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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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	2^415259+77243	125006	Enzo Doria	05/2016
2252	2^415144-3683	124971	Yves Minet	10/2011
2253	2^414874+79	124890	Lelio R Paula	01/2015
2254	(2^414765+7)/1389	124854	Lelio R Paula	05/2014
2255	2^414618+79459	124813	Enzo Doria	06/2016
2256	2^414432-1846709	124757	Enzo Doria	07/2015
2257	2*10^124751-51	124752	Robert Price	04/2018
2258	(56*10^124735+367)/9	124736	Robert Price	06/2019
2259	(13*2^414274-1)/153	124708	Lelio R Paula	05/2014
2260	(7*10^124648+197)/3	124649	Robert Price	07/2018
2262	2^414032-5	124637	Henri Lifchitz	07/2006
2261	2^414032+1872331	124637	Enzo Doria	05/2016
2263	14120^30009-30009^14120	124533	Norbert Schneider	02/2015
2264	64^68909-63^68909	124463	Robert Price	07/2013
2265	2^413387+76253	124442	Enzo Doria	04/2016
2266	2^413352+524287	124432	Paul Underwood	09/2018
2267	287117#+391613	124424	Nicolas PALAU	01/2017
2268	(4*10^124420+83)/3	124421	Robert Price	02/2018
2269	(27*2^413207-1)/108335	124385	Lelio R Paula	05/2014
2270	(41*10^124335-383)/9	124336	Robert Price	11/2018
2271	2^412868-120599	124286	Paul Bourdelais	02/2012
2272	45^75145-2	124231	Lelio R Paula	08/2015
2273	2^412645-112213	124219	Enzo Doria	06/2014
2274	2^412248+74611	124100	Enzo Doria	04/2016
2275	(22*10^124096-13)/9	124097	Robert Price	06/2018
2276	2^412192-3329	124083	Yves Minet	12/2014
2277	(25*2^412191-1)/23	124082	Lelio R Paula	05/2014
2278	(25*10^124076-67)/3	124077	Robert Price	06/2019
2279	F(593689)	124074	Henri Lifchitz	01/2005
2280	(11*2^412161+1)/19	124073	Lelio R Paula	05/2014
2281	2^411884-113279	123990	Enzo Doria	07/2014
2282	(2^411832+1)/257	123972	Lelio R Paula	05/2014
2283	(26*10^123970-89)/9	123971	Robert Price	06/2018
2284	2^411790-1853531	123962	Enzo Doria	08/2015
2285	(5^177337+1)/6	123953	Paul Bourdelais	11/2008
2286	2^411711-113257	123938	Enzo Doria	07/2014
2287	(23*2^411675-1)/3	123928	Lelio R Paula	05/2014
2288	(11*10^123899-179)/3	123900	Robert Price	09/2018
2289	2^411325-351103	123822	Enzo Doria	06/2015
2290	2^411052+1872481	123739	Enzo Doria	05/2016
2291	2^410997+39	123723	Lelio R Paula	05/2014
2292	155^56438+154	123618	Norbert Schneider	01/2019
2293	2^410596-39	123602	Lelio R Paula	05/2014
2294	2^410540-115079	123585	Enzo Doria	06/2015
2295	(7*10^123563+107)/3	123564	Robert Price	02/2018
2296	(3*2^410392-1)/9229	123537	Lelio R Paula	05/2014
2297	2^410206-113081	123485	Enzo Doria	07/2014
2298	(25*2^410192+1)/10397	123478	Lelio R Paula	04/2014
2299	2^409909-189	123395	Enzo Doria	05/2014
2300	2^409896-109043	123391	Enzo Doria	04/2014
2301	2^409890+75409	123390	Enzo Doria	04/2016
2302	133^58076-2	123345	Lelio R Paula	10/2017
2303	F(590041)	123311	Henri Lifchitz	01/2005
2304	2^409566-113501	123292	Enzo Doria	08/2014
2305	2^409533+77747	123282	Enzo Doria	05/2016
2306	2^409436-112799	123253	Enzo Doria	06/2014
2307	2^409225+1873787	123189	Enzo Doria	06/2016
2308	2^409174+73009	123174	Enzo Doria	04/2016
2309	2^409058-112685	123139	Enzo Doria	06/2014
2310	(13*10^123137-61)/3	123138	Robert Price	11/2018
2311	4*10^123113+21	123114	Robert Price	12/2018
2312	2^408778+77689	123055	Enzo Doria	05/2016
