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	2^402715+1874223	121230	Enzo Doria	06/2016
2252	(35*10^121229-593)/9	121230	Robert Price	07/2018
2253	(91^61879+1)/92	121222	Paul Bourdelais	09/2017
2254	7*10^121144+9	121145	Robert Price	09/2015
2255	2^401725-113251	120932	Enzo Doria	07/2014
2256	(15*2^401677-1)/19	120917	Lelio R Paula	05/2014
2257	2^401652+73711	120910	Enzo Doria	04/2016
2258	(2^401632+3)/79	120902	Lelio R Paula	04/2014
2259	2^401406-2791331	120836	Enzo Doria	03/2016
2260	(28^83497+1)/29	120832	Robert Price	07/2013
2261	2^401369+1867367	120825	Enzo Doria	03/2016
2262	(10^120782+29)/3	120782	Serge Batalov	12/2014
2263	2^401215-1657	120778	Yves Minet	07/2014
2264	2^401159+53	120761	Lelio R Paula	10/2013
2265	2^401031-113047	120723	Enzo Doria	07/2014
2266	(29*2^400909-1)/303	120685	Lelio R Paula	04/2014
2267	2^400571-15	120584	Lelio R Paula	10/2013
2268	(10^120574+359)/9	120574	Serge Batalov	12/2014
2269	2^400424-216413	120540	Enzo Doria	04/2013
2270	(17*2^400200-1)/587	120471	Lelio R Paula	05/2014
2271	2^400166+1874899	120462	Enzo Doria	06/2016
2272	(3*2^400045-1)/865	120424	Lelio R Paula	04/2014
2273	2^399966+73759	120402	Enzo Doria	04/2016
2274	(112*10^120395-1)/3	120397	Serge Batalov	12/2014
2275	2^399918-95	120388	Lelio R Paula	04/2013
2276	2^399792-1849259	120350	Enzo Doria	08/2015
2277	9*10^120342-7	120343	Robert Price	09/2015
2278	(13*10^120306-37)/3	120307	Robert Price	01/2019
2279	2^399526-1861721	120270	Enzo Doria	11/2015
2280	(10^(260126+1)+3610^60126-1)/9	120253	Robert Price	10/2015
2281	2^399322-2798111	120208	Enzo Doria	04/2016
2282	72^64693-71^64693	120157	Robert Price	03/2014
2283	2^399111-28489	120145	Enzo Doria	08/2015
2285	2^398877+105	120074	Donovan Johnson	01/2006
2284	(101*10^120072-87)/7	120074	Hans Havermann	02/2015
2286	(88^61751+1)/89	120072	Paul Bourdelais	09/2017
2287	2^398710+57	120024	Lelio R Paula	04/2013
2288	2^398691-115057	120018	Enzo Doria	06/2015
2289	L(574219)	120005	Renaud Lifchitz	03/2004
2290	2^398571+60413	119982	Yves Minet	03/2011
2291	p(24179)#/2-64	119949	Robert Price	04/2017
2292	2^398448+1872001	119945	Enzo Doria	05/2016
2293	8*10^119930-3	119931	Ray Chandler	04/2011
2294	(10^119880+179)/9	119880	Serge Batalov	12/2014
2295	(9*2^398145+1)/73	119853	Lelio R Paula	04/2014
2296	(10^119836+77)/3	119836	Robert Price	01/2018
2297	2^398029+1872527	119819	Enzo Doria	05/2016
2298	2^397897-113541	119779	Enzo Doria	08/2014
2299	(21*2^397661-1)/27593	119705	Lelio R Paula	04/2014
2300	(58^67853-1)/57	119653	Paul Bourdelais	09/2017
2301	2^397426+73849	119638	Enzo Doria	04/2016
2302	2^396933-112723	119489	Enzo Doria	06/2014
2303	11^114738-150	119488	Enzo Doria	10/2012
2304	(4*10^119474+149)/9	119474	Robert Price	04/2018
2305	2^396790-21	119446	Lelio R Paula	04/2013
2306	(2^396633-7)/5	119398	Lelio R Paula	04/2014
2308	105^59050+104	119352	Norbert Schneider	11/2016
2307	126^56824-125	119352	Norbert Schneider	12/2018
2309	2^396374+73729	119321	Enzo Doria	04/2016
2310	2^396258-459491	119286	Enzo Doria	05/2015
2311	2^396128-396128-1	119247	Karsten Bonath	06/2018
2312	(2^395986+5)/76881	119199	Lelio R Paula	04/2014
2313	(23*2^395942-1)/91	119190	Lelio R Paula	04/2014
2314	(11*2^395548+1)/3	119073	Lelio R Paula	04/2014
