Yves Minet	02/2011
2322	262147#+316847	113552	Makoto Morimoto	02/2016
2323	2^377026-458903	113497	Enzo Doria	04/2015
2324	35^73477-34^73477	113454	Robert Price	05/2012
2325	2^376790+27	113426	Lelio R Paula	03/2013
2326	2^376786-112701	113424	Enzo Doria	06/2014
2327	2^376731+21	113408	Lelio R Paula	03/2013
2328	2^376634+1871245	113379	Enzo Doria	05/2016
2329	(4^188318+17)/3	113379	Robert Price	02/2017
2330	2^376576-344369	113361	Enzo Doria	07/2015
2331	(17*2^376526-1)/223	113345	Lelio R Paula	03/2014
2332	(27*2^376441-1)/811	113319	Lelio R Paula	03/2014
2333	2^376128-21237	113226	Enzo Doria	06/2013
2334	2^375638-1787171	113079	Enzo Doria	03/2016
2335	2^375537+4847	113048	Yves Minet	02/2011
2336	(17^91837+16^91837)/33	113000	Robert Price	08/2013
2337	5F(270343)(F(270343)+1)+1	112997	Serge Batalov	04/2015
2338	2^375350-3221	112992	Yves Minet	07/2011
2339	(13*2^375306+1)/7	112979	Lelio R Paula	03/2014
2340	2^375305+76757	112979	Enzo Doria	05/2016
2341	2^375258+1874989	112964	Enzo Doria	07/2016
2342	(29^77237-1)/28	112950	Robert Price	04/2012
2343	2^375154+74959	112933	Enzo Doria	04/2016
2344	2^374993-2787163	112885	Enzo Doria	11/2015
2345	123^53970+2	112793	Lelio R Paula	06/2013
2346	p(22852)#/2+512	112745	Robert Price	05/2017
2347	2^374441-21049	112718	Enzo Doria	06/2013
2348	(2^374321+1)/3	112682	H.&R. Lifchitz	12/2000
2349	(13^101089-1)/12	112607	Paul Bourdelais	03/2010
2350	3^236011-8828	112606	Enzo Doria	05/2014
2351	39^70666+2	112435	Lelio R Paula	11/2013
2352	(2^373350-7)/3	112390	Lelio R Paula	03/2014
2353	2^373306-1840931	112377	Enzo Doria	06/2015
2354	2^373117+1872107	112320	Enzo Doria	05/2016
2355	2^373040+2792761	112297	Enzo Doria	03/2016
2356	EPrime(112280)	112280	Eric W. Weisstein	10/2010
2357	2^372950+7	112270	Lelio R Paula	03/2013
2358	2^372945+1872167	112268	Enzo Doria	05/2016
2359	2^372695+72113	112193	Enzo Doria	04/2016
2360	2^372689-2563	112191	Yves Minet	07/2014
2361	2^372638-1859441	112176	Enzo Doria	03/2016
2362	3^235074-113056	112159	Enzo Doria	07/2014
2363	(91*10^112098-1)/9	112100	Robert Price	04/2015
2364	2^372310-85061	112077	Paul Bourdelais	02/2012
2365	(10^112067+53)/9	112067	Serge Batalov	07/2015
2366	75^59760+2	112054	Lelio R Paula	08/2013
2367	2^372108+74221	112016	Enzo Doria	04/2016
2368	2^371970-459491	111975	Enzo Doria	05/2015
2369	41^69427-40^69427	111971	Robert Price	07/2012
2370	(10^111902+71)/9	111902	Serge Batalov	07/2015
2371	2^371440-112865	111815	Enzo Doria	06/2014
2372	2^371426-459161	111811	Enzo Doria	05/2015
2373	2^371276-461267	111766	Enzo Doria	07/2015
2374	2^371098-113261	111712	Enzo Doria	07/2014
2375	(7*10^111706-61)/9	111706	Erik Branger	01/2011
2376	2^371044+1869391	111696	Enzo Doria	05/2016
2377	88^57416+87	111645	Norbert Schneider	11/2015
2378	2^370829-109693	111631	Enzo Doria	04/2014
2379	15^94906-2	111619	Lelio R Paula	11/2013
2380	2^370643-37	111575	Yves Minet	01/2012
2381	(2^370655-5)/2439	111575	Lelio R Paula	03/2014
2382	2^370610-3911	111565	Yves Minet	04/2017