2313	2^408690-75	123028	Lelio R Paula	11/2013
2314	(29*10^122996+673)/9	122997	Robert Price	12/2018
2315	2^408574-2787341	122994	Enzo Doria	03/2016
2316	3*10^122977+37	122978	Robert Price	08/2018
2317	Phi(157825,10)	122961	Maksym Voznyy	06/2015
2318	(68*10^122933-419)/9	122934	Robert Price	07/2019
2319	(13*2^408283+1)/1665	122904	Lelio R Paula	05/2014
2320	(16*10^122871+77)/3	122872	Robert Price	03/2019
2321	(11*2^408100-1)/35	122850	Lelio R Paula	04/2014
2322	(19*10^122836-43)/3	122837	Robert Price	05/2019
2323	(2^407821-lucasV(1,2,407821)+1)/2	122767	Mike Oakes	11/2016
2324	(32*10^122733-77)/9	122734	Robert Price	06/2018
2325	(21*2^407604-1)/215	122701	Lelio R Paula	04/2014
2326	(22*10^122681+161)/3	122682	Robert Price	05/2019
2327	(21*2^407433-1)/13	122650	Lelio R Paula	04/2014
2328	(73*10^122592-1)/9	122593	Robert Price	01/2015
2329	(5*10^122592+91)/3	122593	Robert Price	04/2018
2330	2^407179-112075	122574	Enzo Doria	06/2014
2331	(21*2^407131+1)/207517523	122552	Lelio R Paula	04/2014
2332	(66^67349+1)/67	122543	Paul Bourdelais	09/2017
2333	2^407008-1867919	122522	Enzo Doria	04/2016
2334	11^117642-300	122512	Enzo Doria	10/2012
2335	(F(397700+1)^2+L(397700+1)^2)/2	122509	Henri Lifchitz	10/2017
2336	2^406949+72197	122504	Enzo Doria	04/2016
2337	(19*10^122501+149)/3	122502	Robert Price	05/2019
2338	2^406826-65	122467	Lelio R Paula	11/2013
2339	2^406821-2797363	122466	Enzo Doria	04/2016
2340	2^406758-17	122447	Lelio R Paula	11/2013
2341	(30^82883-1)/29	122427	Robert Price	12/2011
2342	(2^406583-1)/813167	122388	Jens K. Andersen	02/2009
2343	4*10^122377+19	122378	Robert Price	10/2018
2344	3*10^122345-97	122346	Robert Price	07/2018
2345	97^61575-2	122336	Lelio R Paula	12/2014
2346	2^406298+2799109	122308	Enzo Doria	04/2016
2347	7*10^122294+57	122295	Robert Price	06/2019
2348	(27*2^406241-1)/10277	122289	Lelio R Paula	04/2014
2349	2^406229-1849993	122288	Enzo Doria	08/2015
2350	3*10^122274+7	122275	Robert Price	07/2015
2351	2^406117+1876577	122254	Enzo Doria	07/2016
2352	3^256199-2^256199	122238	Mike Oakes	06/2005
2353	2^405992-78557	122216	Jorge Menendez	03/2018
2354	(8*10^122203+43)/3	122204	Robert Price	06/2018
2355	(58*10^122170+329)/9	122171	Robert Price	05/2019
2356	2^405774+179149	122151	Enzo Doria	06/2016
2357	5*10^122082+41	122083	Robert Price	03/2019
2358	2^405514-3311	122072	Yves Minet	12/2014
2359	2^405514-115511	122072	Enzo Doria	07/2015
2360	2^405422-113261	122045	Enzo Doria	07/2014
2361	2^405173+71237	121970	Enzo Doria	04/2016
2362	(2^405016+1)/257	121920	Lelio R Paula	04/2014
2363	2^404858+71329	121875	Enzo Doria	04/2016
2364	2^404813-114703	121861	Enzo Doria	04/2015
2365	2^404764+77791	121847	Enzo Doria	05/2016
2366	317^48694+48694^317	121787	Norbert Schneider	08/2015
2367	2^404536-115259	121778	Enzo Doria	06/2015
2368	2^404501-631	121767	Yves Minet	07/2012
2369	63^67620+2	121672	Lelio R Paula	08/2015
2370	(16*10^121633+167)/3	121634	Robert Price	06/2019
2371	(17*10^121621+1)/9	121622	Serge Batalov	05/2010
2372	(15*2^403912+1)/271	121589	Lelio R Paula	05/2014
2373	(10^121543-79)/3	121543	Robert Price	01/2018
2374	2^403676+76831	121519	Enzo Doria	05/2016
2375	(7*10^121487+143)/3	121488	Robert Price	03/2018
2376	2^403363-113635	121425	Enzo Doria	08/2014