2315	(30^80599+1)/31	119054	Robert Price	07/2013
2316	(43*10^119024-403)/9	119025	Robert Price	01/2019
2317	2^395062-109121	118926	Enzo Doria	04/2014
2318	(2^394918+78557)/3	118882	Lelio R Paula	01/2015
2319	(2^394739+3)/1883	118826	Lelio R Paula	04/2014
2320	2^394266+71389	118686	Enzo Doria	04/2016
2321	2^394215-51261	118671	Tony Prest / Never Odd Or Even	04/2018
2322	(2^394215-48793)/5/5	118670	Tony Prest / Never Odd Or Even	04/2018
2323	(2^394215-17063)/3/3/5	118669	Tony Prest / Never Odd Or Even	04/2018
2324	(2^394215-24393)/5/5/5/5/5	118668	Tony Prest / Never Odd Or Even	04/2018
2325	(2^394215-35885)/3/71/173	118666	Tony Prest / Never Odd Or Even	04/2018
2326	(2^394215-47925)/353/2269	118665	Tony Prest / Never Odd Or Even	04/2018
2327	(2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673	118650	Tony Prest / Never Odd Or Even	04/2018
2328	(17*10^118635+13)/3	118636	Robert Price	01/2019
2329	5^169727+2	118635	Lelio R Paula	08/2013
2330	2^394034-3	118617	M. Frind & P. Underwood	09/2002
2331	(7*10^118607+179)/3	118608	Robert Price	09/2018
2332	3^248572-6242	118599	Enzo Doria	05/2014
2333	(3*2^393964-1)/181	118594	Lelio R Paula	04/2014
2334	7^140303-6	118570	Robert Price	11/2014
2335	2^393427+75683	118434	Enzo Doria	04/2016
2336	2^393376-114749	118418	Enzo Doria	04/2015
2337	2^393180+73	118359	Lelio R Paula	04/2013
2338	p(23881)#/2+256	118328	Robert Price	05/2017
2339	(10^118324+359)/9	118324	Serge Batalov	12/2014
2340	p(23879)#/2+64	118317	Robert Price	03/2017
2341	(53*10^118216+1)/9	118217	Serge Batalov	11/2010
2342	(7*2^392697+1)/15	118214	Renaud Lifchitz	03/2011
2343	(157^53819-1)/156	118179	Alexander Zhirkov	06/2016
2344	(19*2^392551+1)/3	118171	Lelio R Paula	04/2014
2345	2^392516-29219	118160	Enzo Doria	07/2015
2346	Phi(177231,10)	118152	Maksym Voznyy	09/2015
2347	2^392413-112123	118129	Enzo Doria	06/2014
2348	(2^392342+5)/27	118106	Lelio R Paula	04/2014
2349	2^392300-1841429	118095	Enzo Doria	06/2015
2350	2^392220+75241	118070	Enzo Doria	04/2016
2351	10^118009+664447	118010	Patrick De Geest	07/2018
2352	10^118009-20001	118009	Robert Price	01/2018
2353	(14*10^117991+61)/3	117992	Robert Price	12/2018
2354	2^391933+5897	117984	Yves Minet	02/2011
2355	2^391912-1849259	117978	Enzo Doria	08/2015
2356	(2^391812+5)/14181	117944	Lelio R Paula	04/2014
2357	(7*2^391521+1)/285	117858	Lelio R Paula	04/2014
2358	2^391324+90901	117801	Yves Minet	02/2011
2359	2^391301-1859923	117794	Enzo Doria	03/2016
2360	2^391261-4131	117782	Yves Minet	02/2018
2361	(2^391115-7)/11791	117734	Lelio R Paula	04/2014
2362	2^390960+1880881	117691	Enzo Doria	11/2016
2363	2^390897-1860553	117672	Enzo Doria	11/2015
2364	2^390889-115003	117670	Enzo Doria	06/2015
2365	2^390779-30337	117637	Paul Bourdelais	02/2012
2366	11^112916-780	117590	Enzo Doria	12/2012
2367	(16^97613-5^97613)/11	117537	Robert Price	07/2013
2368	(17*2^390272+1)/1983	117482	Lelio R Paula	04/2014
2369	31^78759-30	117459	Theodore Burton	02/2007
2370	2^389998+37	117402	Lelio R Paula	03/2013
2371	(13*10^117249+161)/3	117250	Robert Price	11/2018
2372	2^389478+43	117245	Lelio R Paula	03/2013
2373	(29*2^389351-1)/9	117207	Lelio R Paula	04/2014
2374	(2^389341-7)/3865	117200	Lelio R Paula	03/2014
