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	11^121910-840	126957	Enzo Doria	12/2012
2252	(71^68539+1)/72	126882	Paul Bourdelais	09/2017
2253	(5*10^126871-119)/3	126872	Robert Price	03/2018
2254	331^50339-10004	126846	Enzo Doria	07/2012
2255	2^421363-2790757	126843	Enzo Doria	03/2016
2256	(106*10^126839-1)/3	126841	Serge Batalov	12/2014
2257	(7*2^421243+1)/39	126807	Lelio R Paula	05/2014
2258	(14*10^126784-83)/3	126785	Robert Price	12/2018
2259	2^421161-286183	126783	Enzo Doria	06/2015
2260	2^420939-113935	126716	Enzo Doria	10/2014
2261	177^56363-2	126703	Lelio R Paula	10/2017
2262	2^420741-113659	126656	Enzo Doria	08/2014
2263	2^420694-21	126642	Lelio R Paula	05/2017
2264	(13*10^126638+437)/9	126639	Robert Price	04/2018
2265	4*10^126625+87	126626	Robert Price	08/2018
2267	(31*2^420556+1)/7	126601	Lelio R Paula	05/2014
2266	7*10^126600-99	126601	Robert Price	06/2019
2268	2^420424-59189	126561	Enzo Doria	10/2015
2269	2^420126+71893	126471	Enzo Doria	04/2016
2270	(43*10^126441+47)/9	126442	Robert Price	12/2018
2271	2^419866+1877059	126393	Enzo Doria	07/2016
2272	F(604711)	126377	Henri Lifchitz	02/2005
2273	2^419757+72707	126360	Enzo Doria	04/2016
2274	2^419720-21569	126349	Enzo Doria	07/2013
2275	2^419637+29	126324	Henri Lifchitz	02/2006
2276	2^419612+1876741	126316	Enzo Doria	07/2016
2277	2^419520+2793271	126289	Enzo Doria	03/2016
2278	(2^419447-5)/369	126264	Lelio R Paula	05/2014
2279	2^419328-1859939	126231	Enzo Doria	03/2016
2280	2^419282-1851507	126217	Enzo Doria	08/2015
2281	2^419251+1866143	126208	Enzo Doria	03/2016
2282	11^121185+2	126202	Robert Price	05/2014
2283	(23*2^419036-1)/1393	126141	Lelio R Paula	05/2014
2284	2^418851+23	126087	Robert Price	09/2015
2285	(2^418849-9)/2681	126083	Lelio R Paula	05/2014
2286	2^418829+167	126081	Lelio R Paula	01/2012
2287	(31*2^418782-1)/75891	126063	Lelio R Paula	05/2014
2288	(19*2^418754-1)/15	126058	Lelio R Paula	05/2014
2289	2^418319-109501	125927	Enzo Doria	04/2014
2290	2^418316-112373	125926	Enzo Doria	06/2014
2291	(8*10^125894-29)/3	125895	Robert Price	07/2018
2292	(26*10^125886-413)/9	125887	Robert Price	05/2018
2293	2^417968+1869811	125821	Enzo Doria	06/2016
2294	2^417902+63	125802	Lelio R Paula	09/2015
2295	(10^125792-91)/9	125792	Serge Batalov	12/2014
2296	(35*10^125754-593)/9	125755	Robert Price	07/2018
2297	(32*10^125751-77)/9	125752	Robert Price	06/2018
2298	2^417704+77011	125742	Enzo Doria	05/2016
2299	(10^125706+149)/3	125706	Serge Batalov	12/2014
2300	2^417419-115309	125656	Enzo Doria	07/2015
2301	2^417300+77281	125620	Enzo Doria	05/2016
2302	2^417095-1657	125559	Yves Minet	07/2014
2303	2^416773-25	125462	Lelio R Paula	09/2015
2304	(289511#+292834)/(2^3*146417)	125444	Makoto Morimoto	10/2017
2305	(11*2^416691+1)/43	125436	Lelio R Paula	05/2014
2306	(289511#+1896)/(23^3797801939911849)	125434	Makoto Morimoto	06/2019
2307	2^416641-2*416641+1	125422	Robert Price	05/2018
2308	(21*2^416566-1)/17	125399	Lelio R Paula	05/2014
2309	2^416530+1870429	125389	Enzo Doria	05/2016
2310	(56*10^125385+691)/9	125386	Robert Price	05/2019
2311	2^416490+1875109	125376	Enzo Doria	09/2016
2312	2^416416-114929	125354	Enzo Doria	05/2015
