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	2^409533+77747	123282	Enzo Doria	05/2016
2252	2^409436-112799	123253	Enzo Doria	06/2014
2253	2^409225+1873787	123189	Enzo Doria	06/2016
2254	2^409174+73009	123174	Enzo Doria	04/2016
2255	2^409058-112685	123139	Enzo Doria	06/2014
2256	(13*10^123137-61)/3	123138	Robert Price	11/2018
2257	4*10^123113+21	123114	Robert Price	12/2018
2258	2^408778+77689	123055	Enzo Doria	05/2016
2259	2^408690-75	123028	Lelio R Paula	11/2013
2260	(29*10^122996+673)/9	122997	Robert Price	12/2018
2261	2^408574-2787341	122994	Enzo Doria	03/2016
2262	3*10^122977+37	122978	Robert Price	08/2018
2263	Phi(157825,10)	122961	Maksym Voznyy	06/2015
2264	(13*2^408283+1)/1665	122904	Lelio R Paula	05/2014
2265	(16*10^122871+77)/3	122872	Robert Price	03/2019
2266	(11*2^408100-1)/35	122850	Lelio R Paula	04/2014
2267	(19*10^122836-43)/3	122837	Robert Price	05/2019
2268	(2^407821-lucasV(1,2,407821)+1)/2	122767	Mike Oakes	11/2016
2269	(32*10^122733-77)/9	122734	Robert Price	06/2018
2270	(21*2^407604-1)/215	122701	Lelio R Paula	04/2014
2271	(22*10^122681+161)/3	122682	Robert Price	05/2019
2272	(21*2^407433-1)/13	122650	Lelio R Paula	04/2014
2273	(73*10^122592-1)/9	122593	Robert Price	01/2015
2274	(5*10^122592+91)/3	122593	Robert Price	04/2018
2275	2^407179-112075	122574	Enzo Doria	06/2014
2276	(21*2^407131+1)/207517523	122552	Lelio R Paula	04/2014
2277	(66^67349+1)/67	122543	Paul Bourdelais	09/2017
2278	2^407008-1867919	122522	Enzo Doria	04/2016
2279	11^117642-300	122512	Enzo Doria	10/2012
2280	(F(397700+1)^2+L(397700+1)^2)/2	122509	Henri Lifchitz	10/2017
2281	2^406949+72197	122504	Enzo Doria	04/2016
2282	(19*10^122501+149)/3	122502	Robert Price	05/2019
2283	2^406826-65	122467	Lelio R Paula	11/2013
2284	2^406821-2797363	122466	Enzo Doria	04/2016
2285	2^406758-17	122447	Lelio R Paula	11/2013
2286	(30^82883-1)/29	122427	Robert Price	12/2011
2287	(2^406583-1)/813167	122388	Jens K. Andersen	02/2009
2288	4*10^122377+19	122378	Robert Price	10/2018
2289	3*10^122345-97	122346	Robert Price	07/2018
2290	97^61575-2	122336	Lelio R Paula	12/2014
2291	2^406298+2799109	122308	Enzo Doria	04/2016
2292	7*10^122294+57	122295	Robert Price	06/2019
2293	(27*2^406241-1)/10277	122289	Lelio R Paula	04/2014
2294	2^406229-1849993	122288	Enzo Doria	08/2015
2295	3*10^122274+7	122275	Robert Price	07/2015
2296	2^406117+1876577	122254	Enzo Doria	07/2016
2297	3^256199-2^256199	122238	Mike Oakes	06/2005
2298	2^405992-78557	122216	Jorge Menendez	03/2018
2299	(8*10^122203+43)/3	122204	Robert Price	06/2018
2300	(58*10^122170+329)/9	122171	Robert Price	05/2019
2301	2^405774+179149	122151	Enzo Doria	06/2016
2302	5*10^122082+41	122083	Robert Price	03/2019
2303	2^405514-3311	122072	Yves Minet	12/2014
2304	2^405514-115511	122072	Enzo Doria	07/2015
2305	2^405422-113261	122045	Enzo Doria	07/2014
2306	2^405173+71237	121970	Enzo Doria	04/2016
2307	(2^405016+1)/257	121920	Lelio R Paula	04/2014
2308	2^404858+71329	121875	Enzo Doria	04/2016
2309	2^404813-114703	121861	Enzo Doria	04/2015
2310	2^404764+77791	121847	Enzo Doria	05/2016
2311	317^48694+48694^317	121787	Norbert Schneider	08/2015
2312	2^404536-115259	121778	Enzo Doria	06/2015
2313	2^404501-631	121767	Yves Minet	07/2012