2375	10^117142+209223	117143	Patrick De Geest	04/2018
2377	10^117142-1000000001	117142	Robert Price	03/2018
2376	10^117142-966057	117142	Patrick De Geest	04/2018
2378	10^117135+360577	117136	Patrick De Geest	07/2018
2379	10^117135-401	117135	Robert Price	01/2018
2380	4*10^117123+79	117124	Robert Price	08/2018
2381	2^389033-12797413	117111	Enzo Doria	04/2016
2382	2^388960-109505	117089	Enzo Doria	04/2014
2383	(2^388928-5)/569	117077	Lelio R Paula	03/2014
2384	2^388888-1529	117067	Yves Minet	01/2013
2385	10^117059+28879	117060	Patrick De Geest	05/2016
2386	(10^117059-71)/1	117059	Serge Batalov	12/2014
2387	(26*10^116999-503)/9	117000	Robert Price	07/2018
2388	3^245154-6256	116969	Enzo Doria	05/2014
2389	5*10^116966-43	116967	Robert Price	01/2019
2390	2^388536-113495	116961	Enzo Doria	08/2014
2391	2^388469-43	116941	Lelio R Paula	03/2013
2392	(7*2^388372-1)/111	116911	Lelio R Paula	04/2014
2393	(7*2^388335-1)/25	116900	Lelio R Paula	04/2014
2394	2^388180+93	116854	Donovan Johnson	07/2008
2395	(2^388081+7)/1179	116821	Lelio R Paula	03/2014
2396	2^387946-113261	116784	Enzo Doria	07/2014
2397	2^387745+75557	116723	Enzo Doria	04/2016
2398	(7*10^116684+179)/3	116685	Robert Price	09/2018
2399	2^387554+71455	116666	Enzo Doria	04/2016
2400	(2^387447+78557)/365	116631	Lelio R Paula	12/2014
2401	(145*10^116610-1)/9	116612	Serge Batalov	12/2014
2402	(25*10^116601-331)/9	116602	Robert Price	08/2018
2403	(17*2^387284-1)/59	116584	Lelio R Paula	04/2014
2404	(31*2^386968+1)/7	116490	Lelio R Paula	03/2014
2405	2^386947+1869143	116483	Enzo Doria	05/2016
2406	(30^78857-1)/29	116480	Robert Price	12/2011
2407	(2^386903-3)/5	116469	Lelio R Paula	03/2014
2408	2^386389-1864783	116315	Enzo Doria	03/2016
2409	(31*2^386231-1)/1711	116266	Lelio R Paula	03/2014
2410	297^47012+47012^297	116250	Norbert Schneider	07/2018
2411	(2^386087-5)/40959	116220	Lelio R Paula	03/2014
2412	2^385969-823	116189	Yves Minet	05/2012
2413	57^66162+2	116173	Lelio R Paula	08/2013
2414	2^385854+75049	116154	Enzo Doria	04/2016
2415	2^385775-109587	116130	Enzo Doria	04/2014
2416	2^385622+71839	116084	Enzo Doria	04/2016
2417	2^385564+781	116067	Lelio R Paula	01/2012
2418	2^385410+71893	116020	Enzo Doria	04/2016
2419	(25*2^385091+1)/27	115924	Lelio R Paula	04/2014
2420	(11*10^115910-131)/3	115911	Robert Price	09/2018
2421	2^384953-111943	115883	Paul Bourdelais	02/2012
2422	43^70942-2	115882	Lelio R Paula	04/2014
2423	7*10^115863+3	115864	Robert Price	08/2015
2424	2^384834+93	115847	Donovan Johnson	07/2008
2425	2^384809+71297	115840	Enzo Doria	04/2016
2426	(7*2^384759-1)/5	115825	Lelio R Paula	04/2014
2427	(71*10^115810-17)/9	115811	Ray Chandler	08/2011
2428	(97*10^115794-1)/3	115796	Serge Batalov	12/2014
2429	2*10^115784-27	115785	Robert Price	05/2018
2430	10^115773+126739	115774	Patrick De Geest	04/2018
2432	10^115773-1000000001	115773	Robert Price	03/2018
2431	10^115773-396221	115773	Patrick De Geest	04/2018
2433	2^384530+1874305	115756	Enzo Doria	06/2016
2434	(3*2^384524-1)/7631	115750	Lelio R Paula	03/2014
2435	2^384312+81091	115690	Yves Minet	02/2010
2436	(4*10^115668-79)/3	115669	Robert Price	02/2018
2437	(266947#+273808)/(2109157)	115646	Makoto Morimoto	10/2017
2438	3^242337-4042	115625	Enzo Doria	05/2014
