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	97^61575-2	122336	Lelio R Paula	12/2014
2252	2^406298+2799109	122308	Enzo Doria	04/2016
2253	(27*2^406241-1)/10277	122289	Lelio R Paula	04/2014
2254	2^406229-1849993	122288	Enzo Doria	08/2015
2255	3*10^122274+7	122275	Robert Price	07/2015
2256	2^406117+1876577	122254	Enzo Doria	07/2016
2257	3^256199-2^256199	122238	Mike Oakes	06/2005
2258	2^405992-78557	122216	Jorge Menendez	03/2018
2259	(8*10^122203+43)/3	122204	Robert Price	06/2018
2260	2^405774+179149	122151	Enzo Doria	06/2016
2261	5*10^122082+41	122083	Robert Price	03/2019
2262	2^405514-3311	122072	Yves Minet	12/2014
2263	2^405514-115511	122072	Enzo Doria	07/2015
2264	2^405422-113261	122045	Enzo Doria	07/2014
2265	2^405173+71237	121970	Enzo Doria	04/2016
2266	(2^405016+1)/257	121920	Lelio R Paula	04/2014
2267	2^404858+71329	121875	Enzo Doria	04/2016
2268	2^404813-114703	121861	Enzo Doria	04/2015
2269	2^404764+77791	121847	Enzo Doria	05/2016
2270	317^48694+48694^317	121787	Norbert Schneider	08/2015
2271	2^404536-115259	121778	Enzo Doria	06/2015
2272	2^404501-631	121767	Yves Minet	07/2012
2273	63^67620+2	121672	Lelio R Paula	08/2015
2274	(17*10^121621+1)/9	121622	Serge Batalov	05/2010
2275	(15*2^403912+1)/271	121589	Lelio R Paula	05/2014
2276	(10^121543-79)/3	121543	Robert Price	01/2018
2277	2^403676+76831	121519	Enzo Doria	05/2016
2278	(7*10^121487+143)/3	121488	Robert Price	03/2018
2279	2^403363-113635	121425	Enzo Doria	08/2014
2280	2^403336-1861469	121417	Enzo Doria	03/2016
2281	p(24442)#/2-64	121381	Robert Price	04/2017
2282	11^116555-720	121380	Enzo Doria	11/2012
2283	2^403100-461267	121346	Enzo Doria	07/2015
2284	2^403093-112213	121344	Enzo Doria	06/2014
2285	(316^48539+1)/317	121330	Eric Chen	10/2017
2286	2^403004+1866361	121317	Enzo Doria	03/2016
2287	2^402953+89	121301	Lelio R Paula	10/2013
2288	2^402944-2788319	121299	Enzo Doria	03/2016
2289	(44*10^121297-719)/9	121298	Robert Price	12/2018
2290	(27*2^402865+1)/5	121276	Lelio R Paula	04/2014
2291	2^402828-113183	121264	Enzo Doria	07/2014
2292	(17*10^121242+1)/9	121243	Serge Batalov	05/2010
2293	(15*2^402757+1)/101	121242	Lelio R Paula	05/2014
2295	2^402715+1874223	121230	Enzo Doria	06/2016
2294	(35*10^121229-593)/9	121230	Robert Price	07/2018
2296	(91^61879+1)/92	121222	Paul Bourdelais	09/2017
2297	7*10^121144+9	121145	Robert Price	09/2015
2298	2^401725-113251	120932	Enzo Doria	07/2014
2299	(15*2^401677-1)/19	120917	Lelio R Paula	05/2014
2300	2^401652+73711	120910	Enzo Doria	04/2016
2301	(2^401632+3)/79	120902	Lelio R Paula	04/2014
2302	2^401406-2791331	120836	Enzo Doria	03/2016
2303	(28^83497+1)/29	120832	Robert Price	07/2013
2304	2^401369+1867367	120825	Enzo Doria	03/2016
2305	(10^120782+29)/3	120782	Serge Batalov	12/2014
2306	2^401215-1657	120778	Yves Minet	07/2014
2307	2^401159+53	120761	Lelio R Paula	10/2013
2308	2^401031-113047	120723	Enzo Doria	07/2014
2309	(29*2^400909-1)/303	120685	Lelio R Paula	04/2014
2310	2^400571-15	120584	Lelio R Paula	10/2013
2311	(10^120574+359)/9	120574	Serge Batalov	12/2014
2312	2^400424-216413	120540	Enzo Doria	04/2013
2313	(17*2^400200-1)/587	120471	Lelio R Paula	05/2014
2314	2^400166+1874899	120462	Enzo Doria	06/2016
2315	(3*2^400045-1)/865	120424	Lelio R Paula	04/2014