2314	63^67620+2	121672	Lelio R Paula	08/2015
2315	(17*10^121621+1)/9	121622	Serge Batalov	05/2010
2316	(15*2^403912+1)/271	121589	Lelio R Paula	05/2014
2317	(10^121543-79)/3	121543	Robert Price	01/2018
2318	2^403676+76831	121519	Enzo Doria	05/2016
2319	(7*10^121487+143)/3	121488	Robert Price	03/2018
2320	2^403363-113635	121425	Enzo Doria	08/2014
2321	2^403336-1861469	121417	Enzo Doria	03/2016
2322	p(24442)#/2-64	121381	Robert Price	04/2017
2323	11^116555-720	121380	Enzo Doria	11/2012
2324	2^403100-461267	121346	Enzo Doria	07/2015
2325	2^403093-112213	121344	Enzo Doria	06/2014
2326	(316^48539+1)/317	121330	Eric Chen	10/2017
2327	2^403004+1866361	121317	Enzo Doria	03/2016
2328	2^402953+89	121301	Lelio R Paula	10/2013
2329	2^402944-2788319	121299	Enzo Doria	03/2016
2330	(44*10^121297-719)/9	121298	Robert Price	12/2018
2331	(27*2^402865+1)/5	121276	Lelio R Paula	04/2014
2332	2^402828-113183	121264	Enzo Doria	07/2014
2333	(17*10^121242+1)/9	121243	Serge Batalov	05/2010
2334	(15*2^402757+1)/101	121242	Lelio R Paula	05/2014
2336	2^402715+1874223	121230	Enzo Doria	06/2016
2335	(35*10^121229-593)/9	121230	Robert Price	07/2018
2337	(91^61879+1)/92	121222	Paul Bourdelais	09/2017
2338	7*10^121144+9	121145	Robert Price	09/2015
2339	2^401725-113251	120932	Enzo Doria	07/2014
2340	(15*2^401677-1)/19	120917	Lelio R Paula	05/2014
2341	2^401652+73711	120910	Enzo Doria	04/2016
2342	(2^401632+3)/79	120902	Lelio R Paula	04/2014
2343	2^401406-2791331	120836	Enzo Doria	03/2016
2344	(28^83497+1)/29	120832	Robert Price	07/2013
2345	(22*10^120828+161)/3	120829	Robert Price	05/2019
2346	2^401369+1867367	120825	Enzo Doria	03/2016
2347	(10^120782+29)/3	120782	Serge Batalov	12/2014
2348	2^401215-1657	120778	Yves Minet	07/2014
2349	2^401159+53	120761	Lelio R Paula	10/2013
2350	2^401031-113047	120723	Enzo Doria	07/2014
2351	(29*2^400909-1)/303	120685	Lelio R Paula	04/2014
2352	2^400571-15	120584	Lelio R Paula	10/2013
2353	(10^120574+359)/9	120574	Serge Batalov	12/2014
2354	2^400424-216413	120540	Enzo Doria	04/2013
2355	(17*2^400200-1)/587	120471	Lelio R Paula	05/2014
2356	2^400166+1874899	120462	Enzo Doria	06/2016
2357	(3*2^400045-1)/865	120424	Lelio R Paula	04/2014
2358	2^399966+73759	120402	Enzo Doria	04/2016
2359	(112*10^120395-1)/3	120397	Serge Batalov	12/2014
2360	2^399918-95	120388	Lelio R Paula	04/2013
2361	(49*10^120380-139)/9	120381	Robert Price	03/2019
2362	2^399792-1849259	120350	Enzo Doria	08/2015
2363	9*10^120342-7	120343	Robert Price	09/2015
2364	(13*10^120306-37)/3	120307	Robert Price	01/2019
2365	2^399526-1861721	120270	Enzo Doria	11/2015
2366	(10^(260126+1)+3610^60126-1)/9	120253	Robert Price	10/2015
2367	2^399322-2798111	120208	Enzo Doria	04/2016
2368	72^64693-71^64693	120157	Robert Price	03/2014
2369	2^399111-28489	120145	Enzo Doria	08/2015
2371	2^398877+105	120074	Donovan Johnson	01/2006
2370	(101*10^120072-87)/7	120074	Hans Havermann	02/2015
2372	(88^61751+1)/89	120072	Paul Bourdelais	09/2017
2373	2^398710+57	120024	Lelio R Paula	04/2013
2374	2^398691-115057	120018	Enzo Doria	06/2015
2375	L(574219)	120005	Renaud Lifchitz	03/2004
2376	2^398571+60413	119982	Yves Minet	03/2011
2377	p(24179)#/2-64	119949	Robert Price	04/2017