2377	2^403336-1861469	121417	Enzo Doria	03/2016
2378	p(24442)#/2-64	121381	Robert Price	04/2017
2379	11^116555-720	121380	Enzo Doria	11/2012
2380	2^403100-461267	121346	Enzo Doria	07/2015
2381	2^403093-112213	121344	Enzo Doria	06/2014
2382	(316^48539+1)/317	121330	Eric Chen	10/2017
2383	2^403004+1866361	121317	Enzo Doria	03/2016
2384	2^402953+89	121301	Lelio R Paula	10/2013
2385	2^402944-2788319	121299	Enzo Doria	03/2016
2386	(44*10^121297-719)/9	121298	Robert Price	12/2018
2387	(27*2^402865+1)/5	121276	Lelio R Paula	04/2014
2388	2^402828-113183	121264	Enzo Doria	07/2014
2389	(17*10^121242+1)/9	121243	Serge Batalov	05/2010
2390	(15*2^402757+1)/101	121242	Lelio R Paula	05/2014
2392	2^402715+1874223	121230	Enzo Doria	06/2016
2391	(35*10^121229-593)/9	121230	Robert Price	07/2018
2393	(91^61879+1)/92	121222	Paul Bourdelais	09/2017
2394	7*10^121144+9	121145	Robert Price	09/2015
2395	2^401725-113251	120932	Enzo Doria	07/2014
2396	(15*2^401677-1)/19	120917	Lelio R Paula	05/2014
2397	2^401652+73711	120910	Enzo Doria	04/2016
2398	(2^401632+3)/79	120902	Lelio R Paula	04/2014
2399	2^401406-2791331	120836	Enzo Doria	03/2016
2400	(28^83497+1)/29	120832	Robert Price	07/2013
2401	(22*10^120828+161)/3	120829	Robert Price	05/2019
2402	2^401369+1867367	120825	Enzo Doria	03/2016
2403	(10^120782+29)/3	120782	Serge Batalov	12/2014
2404	2^401215-1657	120778	Yves Minet	07/2014
2405	2^401159+53	120761	Lelio R Paula	10/2013
2406	2^401031-113047	120723	Enzo Doria	07/2014
2407	(29*2^400909-1)/303	120685	Lelio R Paula	04/2014
2408	2^400571-15	120584	Lelio R Paula	10/2013
2409	(10^120574+359)/9	120574	Serge Batalov	12/2014
2410	2^400424-216413	120540	Enzo Doria	04/2013
2411	(17*2^400200-1)/587	120471	Lelio R Paula	05/2014
2412	2^400166+1874899	120462	Enzo Doria	06/2016
2413	(3*2^400045-1)/865	120424	Lelio R Paula	04/2014
2414	2^399966+73759	120402	Enzo Doria	04/2016
2415	(112*10^120395-1)/3	120397	Serge Batalov	12/2014
2416	2^399918-95	120388	Lelio R Paula	04/2013
2417	(49*10^120380-139)/9	120381	Robert Price	03/2019
2418	2^399792-1849259	120350	Enzo Doria	08/2015
2419	9*10^120342-7	120343	Robert Price	09/2015
2420	(13*10^120306-37)/3	120307	Robert Price	01/2019
2421	2^399526-1861721	120270	Enzo Doria	11/2015
2422	(10^(260126+1)+3610^60126-1)/9	120253	Robert Price	10/2015
2423	2^399322-2798111	120208	Enzo Doria	04/2016
2424	72^64693-71^64693	120157	Robert Price	03/2014
2425	2^399111-28489	120145	Enzo Doria	08/2015
2427	2^398877+105	120074	Donovan Johnson	01/2006
2426	(101*10^120072-87)/7	120074	Hans Havermann	02/2015
2428	(88^61751+1)/89	120072	Paul Bourdelais	09/2017
2429	2^398710+57	120024	Lelio R Paula	04/2013
2430	2^398691-115057	120018	Enzo Doria	06/2015
2431	L(574219)	120005	Renaud Lifchitz	03/2004
2432	2^398571+60413	119982	Yves Minet	03/2011
2433	p(24179)#/2-64	119949	Robert Price	04/2017
2434	2^398448+1872001	119945	Enzo Doria	05/2016
2435	634^42803+42803^634	119938	Norbert Schneider	07/2019
2436	8*10^119930-3	119931	Ray Chandler	04/2011
2437	(10^119880+179)/9	119880	Serge Batalov	12/2014
2438	(9*2^398145+1)/73	119853	Lelio R Paula	04/2014
2439	(10^119836+77)/3	119836	Robert Price	01/2018
2440	2^398029+1872527	119819	Enzo Doria	05/2016
2441	2^397897-113541	119779	Enzo Doria	08/2014