2316	2^399966+73759	120402	Enzo Doria	04/2016
2317	(112*10^120395-1)/3	120397	Serge Batalov	12/2014
2318	2^399918-95	120388	Lelio R Paula	04/2013
2319	(49*10^120380-139)/9	120381	Robert Price	03/2019
2320	2^399792-1849259	120350	Enzo Doria	08/2015
2321	9*10^120342-7	120343	Robert Price	09/2015
2322	(13*10^120306-37)/3	120307	Robert Price	01/2019
2323	2^399526-1861721	120270	Enzo Doria	11/2015
2324	(10^(260126+1)+3610^60126-1)/9	120253	Robert Price	10/2015
2325	2^399322-2798111	120208	Enzo Doria	04/2016
2326	72^64693-71^64693	120157	Robert Price	03/2014
2327	2^399111-28489	120145	Enzo Doria	08/2015
2329	2^398877+105	120074	Donovan Johnson	01/2006
2328	(101*10^120072-87)/7	120074	Hans Havermann	02/2015
2330	(88^61751+1)/89	120072	Paul Bourdelais	09/2017
2331	2^398710+57	120024	Lelio R Paula	04/2013
2332	2^398691-115057	120018	Enzo Doria	06/2015
2333	L(574219)	120005	Renaud Lifchitz	03/2004
2334	2^398571+60413	119982	Yves Minet	03/2011
2335	p(24179)#/2-64	119949	Robert Price	04/2017
2336	2^398448+1872001	119945	Enzo Doria	05/2016
2337	8*10^119930-3	119931	Ray Chandler	04/2011
2338	(10^119880+179)/9	119880	Serge Batalov	12/2014
2339	(9*2^398145+1)/73	119853	Lelio R Paula	04/2014
2340	(10^119836+77)/3	119836	Robert Price	01/2018
2341	2^398029+1872527	119819	Enzo Doria	05/2016
2342	2^397897-113541	119779	Enzo Doria	08/2014
2343	(21*2^397661-1)/27593	119705	Lelio R Paula	04/2014
2344	(58^67853-1)/57	119653	Paul Bourdelais	09/2017
2345	2^397426+73849	119638	Enzo Doria	04/2016
2346	2^396933-112723	119489	Enzo Doria	06/2014
2347	11^114738-150	119488	Enzo Doria	10/2012
2348	(4*10^119474+149)/9	119474	Robert Price	04/2018
2349	2^396790-21	119446	Lelio R Paula	04/2013
2350	(2^396633-7)/5	119398	Lelio R Paula	04/2014
2351	105^59050+104	119352	Norbert Schneider	11/2016
2352	126^56824-125	119352	Norbert Schneider	12/2018
2353	2^396374+73729	119321	Enzo Doria	04/2016
2354	2^396258-459491	119286	Enzo Doria	05/2015
2355	2^396128-396128-1	119247	Karsten Bonath	06/2018
2356	(2^395986+5)/76881	119199	Lelio R Paula	04/2014
2357	(23*2^395942-1)/91	119190	Lelio R Paula	04/2014
2358	(11*2^395548+1)/3	119073	Lelio R Paula	04/2014
2359	(30^80599+1)/31	119054	Robert Price	07/2013
2360	(43*10^119024-403)/9	119025	Robert Price	01/2019
2361	2^395062-109121	118926	Enzo Doria	04/2014
2362	(2^394918+78557)/3	118882	Lelio R Paula	01/2015
2363	(16*10^118852+77)/3	118853	Robert Price	03/2019
2364	(2^394739+3)/1883	118826	Lelio R Paula	04/2014
2365	2^394266+71389	118686	Enzo Doria	04/2016
2366	2^394215-51261	118671	Tony Prest / Never Odd Or Even	04/2018
2367	(2^394215-48793)/5/5	118670	Tony Prest / Never Odd Or Even	04/2018
2368	(2^394215-17063)/3/3/5	118669	Tony Prest / Never Odd Or Even	04/2018
2369	(2^394215-24393)/5/5/5/5/5	118668	Tony Prest / Never Odd Or Even	04/2018
2370	(2^394215-35885)/3/71/173	118666	Tony Prest / Never Odd Or Even	04/2018
2371	(2^394215-47925)/353/2269	118665	Tony Prest / Never Odd Or Even	04/2018
2372	(2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673	118650	Tony Prest / Never Odd Or Even	04/2018
2373	(17*10^118635+13)/3	118636	Robert Price	01/2019
2374	5^169727+2	118635	Lelio R Paula	08/2013
2375	2^394034-3	118617	M. Frind & P. Underwood	09/2002
