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	2^428502-113285	128992	Enzo Doria	07/2014
2252	2^428421-21373	128968	Enzo Doria	06/2013
2253	L(616787)	128901	Henri Lifchitz	09/2008
2254	91^65772-2	128851	Lelio R Paula	05/2017
2255	2^428022+43	128848	Lelio R Paula	05/2017
2256	2^427999-459397	128841	Enzo Doria	05/2015
2257	2^427993+76847	128839	Enzo Doria	05/2016
2258	2^427824-1851507	128788	Enzo Doria	08/2015
2259	2^427807-21469	128783	Enzo Doria	07/2013
2260	11^123594-240	128710	Enzo Doria	09/2012
2261	2^427504-21503	128692	Enzo Doria	07/2013
2262	2^427420+91	128667	Lelio R Paula	05/2017
2263	(68*10^128645-257)/9	128646	Robert Price	07/2019
2264	2^427269-113635	128621	Enzo Doria	08/2014
2265	2^427130+1877569	128579	Enzo Doria	08/2016
2266	2^427016-115349	128545	Enzo Doria	07/2015
2267	(4*10^128510+137)/3	128511	Robert Price	03/2018
2268	2^426889-112879	128507	Enzo Doria	06/2014
2269	2^426804+1869931	128481	Enzo Doria	05/2016
2270	2^426750+77635	128465	Enzo Doria	05/2016
2271	2^426425-91	128367	Lelio R Paula	05/2017
2272	(15*2^426398-1)/11	128359	Lelio R Paula	05/2014
2273	2^426352+74971	128345	Enzo Doria	04/2016
2274	4*10^128343-21	128344	Robert Price	09/2018
2275	2^426300-1863689	128330	Enzo Doria	03/2016
2276	2^426293+1881017	128327	Enzo Doria	11/2016
2277	2^426043+35	128252	Robert Price	11/2015
2278	(4*10^128244-19)/3	128245	Robert Price	03/2018
2279	(305*10^128198+1)/9	128200	Robert Price	02/2020
2280	2^425808-459959	128181	Enzo Doria	06/2015
2281	2^425627-113605	128127	Enzo Doria	08/2014
2282	(22*10^128094+53)/3	128095	Robert Price	07/2019
2283	(86*10^128086-221)/9	128087	Robert Price	09/2019
2284	18565^30002-30002^18565	128070	Norbert Schneider	01/2015
2285	(2^425287-9)/2737	128021	Lelio R Paula	05/2015
2286	(3*2^425233-1)/25	128007	Lelio R Paula	05/2014
2287	2^425205+4911	128000	Marek Hubal	02/2017
2288	2^425118-113663	127974	Enzo Doria	08/2014
2289	(86*10^127967-329)/9	127968	Robert Price	01/2020
2290	2^425061+1869761	127957	Enzo Doria	05/2016
2291	746^44541+44541^746	127955	Norbert Schneider	07/2019
2292	2^424918-21141	127914	Enzo Doria	07/2013
2293	2^424864-29489	127897	Enzo Doria	08/2015
2294	(97*10^127858-1)/3	127860	Serge Batalov	12/2014
2295	2^424632-2786639	127827	Enzo Doria	03/2016
2296	2^424577-113755	127811	Enzo Doria	09/2014
2297	(7*2^424512-1)/3	127792	Lelio R Paula	05/2014
2298	(56*10^127752+691)/9	127753	Robert Price	05/2019
2299	11^122629-720	127705	Enzo Doria	11/2012
2300	22*10^127645+3	127647	Robert Price	01/2020
2301	2^423696-21429	127546	Enzo Doria	07/2013
2302	2^423664-1864559	127536	Enzo Doria	03/2016
2303	3^267267-4	127519	Henri Lifchitz	10/2014
2304	(19^99689+5^99689)/24	127477	Robert Price	09/2013
2305	(21*2^423372+1)/101	127447	Lelio R Paula	05/2014
2306	2^423328-21537	127435	Enzo Doria	07/2013
2307	(67*10^127413-7)/3	127415	Robert Price	01/2020
2308	(2^423165-7)/25	127384	Lelio R Paula	05/2015
2309	(112*10^127324+17)/3	127326	Robert Price	03/2020
2310	(F(5)^182099-F(4)^182099)/F(3)	127282	Wayne Halsdorf	08/2013