2313	(77*10^125330-293)/9	125331	Robert Price	09/2019
2314	(172*10^125292-1)/9	125294	Serge Batalov	12/2014
2315	2^416134+1865899	125269	Enzo Doria	03/2016
2316	153^57337-152	125264	Norbert Schneider	12/2018
2317	(9*2^415992+1)/13560845	125220	Lelio R Paula	05/2014
2318	(23^91943-1)/22	125201	Robert Price	01/2012
2319	43125^27010-106	125185	Enzo Doria	08/2012
2320	(38*10^125166+349)/9	125167	Robert Price	10/2018
2321	2^415765-112603	125158	Enzo Doria	06/2014
2322	8*10^125088-13	125089	Robert Price	08/2019
2323	(25*10^125076-13)/3	125077	Robert Price	09/2019
2324	(29*10^125021-113)/3	125022	Robert Price	10/2019
2325	2^415290-113591	125015	Enzo Doria	08/2014
2326	2^415276-460919	125011	Enzo Doria	06/2015
2327	2^415259+77243	125006	Enzo Doria	05/2016
2328	2^415144-3683	124971	Yves Minet	10/2011
2329	2^414874+79	124890	Lelio R Paula	01/2015
2330	(2^414765+7)/1389	124854	Lelio R Paula	05/2014
2331	2^414618+79459	124813	Enzo Doria	06/2016
2332	2^414432-1846709	124757	Enzo Doria	07/2015
2333	2*10^124751-51	124752	Robert Price	04/2018
2334	(56*10^124735+367)/9	124736	Robert Price	06/2019
2335	(13*2^414274-1)/153	124708	Lelio R Paula	05/2014
2336	(7*10^124648+197)/3	124649	Robert Price	07/2018
2338	2^414032-5	124637	Henri Lifchitz	07/2006
2337	2^414032+1872331	124637	Enzo Doria	05/2016
2339	14120^30009-30009^14120	124533	Norbert Schneider	02/2015
2340	64^68909-63^68909	124463	Robert Price	07/2013
2341	2^413387+76253	124442	Enzo Doria	04/2016
2342	2^413352+524287	124432	Paul Underwood	09/2018
2343	287117#+391613	124424	Nicolas PALAU	01/2017
2344	(4*10^124420+83)/3	124421	Robert Price	02/2018
2345	(27*2^413207-1)/108335	124385	Lelio R Paula	05/2014
2346	(41*10^124335-383)/9	124336	Robert Price	11/2018
2347	2^412868-120599	124286	Paul Bourdelais	02/2012
2348	45^75145-2	124231	Lelio R Paula	08/2015
2349	2^412645-112213	124219	Enzo Doria	06/2014
2350	2^412248+74611	124100	Enzo Doria	04/2016
2351	(22*10^124096-13)/9	124097	Robert Price	06/2018
2352	2^412192-3329	124083	Yves Minet	12/2014
2353	(25*2^412191-1)/23	124082	Lelio R Paula	05/2014
2354	(25*10^124076-67)/3	124077	Robert Price	06/2019
2355	F(593689)	124074	Henri Lifchitz	01/2005
2356	(11*2^412161+1)/19	124073	Lelio R Paula	05/2014
2357	2^411884-113279	123990	Enzo Doria	07/2014
2358	(2^411832+1)/257	123972	Lelio R Paula	05/2014
2359	(26*10^123970-89)/9	123971	Robert Price	06/2018
2360	2^411790-1853531	123962	Enzo Doria	08/2015
2361	(5^177337+1)/6	123953	Paul Bourdelais	11/2008
2362	2^411711-113257	123938	Enzo Doria	07/2014
2363	(23*2^411675-1)/3	123928	Lelio R Paula	05/2014
2364	(11*10^123899-179)/3	123900	Robert Price	09/2018
2365	2^411325-351103	123822	Enzo Doria	06/2015
2366	2^411052+1872481	123739	Enzo Doria	05/2016
2367	2^410997+39	123723	Lelio R Paula	05/2014
2368	8*10^123657+87	123658	Robert Price	10/2019
2369	155^56438+154	123618	Norbert Schneider	01/2019
2370	2^410596-39	123602	Lelio R Paula	05/2014
2371	2^410540-115079	123585	Enzo Doria	06/2015
2372	(7*10^123563+107)/3	123564	Robert Price	02/2018
2373	9*10^123549+89	123550	Robert Price	11/2019
2374	(3*2^410392-1)/9229	123537	Lelio R Paula	05/2014
2375	2^410206-113081	123485	Enzo Doria	07/2014