2376	(7*10^118607+179)/3	118608	Robert Price	09/2018
2377	3^248572-6242	118599	Enzo Doria	05/2014
2378	(3*2^393964-1)/181	118594	Lelio R Paula	04/2014
2379	7^140303-6	118570	Robert Price	11/2014
2380	2^393427+75683	118434	Enzo Doria	04/2016
2381	2^393376-114749	118418	Enzo Doria	04/2015
2382	2^393180+73	118359	Lelio R Paula	04/2013
2383	p(23881)#/2+256	118328	Robert Price	05/2017
2384	(10^118324+359)/9	118324	Serge Batalov	12/2014
2385	p(23879)#/2+64	118317	Robert Price	03/2017
2386	(53*10^118216+1)/9	118217	Serge Batalov	11/2010
2387	(7*2^392697+1)/15	118214	Renaud Lifchitz	03/2011
2388	(157^53819-1)/156	118179	Alexander Zhirkov	06/2016
2389	(19*2^392551+1)/3	118171	Lelio R Paula	04/2014
2390	2^392516-29219	118160	Enzo Doria	07/2015
2391	Phi(177231,10)	118152	Maksym Voznyy	09/2015
2392	2^392413-112123	118129	Enzo Doria	06/2014
2393	(2^392342+5)/27	118106	Lelio R Paula	04/2014
2394	2^392300-1841429	118095	Enzo Doria	06/2015
2395	2^392220+75241	118070	Enzo Doria	04/2016
2396	10^118009+664447	118010	Patrick De Geest	07/2018
2397	10^118009-20001	118009	Robert Price	01/2018
2398	(14*10^117991+61)/3	117992	Robert Price	12/2018
2399	2^391933+5897	117984	Yves Minet	02/2011
2400	2^391912-1849259	117978	Enzo Doria	08/2015
2401	(2^391812+5)/14181	117944	Lelio R Paula	04/2014
2402	(46*10^117902+683)/9	117903	Robert Price	03/2019
2403	(7*2^391521+1)/285	117858	Lelio R Paula	04/2014
2404	2^391324+90901	117801	Yves Minet	02/2011
2405	2^391301-1859923	117794	Enzo Doria	03/2016
2406	2^391261-4131	117782	Yves Minet	02/2018
2407	(2^391115-7)/11791	117734	Lelio R Paula	04/2014
2408	2^390960+1880881	117691	Enzo Doria	11/2016
2409	2^390897-1860553	117672	Enzo Doria	11/2015
2410	2^390889-115003	117670	Enzo Doria	06/2015
2411	2^390779-30337	117637	Paul Bourdelais	02/2012
2412	11^112916-780	117590	Enzo Doria	12/2012
2413	(16^97613-5^97613)/11	117537	Robert Price	07/2013
2414	(17*2^390272+1)/1983	117482	Lelio R Paula	04/2014
2415	31^78759-30	117459	Theodore Burton	02/2007
2416	2^389998+37	117402	Lelio R Paula	03/2013
2417	(13*10^117249+161)/3	117250	Robert Price	11/2018
2418	2^389478+43	117245	Lelio R Paula	03/2013
2419	(29*2^389351-1)/9	117207	Lelio R Paula	04/2014
2420	5*10^117205+23	117206	Robert Price	03/2019
2421	(2^389341-7)/3865	117200	Lelio R Paula	03/2014
2422	10^117142+209223	117143	Patrick De Geest	04/2018
2424	10^117142-1000000001	117142	Robert Price	03/2018
2423	10^117142-966057	117142	Patrick De Geest	04/2018
2425	10^117135+360577	117136	Patrick De Geest	07/2018
2426	10^117135-401	117135	Robert Price	01/2018
2427	4*10^117123+79	117124	Robert Price	08/2018
2428	2^389033-12797413	117111	Enzo Doria	04/2016
2429	2^388960-109505	117089	Enzo Doria	04/2014
2430	(2^388928-5)/569	117077	Lelio R Paula	03/2014
2431	2^388888-1529	117067	Yves Minet	01/2013
2432	10^117059+28879	117060	Patrick De Geest	05/2016
2433	(10^117059-71)/1	117059	Serge Batalov	12/2014
2434	(26*10^116999-503)/9	117000	Robert Price	07/2018
2435	3^245154-6256	116969	Enzo Doria	05/2014
2436	5*10^116966-43	116967	Robert Price	01/2019
2437	2^388536-113495	116961	Enzo Doria	08/2014
2438	2^388469-43	116941	Lelio R Paula	03/2013
2439	(7*2^388372-1)/111	116911	Lelio R Paula	04/2014