2383	286^45405+45405^286	111532	Norbert Schneider	04/2015
2384	4*5^159563-9	111531	Lelio R Paula	11/2014
2385	2^370393-2797093	111500	Enzo Doria	03/2016
2386	(21*2^370382-1)/629	111495	Lelio R Paula	03/2014
2387	2^370292-2791979	111469	Enzo Doria	03/2016
2388	2^370177-461551	111435	Enzo Doria	07/2015
2389	109^54683-108	111413	Norbert Schneider	02/2017
2390	numbpart(10^10+76282)	111391	Serge Batalov	04/2015
2391	2^369974+733	111374	Lelio R Paula	05/2013
2392	2^369915-286267	111356	Enzo Doria	07/2015
2393	2^369855-1615	111338	Lelio R Paula	05/2017
2394	7*10^111325+3	111326	Robert Price	08/2015
2395	51^65176+2	111293	Lelio R Paula	08/2013
2396	2^369643-1865767	111274	Enzo Doria	03/2016
2397	2^369603+885	111262	Lelio R Paula	05/2017
2398	L(532277)	111240	Renaud Lifchitz	03/2004
2399	105^55033-2	111233	Lelio R Paula	10/2017
2400	2^369392+29835	111199	Lelio R Paula	05/2017
2401	2^369354-3413	111187	Yves Minet	12/2016
2402	2^369296-27	111170	Lelio R Paula	02/2013
2403	2^369239-109837	111153	Enzo Doria	05/2014
2404	2^369224-291839	111148	Enzo Doria	07/2015
2405	2^369216+2798881	111146	Enzo Doria	04/2016
2406	10^111111+163849	111112	Patrick De Geest	03/2017
2407	10^111111-312911	111111	Patrick De Geest	03/2017
2408	2^369092-216923	111108	Enzo Doria	05/2014
2409	2^369081-55	111105	Lelio R Paula	02/2013
2410	88^57124-87	111077	Norbert Schneider	11/2015
2411	2^368980+753	111075	Lelio R Paula	05/2013
2412	2^368946-3623	111064	Yves Minet	03/2017
2413	2^368929+29835	111059	Lelio R Paula	05/2017
2414	4^184463-3^184463	111058	Jean-Louis Charton	12/2004
2415	111^54298+110	111057	Norbert Schneider	04/2017
2416	(4*10^111032-7)/3	111033	Ray Chandler	04/2011
2417	2^368641-460303	110972	Enzo Doria	06/2015
2418	2^368619-109087	110966	Enzo Doria	04/2014
2419	3*2^368489+7	110927	Lelio R Paula	09/2014
2420	97411!4-2	110913	Robert Price	07/2017
2421	(9179*2^368330-1)/35	110881	Lelio R Paula	05/2015
2422	(34*10^110882-7)/9/13/29/1019374319	110871	Makoto Morimoto	05/2016
2423	2^368050-64875	110795	Lelio R Paula	05/2017
2424	2^368048+25	110794	Lelio R Paula	02/2013
2425	69^60239-2	110771	Lelio R Paula	10/2013
2426	(23*2^367952+1)/15717	110762	Lelio R Paula	03/2014
2427	2^367924-69	110757	Lelio R Paula	02/2013
2428	2^367709-109723	110692	Enzo Doria	04/2014
2429	(3*2^367644-1)/107	110671	Lelio R Paula	03/2014
2430	(23*2^367398+1)/57963	110595	Lelio R Paula	03/2014
2431	2^367215+1879223	110543	Enzo Doria	09/2016
2432	2^367141+41	110521	Lelio R Paula	02/2013
2433	2^367126+29835	110516	Lelio R Paula	05/2017
2434	(31*2^366976+1)/7	110472	Lelio R Paula	03/2014
2435	2^366853+5711	110434	Lelio R Paula	05/2017
2436	(21181*2^366833+1)/3	110432	Lelio R Paula	07/2014
2437	2^366816+315	110423	Lelio R Paula	05/2017
2438	2^366775-2787037	110411	Enzo Doria	03/2016
2439	(112*10^110405-1)/3	110407	Serge Batalov	12/2014
2440	2^366751+2797553	110404	Enzo Doria	03/2016
2441	2^366748+255	110403	Lelio R Paula	05/2017
2442	2^366738-2985	110400	Yves Minet	09/2014