2376	(25*2^410192+1)/10397	123478	Lelio R Paula	04/2014
2377	2^409909-189	123395	Enzo Doria	05/2014
2378	2^409896-109043	123391	Enzo Doria	04/2014
2379	2^409890+75409	123390	Enzo Doria	04/2016
2380	133^58076-2	123345	Lelio R Paula	10/2017
2381	F(590041)	123311	Henri Lifchitz	01/2005
2382	2^409566-113501	123292	Enzo Doria	08/2014
2383	2^409533+77747	123282	Enzo Doria	05/2016
2384	2^409436-112799	123253	Enzo Doria	06/2014
2385	2^409225+1873787	123189	Enzo Doria	06/2016
2386	2^409174+73009	123174	Enzo Doria	04/2016
2387	2^409058-112685	123139	Enzo Doria	06/2014
2388	(13*10^123137-61)/3	123138	Robert Price	11/2018
2389	4*10^123113+21	123114	Robert Price	12/2018
2390	2^408778+77689	123055	Enzo Doria	05/2016
2391	2^408690-75	123028	Lelio R Paula	11/2013
2392	(29*10^122996+673)/9	122997	Robert Price	12/2018
2393	2^408574-2787341	122994	Enzo Doria	03/2016
2394	3*10^122977+37	122978	Robert Price	08/2018
2395	Phi(157825,10)	122961	Maksym Voznyy	06/2015
2396	(68*10^122933-419)/9	122934	Robert Price	07/2019
2397	(13*2^408283+1)/1665	122904	Lelio R Paula	05/2014
2398	(16*10^122871+77)/3	122872	Robert Price	03/2019
2399	(11*2^408100-1)/35	122850	Lelio R Paula	04/2014
2400	(19*10^122836-43)/3	122837	Robert Price	05/2019
2401	(2^407821-lucasV(1,2,407821)+1)/2	122767	Mike Oakes	11/2016
2402	(32*10^122733-77)/9	122734	Robert Price	06/2018
2403	(21*2^407604-1)/215	122701	Lelio R Paula	04/2014
2404	(22*10^122681+161)/3	122682	Robert Price	05/2019
2405	(21*2^407433-1)/13	122650	Lelio R Paula	04/2014
2406	(26*10^122625-131)/3	122626	Robert Price	10/2019
2408	(73*10^122592-1)/9	122593	Robert Price	01/2015
2407	(5*10^122592+91)/3	122593	Robert Price	04/2018
2409	2^407179-112075	122574	Enzo Doria	06/2014
2410	(21*2^407131+1)/207517523	122552	Lelio R Paula	04/2014
2411	(66^67349+1)/67	122543	Paul Bourdelais	09/2017
2412	2^407008-1867919	122522	Enzo Doria	04/2016
2413	11^117642-300	122512	Enzo Doria	10/2012
2414	(F(397700+1)^2+L(397700+1)^2)/2	122509	Henri Lifchitz	10/2017
2415	2^406949+72197	122504	Enzo Doria	04/2016
2416	(19*10^122501+149)/3	122502	Robert Price	05/2019
2417	2^406826-65	122467	Lelio R Paula	11/2013
2418	2^406821-2797363	122466	Enzo Doria	04/2016
2419	2^406758-17	122447	Lelio R Paula	11/2013
2420	(30^82883-1)/29	122427	Robert Price	12/2011
2421	(2^406583-1)/813167	122388	Jens K. Andersen	02/2009
2422	4*10^122377+19	122378	Robert Price	10/2018
2423	Phi(246362,10)	122365	Makoto Kamada	09/2019
2424	3*10^122345-97	122346	Robert Price	07/2018
2425	97^61575-2	122336	Lelio R Paula	12/2014
2426	2^406298+2799109	122308	Enzo Doria	04/2016
2427	7*10^122294+57	122295	Robert Price	06/2019
2428	(27*2^406241-1)/10277	122289	Lelio R Paula	04/2014
2429	2^406229-1849993	122288	Enzo Doria	08/2015
2430	3*10^122274+7	122275	Robert Price	07/2015
2431	2^406117+1876577	122254	Enzo Doria	07/2016
2432	3^256199-2^256199	122238	Mike Oakes	06/2005
2433	2^405992-78557	122216	Jorge Menendez	03/2018
2434	(8*10^122203+43)/3	122204	Robert Price	06/2018
2435	(58*10^122170+329)/9	122171	Robert Price	05/2019
2436	2^405774+179149	122151	Enzo Doria	06/2016
2437	5*10^122082+41	122083	Robert Price	03/2019
2438	2^405514-3311	122072	Yves Minet	12/2014