2378	2^398448+1872001	119945	Enzo Doria	05/2016
2379	8*10^119930-3	119931	Ray Chandler	04/2011
2380	(10^119880+179)/9	119880	Serge Batalov	12/2014
2381	(9*2^398145+1)/73	119853	Lelio R Paula	04/2014
2382	(10^119836+77)/3	119836	Robert Price	01/2018
2383	2^398029+1872527	119819	Enzo Doria	05/2016
2384	2^397897-113541	119779	Enzo Doria	08/2014
2385	(21*2^397661-1)/27593	119705	Lelio R Paula	04/2014
2386	(58^67853-1)/57	119653	Paul Bourdelais	09/2017
2387	2^397426+73849	119638	Enzo Doria	04/2016
2388	2^396933-112723	119489	Enzo Doria	06/2014
2389	11^114738-150	119488	Enzo Doria	10/2012
2390	(4*10^119474+149)/9	119474	Robert Price	04/2018
2391	2^396790-21	119446	Lelio R Paula	04/2013
2392	(2^396633-7)/5	119398	Lelio R Paula	04/2014
2393	105^59050+104	119352	Norbert Schneider	11/2016
2394	126^56824-125	119352	Norbert Schneider	12/2018
2395	139^55690-138	119345	Norbert Schneider	04/2019
2396	790^41179+41179^790	119322	Norbert Schneider	04/2019
2397	2^396374+73729	119321	Enzo Doria	04/2016
2398	2^396258-459491	119286	Enzo Doria	05/2015
2399	2^396128-396128-1	119247	Karsten Bonath	06/2018
2400	(2^395986+5)/76881	119199	Lelio R Paula	04/2014
2401	(23*2^395942-1)/91	119190	Lelio R Paula	04/2014
2402	(11*2^395548+1)/3	119073	Lelio R Paula	04/2014
2403	(30^80599+1)/31	119054	Robert Price	07/2013
2404	(43*10^119024-403)/9	119025	Robert Price	01/2019
2405	2^395062-109121	118926	Enzo Doria	04/2014
2406	2^395055-4627	118924	Yves Minet	05/2019
2407	(2^394918+78557)/3	118882	Lelio R Paula	01/2015
2408	(16*10^118852+77)/3	118853	Robert Price	03/2019
2409	(2^394739+3)/1883	118826	Lelio R Paula	04/2014
2410	2^394266+71389	118686	Enzo Doria	04/2016
2411	2^394215-51261	118671	Tony Prest / Never Odd Or Even	04/2018
2412	(2^394215-48793)/5/5	118670	Tony Prest / Never Odd Or Even	04/2018
2413	(2^394215-17063)/3/3/5	118669	Tony Prest / Never Odd Or Even	04/2018
2414	(2^394215-24393)/5/5/5/5/5	118668	Tony Prest / Never Odd Or Even	04/2018
2415	(2^394215-35885)/3/71/173	118666	Tony Prest / Never Odd Or Even	04/2018
2416	(2^394215-47925)/353/2269	118665	Tony Prest / Never Odd Or Even	04/2018
2417	(2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673	118650	Tony Prest / Never Odd Or Even	04/2018
2418	(17*10^118635+13)/3	118636	Robert Price	01/2019
2419	5^169727+2	118635	Lelio R Paula	08/2013
2420	2^394034-3	118617	M. Frind & P. Underwood	09/2002
2421	(7*10^118607+179)/3	118608	Robert Price	09/2018
2422	3^248572-6242	118599	Enzo Doria	05/2014
2423	(3*2^393964-1)/181	118594	Lelio R Paula	04/2014
2424	7^140303-6	118570	Robert Price	11/2014
2425	2^393427+75683	118434	Enzo Doria	04/2016
2426	2^393376-114749	118418	Enzo Doria	04/2015
2427	2^393180+73	118359	Lelio R Paula	04/2013
2428	p(23881)#/2+256	118328	Robert Price	05/2017
2429	(10^118324+359)/9	118324	Serge Batalov	12/2014
2430	p(23879)#/2+64	118317	Robert Price	03/2017
2431	(53*10^118216+1)/9	118217	Serge Batalov	11/2010
2432	(7*2^392697+1)/15	118214	Renaud Lifchitz	03/2011
2433	(157^53819-1)/156	118179	Alexander Zhirkov	06/2016
2434	(19*2^392551+1)/3	118171	Lelio R Paula	04/2014
2435	2^392516-29219	118160	Enzo Doria	07/2015
2436	Phi(177231,10)	118152	Maksym Voznyy	09/2015
2437	2^392413-112123	118129	Enzo Doria	06/2014