2439	(11*2^383859-13)/15	115553	Renaud Lifchitz	03/2011
2440	2^383780-3149	115530	Yves Minet	10/2014
2441	(41*10^115523-383)/9	115524	Robert Price	11/2018
2442	2^383560-455	115464	Yves Minet	03/2012
2443	(2^383544+5)/3	115458	Lelio R Paula	03/2014
2444	89^59221-88^59221	115445	Robert Price	06/2015
2445	2^383347+1869413	115399	Enzo Doria	05/2016
2446	(2^383130-7)/131793	115329	Lelio R Paula	03/2014
2447	(12^106859+1)/13	115320	Paul Bourdelais	02/2010
2448	2^383039+1869509	115307	Enzo Doria	05/2016
2449	(13*2^382968+1)/7	115286	Lelio R Paula	04/2014
2450	2^382633+73697	115185	Enzo Doria	04/2016
2451	2^382509-113593	115147	Enzo Doria	08/2014
2452	2^382502-2791721	115145	Enzo Doria	03/2016
2453	9^120590-120590	115073	Robert Price	03/2014
2454	2^382198+9	115054	Lelio R Paula	03/2013
2455	2^381883-59197	114959	Enzo Doria	10/2015
2457	2^381806-4481	114936	Yves Minet	07/2011
2456	2^381808-1851507	114936	Enzo Doria	08/2015
2458	2^381774-112373	114926	Enzo Doria	06/2014
2459	2^381555-109051	114860	Enzo Doria	04/2014
2460	2^381546-113501	114857	Enzo Doria	08/2014
2461	2^381360-110429	114801	Enzo Doria	05/2014
2462	(66^63079+1)/67	114774	Paul Bourdelais	09/2017
2463	2^381252-115079	114769	Enzo Doria	06/2015
2464	2^381209-29323	114756	Enzo Doria	07/2015
2465	569^41651-568^41651	114754	Jean-Louis Charton	11/2009
2466	2^381201+1873205	114753	Enzo Doria	06/2016
2467	2^380974-112991	114685	Enzo Doria	07/2014
2468	88^58949-87	114626	Norbert Schneider	11/2015
2469	2^380700+91	114603	Lelio R Paula	03/2013
2471	10^114575+3^114576	114576	Mike Oakes	09/2010
2470	10^114575+66561	114576	Patrick De Geest	02/2017
2472	10^114575-581081	114575	Patrick De Geest	02/2017
2473	2^380587-115315	114569	Enzo Doria	06/2015
2474	2^380513-216925	114546	Enzo Doria	05/2014
2475	2^380451-1840087	114528	Enzo Doria	06/2015
2476	(15*2^380388-1)/539	114507	Lelio R Paula	04/2014
2477	2^380279-461347	114476	Enzo Doria	07/2015
2478	2^380021+1871147	114398	Enzo Doria	05/2016
2479	2^380005+1869707	114393	Enzo Doria	05/2016
2480	2^379958-113297	114379	Enzo Doria	07/2014
2481	2^379881-109105	114356	Enzo Doria	04/2014
2482	(21*2^379857-1)/13	114349	Lelio R Paula	03/2014
2483	(4*10^114340+83)/3	114341	Robert Price	02/2018
2484	(4*10^114296+149)/9	114296	Robert Price	04/2018
2485	88^58773-87	114284	Norbert Schneider	11/2015
2486	2^379529-2790283	114250	Enzo Doria	03/2016
2487	2^379522+1869115	114248	Enzo Doria	05/2016
2488	(145*10^114226-1)/9	114228	Serge Batalov	12/2014
2489	2^379317-115033	114186	Enzo Doria	06/2015
2490	(17*2^379246-1)/17407	114162	Lelio R Paula	03/2014
2491	(4*10^114076+143)/3	114077	Robert Price	03/2018
2492	2*10^113941+9	113942	Dmitry Domanov	11/2010
2493	4*10^113905+91	113906	Robert Price	08/2018
2494	4*10^113874-21	113875	Robert Price	09/2018
2495	2^378272-16565	113872	Enzo Doria	04/2013
2496	2^378217-109075	113855	Enzo Doria	04/2014
2497	2^378198+67	113849	Lelio R Paula	03/2013
2498	2^378173-3249	113842	Yves Minet	12/2014
2499	(2^378155-5)/6597	113833	Lelio R Paula	03/2014
2500	92941#+(355049#)/(92941#)	113830	Makoto Morimoto	10/2017

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Probable Primes Top 10000

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