2442	(21*2^397661-1)/27593	119705	Lelio R Paula	04/2014
2443	(58^67853-1)/57	119653	Paul Bourdelais	09/2017
2444	2^397426+73849	119638	Enzo Doria	04/2016
2445	2^396933-112723	119489	Enzo Doria	06/2014
2446	11^114738-150	119488	Enzo Doria	10/2012
2447	(4*10^119474+149)/9	119474	Robert Price	04/2018
2448	2^396790-21	119446	Lelio R Paula	04/2013
2449	(2^396633-7)/5	119398	Lelio R Paula	04/2014
2450	105^59050+104	119352	Norbert Schneider	11/2016
2451	126^56824-125	119352	Norbert Schneider	12/2018
2452	139^55690-138	119345	Norbert Schneider	04/2019
2453	790^41179+41179^790	119322	Norbert Schneider	04/2019
2454	2^396374+73729	119321	Enzo Doria	04/2016
2455	2^396258-459491	119286	Enzo Doria	05/2015
2456	2^396128-396128-1	119247	Karsten Bonath	06/2018
2457	(2^395986+5)/76881	119199	Lelio R Paula	04/2014
2458	(23*2^395942-1)/91	119190	Lelio R Paula	04/2014
2459	(11*2^395548+1)/3	119073	Lelio R Paula	04/2014
2460	(30^80599+1)/31	119054	Robert Price	07/2013
2461	(43*10^119024-403)/9	119025	Robert Price	01/2019
2462	2^395062-109121	118926	Enzo Doria	04/2014
2463	2^395055-4627	118924	Yves Minet	05/2019
2464	(2^394918+78557)/3	118882	Lelio R Paula	01/2015
2465	(16*10^118852+77)/3	118853	Robert Price	03/2019
2466	(2^394739+3)/1883	118826	Lelio R Paula	04/2014
2467	2^394266+71389	118686	Enzo Doria	04/2016
2468	2^394215-51261	118671	Tony Prest / Never Odd Or Even	04/2018
2469	(2^394215-48793)/5/5	118670	Tony Prest / Never Odd Or Even	04/2018
2470	(2^394215-17063)/3/3/5	118669	Tony Prest / Never Odd Or Even	04/2018
2471	(2^394215-24393)/5/5/5/5/5	118668	Tony Prest / Never Odd Or Even	04/2018
2472	(2^394215-35885)/3/71/173	118666	Tony Prest / Never Odd Or Even	04/2018
2473	(2^394215-47925)/353/2269	118665	Tony Prest / Never Odd Or Even	04/2018
2474	(2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673	118650	Tony Prest / Never Odd Or Even	04/2018
2475	(17*10^118635+13)/3	118636	Robert Price	01/2019
2476	5^169727+2	118635	Lelio R Paula	08/2013
2477	2^394034-3	118617	M. Frind & P. Underwood	09/2002
2478	(7*10^118607+179)/3	118608	Robert Price	09/2018
2479	3^248572-6242	118599	Enzo Doria	05/2014
2480	(3*2^393964-1)/181	118594	Lelio R Paula	04/2014
2481	7^140303-6	118570	Robert Price	11/2014
2482	2^393427+75683	118434	Enzo Doria	04/2016
2483	2^393376-114749	118418	Enzo Doria	04/2015
2484	2^393180+73	118359	Lelio R Paula	04/2013
2485	p(23881)#/2+256	118328	Robert Price	05/2017
2486	(10^118324+359)/9	118324	Serge Batalov	12/2014
2487	p(23879)#/2+64	118317	Robert Price	03/2017
2488	(53*10^118216+1)/9	118217	Serge Batalov	11/2010
2489	(7*2^392697+1)/15	118214	Renaud Lifchitz	03/2011
2490	(157^53819-1)/156	118179	Alexander Zhirkov	06/2016
2491	(19*2^392551+1)/3	118171	Lelio R Paula	04/2014
2492	2^392516-29219	118160	Enzo Doria	07/2015
2493	Phi(177231,10)	118152	Maksym Voznyy	09/2015
2494	2^392413-112123	118129	Enzo Doria	06/2014
2495	(2^392342+5)/27	118106	Lelio R Paula	04/2014
2496	2^392300-1841429	118095	Enzo Doria	06/2015
2497	2^392220+75241	118070	Enzo Doria	04/2016
2498	10^118009+664447	118010	Patrick De Geest	07/2018
2499	10^118009-20001	118009	Robert Price	01/2018
2500	(14*10^117991+61)/3	117992	Robert Price	12/2018

Find by discoverer :

PRP Records

Probable Primes Top 10000

(253466 PRPs in the top)