2439	2^405514-115511	122072	Enzo Doria	07/2015
2440	2^405422-113261	122045	Enzo Doria	07/2014
2441	2^405173+71237	121970	Enzo Doria	04/2016
2442	(2^405016+1)/257	121920	Lelio R Paula	04/2014
2443	2^404858+71329	121875	Enzo Doria	04/2016
2444	2^404813-114703	121861	Enzo Doria	04/2015
2445	2^404764+77791	121847	Enzo Doria	05/2016
2446	317^48694+48694^317	121787	Norbert Schneider	08/2015
2447	2^404536-115259	121778	Enzo Doria	06/2015
2448	2^404501-631	121767	Yves Minet	07/2012
2449	63^67620+2	121672	Lelio R Paula	08/2015
2450	(16*10^121633+167)/3	121634	Robert Price	06/2019
2451	(17*10^121621+1)/9	121622	Serge Batalov	05/2010
2452	(15*2^403912+1)/271	121589	Lelio R Paula	05/2014
2453	(10^121543-79)/3	121543	Robert Price	01/2018
2454	2^403676+76831	121519	Enzo Doria	05/2016
2455	(7*10^121487+143)/3	121488	Robert Price	03/2018
2456	2^403363-113635	121425	Enzo Doria	08/2014
2457	2^403336-1861469	121417	Enzo Doria	03/2016
2458	p(24442)#/2-64	121381	Robert Price	04/2017
2459	11^116555-720	121380	Enzo Doria	11/2012
2460	2^403100-461267	121346	Enzo Doria	07/2015
2461	2^403093-112213	121344	Enzo Doria	06/2014
2462	(316^48539+1)/317	121330	Eric Chen	10/2017
2463	2^403004+1866361	121317	Enzo Doria	03/2016
2464	2^402953+89	121301	Lelio R Paula	10/2013
2465	2^402944-2788319	121299	Enzo Doria	03/2016
2466	(44*10^121297-719)/9	121298	Robert Price	12/2018
2467	(27*2^402865+1)/5	121276	Lelio R Paula	04/2014
2468	2^402828-113183	121264	Enzo Doria	07/2014
2469	(17*10^121242+1)/9	121243	Serge Batalov	05/2010
2470	(15*2^402757+1)/101	121242	Lelio R Paula	05/2014
2472	2^402715+1874223	121230	Enzo Doria	06/2016
2471	(35*10^121229-593)/9	121230	Robert Price	07/2018
2473	(91^61879+1)/92	121222	Paul Bourdelais	09/2017
2474	7*10^121144+9	121145	Robert Price	09/2015
2475	2^401725-113251	120932	Enzo Doria	07/2014
2476	(15*2^401677-1)/19	120917	Lelio R Paula	05/2014
2477	2^401652+73711	120910	Enzo Doria	04/2016
2478	(2^401632+3)/79	120902	Lelio R Paula	04/2014
2479	2^401406-2791331	120836	Enzo Doria	03/2016
2480	(28^83497+1)/29	120832	Robert Price	07/2013
2481	(22*10^120828+161)/3	120829	Robert Price	05/2019
2482	2^401369+1867367	120825	Enzo Doria	03/2016
2483	(10^120782+29)/3	120782	Serge Batalov	12/2014
2484	2^401215-1657	120778	Yves Minet	07/2014
2485	2^401159+53	120761	Lelio R Paula	10/2013
2486	2^401031-113047	120723	Enzo Doria	07/2014
2487	(71*10^120703-287)/9	120704	Robert Price	09/2019
2488	(29*2^400909-1)/303	120685	Lelio R Paula	04/2014
2489	2^400571-15	120584	Lelio R Paula	10/2013
2490	(10^120574+359)/9	120574	Serge Batalov	12/2014
2491	2^400424-216413	120540	Enzo Doria	04/2013
2492	(17*2^400200-1)/587	120471	Lelio R Paula	05/2014
2493	2^400166+1874899	120462	Enzo Doria	06/2016
2494	(3*2^400045-1)/865	120424	Lelio R Paula	04/2014
2495	2^399966+73759	120402	Enzo Doria	04/2016
2496	(112*10^120395-1)/3	120397	Serge Batalov	12/2014
2497	2^399918-95	120388	Lelio R Paula	04/2013
2498	(49*10^120380-139)/9	120381	Robert Price	03/2019
2499	2^399792-1849259	120350	Enzo Doria	08/2015
2500	9*10^120342-7	120343	Robert Price	09/2015

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PRP Records

Probable Primes Top 10000

(255312 PRPs in the top)