2443	(23*2^366739+1)/74575	110396	Lelio R Paula	03/2014
2444	2^366716+1871791	110393	Enzo Doria	05/2016
2445	2^366649+1871687	110373	Enzo Doria	05/2016
2446	2^366629-351205	110367	Enzo Doria	06/2015
2447	2^366558+1874479	110345	Enzo Doria	06/2016
2448	18^87853-4409	110280	Enzo Doria	03/2013
2449	2^366218-23	110243	Lelio R Paula	02/2013
2450	(21*2^366193-1)/197	110235	Lelio R Paula	03/2014
2451	2^366178-343991	110231	Enzo Doria	07/2015
2452	2^365944+1871341	110161	Enzo Doria	05/2016
2453	2^365838-461267	110129	Enzo Doria	07/2015
2454	2^365763-6555	110106	Lelio R Paula	04/2017
2455	(2^365689+2^182845+1)/5	110083		11/2006
2456	2^365666-459161	110077	Enzo Doria	05/2015
2457	3*10^110076-7	110077	Robert Price	08/2015
2458	13^98785-72	110041	Lelio R Paula	03/2017
2459	(25^78707+1)/26	110027	Robert Price	06/2013
2460	(7*10^110006-151)/9	110006	Robert Price	02/2018
2461	6^141361-7	110001	Lelio R Paula	11/2014
2462	20^84536+81	109984	Lelio R Paula	03/2017
2463	5*2^365347-9	109982	Lelio R Paula	09/2014
2464	9*6^141303+7	109957	Lelio R Paula	11/2014
2465	78^58099+77	109929	Norbert Schneider	02/2015
2466	2*10^109928-7	109929	Robert Price	10/2015
2467	(27*2^365137-1)/2021	109916	Lelio R Paula	03/2014
2468	(4441*29^75152-24)/7	109905	Curtis Bright	05/2015
2469	(2^365087+7)/6015	109899	Lelio R Paula	01/2014
2470	18^87533-11	109878	Lelio R Paula	04/2017
2471	2^364982-5	109871	Henri Lifchitz	04/2006
2472	2^364936-1867979	109857	Enzo Doria	04/2016
2473	2^364867-112087	109836	Enzo Doria	06/2014
2474	4^182415-85061	109825	Mike Oakes	06/2011
2475	(17^89227+16^89227)/33	109788	Robert Price	08/2013
2476	2^364687-187	109782	Lelio R Paula	01/2012
2477	2^364644+67	109769	Lelio R Paula	01/2012
2478	(9787*2^364625-1)/24947	109763	Lelio R Paula	05/2015
2479	(2^364616+5)/9	109760	Lelio R Paula	01/2014
2480	12^101694+73	109747	Lelio R Paula	03/2017
2481	13^98518-66	109744	Lelio R Paula	03/2017
2482	2^364478-113261	109719	Enzo Doria	07/2014
2483	(24737*2^364454+1)/3	109716	Lelio R Paula	07/2014
2484	(62*10^109673+1)/9	109674	Serge Batalov	11/2010
2485	3^229824+340	109654	Lelio R Paula	03/2017
2486	(2*10^109645-71)/3	109645	Robert Price	12/2017
2487	2^364169-112813	109626	Enzo Doria	06/2014
2488	10^109615+21	109616	Lelio R Paula	03/2017
2489	10^109615-456267	109615	Patrick De Geest	03/2017
2490	2^364094-113	109604	Lelio R Paula	01/2012
2491	(4^182026+11)/3	109591	Robert Price	02/2017
2492	2^364041-6883	109588	Lelio R Paula	09/2011
2493	12^101545+11	109586	Lelio R Paula	03/2017
2494	2^363842-2787101	109528	Enzo Doria	03/2016
2495	(22699*2^363782+1)/763	109511	Lelio R Paula	07/2014
2496	2^363769+5711	109506	Lelio R Paula	04/2017
2497	(31*2^363748+1)/49	109499	Lelio R Paula	03/2014
2498	p(22245)#/2-8	109462	Robert Price	01/2017
2499	2^363556+55	109442	Lelio R Paula	01/2012
2500	(55459*2^363411+1)/81	109401	Lelio R Paula	07/2014

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Probable Primes Top 10000

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