2438	(2^392342+5)/27	118106	Lelio R Paula	04/2014
2439	2^392300-1841429	118095	Enzo Doria	06/2015
2440	2^392220+75241	118070	Enzo Doria	04/2016
2441	10^118009+664447	118010	Patrick De Geest	07/2018
2442	10^118009-20001	118009	Robert Price	01/2018
2443	(14*10^117991+61)/3	117992	Robert Price	12/2018
2444	2^391933+5897	117984	Yves Minet	02/2011
2445	2^391912-1849259	117978	Enzo Doria	08/2015
2446	(2^391812+5)/14181	117944	Lelio R Paula	04/2014
2447	(46*10^117902+683)/9	117903	Robert Price	03/2019
2448	(7*2^391521+1)/285	117858	Lelio R Paula	04/2014
2449	2^391324+90901	117801	Yves Minet	02/2011
2450	2^391301-1859923	117794	Enzo Doria	03/2016
2451	2^391261-4131	117782	Yves Minet	02/2018
2452	(2^391115-7)/11791	117734	Lelio R Paula	04/2014
2453	2^390960+1880881	117691	Enzo Doria	11/2016
2454	2^390897-1860553	117672	Enzo Doria	11/2015
2455	2^390889-115003	117670	Enzo Doria	06/2015
2456	2^390779-30337	117637	Paul Bourdelais	02/2012
2457	11^112916-780	117590	Enzo Doria	12/2012
2458	(16^97613-5^97613)/11	117537	Robert Price	07/2013
2459	(17*2^390272+1)/1983	117482	Lelio R Paula	04/2014
2460	31^78759-30	117459	Theodore Burton	02/2007
2461	2^389998+37	117402	Lelio R Paula	03/2013
2462	(13*10^117249+161)/3	117250	Robert Price	11/2018
2463	2^389478+43	117245	Lelio R Paula	03/2013
2464	(29*2^389351-1)/9	117207	Lelio R Paula	04/2014
2465	5*10^117205+23	117206	Robert Price	03/2019
2466	(2^389341-7)/3865	117200	Lelio R Paula	03/2014
2467	10^117142+209223	117143	Patrick De Geest	04/2018
2469	10^117142-1000000001	117142	Robert Price	03/2018
2468	10^117142-966057	117142	Patrick De Geest	04/2018
2470	10^117135+360577	117136	Patrick De Geest	07/2018
2471	10^117135-401	117135	Robert Price	01/2018
2472	4*10^117123+79	117124	Robert Price	08/2018
2473	2^389033-12797413	117111	Enzo Doria	04/2016
2474	2^388960-109505	117089	Enzo Doria	04/2014
2475	(2^388928-5)/569	117077	Lelio R Paula	03/2014
2476	2^388888-1529	117067	Yves Minet	01/2013
2477	10^117059+28879	117060	Patrick De Geest	05/2016
2478	(10^117059-71)/1	117059	Serge Batalov	12/2014
2479	(26*10^116999-503)/9	117000	Robert Price	07/2018
2480	3^245154-6256	116969	Enzo Doria	05/2014
2481	5*10^116966-43	116967	Robert Price	01/2019
2482	2^388536-113495	116961	Enzo Doria	08/2014
2483	2^388469-43	116941	Lelio R Paula	03/2013
2484	(7*2^388372-1)/111	116911	Lelio R Paula	04/2014
2485	(7*2^388335-1)/25	116900	Lelio R Paula	04/2014
2486	2^388180+93	116854	Donovan Johnson	07/2008
2487	(2^388081+7)/1179	116821	Lelio R Paula	03/2014
2488	2^387946-113261	116784	Enzo Doria	07/2014
2489	2^387745+75557	116723	Enzo Doria	04/2016
2490	(7*10^116684+179)/3	116685	Robert Price	09/2018
2491	2^387554+71455	116666	Enzo Doria	04/2016
2492	(2^387447+78557)/365	116631	Lelio R Paula	12/2014
2493	(145*10^116610-1)/9	116612	Serge Batalov	12/2014
2494	(25*10^116601-331)/9	116602	Robert Price	08/2018
2495	(17*2^387284-1)/59	116584	Lelio R Paula	04/2014
2496	(31*2^386968+1)/7	116490	Lelio R Paula	03/2014
2497	2^386947+1869143	116483	Enzo Doria	05/2016
2498	(30^78857-1)/29	116480	Robert Price	12/2011
2499	(2^386903-3)/5	116469	Lelio R Paula	03/2014
2500	2^386389-1864783	116315	Enzo Doria	03/2016

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