2440	(7*2^388335-1)/25	116900	Lelio R Paula	04/2014
2441	2^388180+93	116854	Donovan Johnson	07/2008
2442	(2^388081+7)/1179	116821	Lelio R Paula	03/2014
2443	2^387946-113261	116784	Enzo Doria	07/2014
2444	2^387745+75557	116723	Enzo Doria	04/2016
2445	(7*10^116684+179)/3	116685	Robert Price	09/2018
2446	2^387554+71455	116666	Enzo Doria	04/2016
2447	(2^387447+78557)/365	116631	Lelio R Paula	12/2014
2448	(145*10^116610-1)/9	116612	Serge Batalov	12/2014
2449	(25*10^116601-331)/9	116602	Robert Price	08/2018
2450	(17*2^387284-1)/59	116584	Lelio R Paula	04/2014
2451	(31*2^386968+1)/7	116490	Lelio R Paula	03/2014
2452	2^386947+1869143	116483	Enzo Doria	05/2016
2453	(30^78857-1)/29	116480	Robert Price	12/2011
2454	(2^386903-3)/5	116469	Lelio R Paula	03/2014
2455	2^386389-1864783	116315	Enzo Doria	03/2016
2456	(31*2^386231-1)/1711	116266	Lelio R Paula	03/2014
2457	297^47012+47012^297	116250	Norbert Schneider	07/2018
2458	(2^386087-5)/40959	116220	Lelio R Paula	03/2014
2459	2^385969-823	116189	Yves Minet	05/2012
2460	57^66162+2	116173	Lelio R Paula	08/2013
2461	2^385854+75049	116154	Enzo Doria	04/2016
2462	2^385775-109587	116130	Enzo Doria	04/2014
2463	(14*10^116112-101)/3	116113	Robert Price	02/2019
2464	2^385622+71839	116084	Enzo Doria	04/2016
2465	2^385564+781	116067	Lelio R Paula	01/2012
2466	2^385410+71893	116020	Enzo Doria	04/2016
2467	(25*2^385091+1)/27	115924	Lelio R Paula	04/2014
2468	(11*10^115910-131)/3	115911	Robert Price	09/2018
2469	2^384953-111943	115883	Paul Bourdelais	02/2012
2470	43^70942-2	115882	Lelio R Paula	04/2014
2471	7*10^115863+3	115864	Robert Price	08/2015
2472	2^384834+93	115847	Donovan Johnson	07/2008
2473	2^384809+71297	115840	Enzo Doria	04/2016
2474	(7*2^384759-1)/5	115825	Lelio R Paula	04/2014
2475	(71*10^115810-17)/9	115811	Ray Chandler	08/2011
2476	(97*10^115794-1)/3	115796	Serge Batalov	12/2014
2477	2*10^115784-27	115785	Robert Price	05/2018
2478	10^115773+126739	115774	Patrick De Geest	04/2018
2480	10^115773-1000000001	115773	Robert Price	03/2018
2479	10^115773-396221	115773	Patrick De Geest	04/2018
2481	2^384530+1874305	115756	Enzo Doria	06/2016
2482	(3*2^384524-1)/7631	115750	Lelio R Paula	03/2014
2483	(44*10^115697-413)/9	115698	Robert Price	03/2019
2484	2^384312+81091	115690	Yves Minet	02/2010
2485	(4*10^115668-79)/3	115669	Robert Price	02/2018
2486	(266947#+273808)/(2109157)	115646	Makoto Morimoto	10/2017
2487	3^242337-4042	115625	Enzo Doria	05/2014
2488	(11*2^383859-13)/15	115553	Renaud Lifchitz	03/2011
2489	2^383780-3149	115530	Yves Minet	10/2014
2490	(41*10^115523-383)/9	115524	Robert Price	11/2018
2491	2^383560-455	115464	Yves Minet	03/2012
2492	(2^383544+5)/3	115458	Lelio R Paula	03/2014
2493	89^59221-88^59221	115445	Robert Price	06/2015
2494	2^383347+1869413	115399	Enzo Doria	05/2016
2495	(2^383130-7)/131793	115329	Lelio R Paula	03/2014
2496	(12^106859+1)/13	115320	Paul Bourdelais	02/2010
2497	2^383039+1869509	115307	Enzo Doria	05/2016
2498	(13*2^382968+1)/7	115286	Lelio R Paula	04/2014
2499	2^382633+73697	115185	Enzo Doria	04/2016
2500	2^382509-113593	115147	Enzo Doria	08/2014

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Probable Primes Top 10000

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