2311	(16*10^127259+197)/3	127260	Robert Price	04/2019
2312	(26*10^127240+61)/3	127241	Robert Price	10/2019
2313	(234483*27^88884-145)/26	127230	Curtis Bright	05/2015
2314	2^422515-114997	127190	Enzo Doria	06/2015
2315	5*10^127179-3	127180	Robert Price	07/2015
2316	(44*10^127169-233)/9	127170	Robert Price	01/2019
2317	5*10^127153+77	127154	Robert Price	12/2018
2318	736^44335+44335^736	127104	Norbert Schneider	07/2019
2319	-516776642557847117490*Bern(37960)/34256837217082767928421792453	127042	Thomas Ritschel	06/2017
2320	(78^67141-1)/77	127036	Paul Bourdelais	09/2017
2321	2^421860-113285	126993	Enzo Doria	07/2014
2322	(2^421827-7)/11	126982	Lelio R Paula	05/2015
2323	11^121910-840	126957	Enzo Doria	12/2012
2324	(29*10^126928-77)/3	126929	Robert Price	02/2020
2325	(71^68539+1)/72	126882	Paul Bourdelais	09/2017
2326	(5*10^126871-119)/3	126872	Robert Price	03/2018
2327	331^50339-10004	126846	Enzo Doria	07/2012
2328	2^421363-2790757	126843	Enzo Doria	03/2016
2329	(106*10^126839-1)/3	126841	Serge Batalov	12/2014
2330	(7*2^421243+1)/39	126807	Lelio R Paula	05/2014
2331	(14*10^126784-83)/3	126785	Robert Price	12/2018
2332	2^421161-286183	126783	Enzo Doria	06/2015
2333	2^420939-113935	126716	Enzo Doria	10/2014
2334	177^56363-2	126703	Lelio R Paula	10/2017
2335	2^420741-113659	126656	Enzo Doria	08/2014
2336	2^420694-21	126642	Lelio R Paula	05/2017
2338	(13*10^126638+437)/9	126639	Robert Price	04/2018
2337	(167*10^126637-17)/3	126639	Robert Price	03/2020
2339	4*10^126625+87	126626	Robert Price	08/2018
2340	(31*2^420556+1)/7	126601	Lelio R Paula	05/2014
2341	7*10^126600-99	126601	Robert Price	06/2019
2342	2^420424-59189	126561	Enzo Doria	10/2015
2343	2^420126+71893	126471	Enzo Doria	04/2016
2344	(43*10^126441+47)/9	126442	Robert Price	12/2018
2345	2^419866+1877059	126393	Enzo Doria	07/2016
2346	F(604711)	126377	Henri Lifchitz	02/2005
2347	2^419757+72707	126360	Enzo Doria	04/2016
2348	2^419720-21569	126349	Enzo Doria	07/2013
2349	2^419637+29	126324	Henri Lifchitz	02/2006
2350	2^419612+1876741	126316	Enzo Doria	07/2016
2351	2^419520+2793271	126289	Enzo Doria	03/2016
2352	(2^419447-5)/369	126264	Lelio R Paula	05/2014
2353	2^419328-1859939	126231	Enzo Doria	03/2016
2354	2^419282-1851507	126217	Enzo Doria	08/2015
2355	2^419251+1866143	126208	Enzo Doria	03/2016
2356	11^121185+2	126202	Robert Price	05/2014
2357	(23*2^419036-1)/1393	126141	Lelio R Paula	05/2014
2358	2^418851+23	126087	Robert Price	09/2015
2359	(2^418849-9)/2681	126083	Lelio R Paula	05/2014
2360	2^418829+167	126081	Lelio R Paula	01/2012
2361	(31*2^418782-1)/75891	126063	Lelio R Paula	05/2014
2362	(19*2^418754-1)/15	126058	Lelio R Paula	05/2014
2363	2^418319-109501	125927	Enzo Doria	04/2014
2364	2^418316-112373	125926	Enzo Doria	06/2014
2365	(8*10^125894-29)/3	125895	Robert Price	07/2018
2366	(26*10^125886-413)/9	125887	Robert Price	05/2018
2367	2^417968+1869811	125821	Enzo Doria	06/2016
2368	2^417902+63	125802	Lelio R Paula	09/2015
2369	(10^125792-91)/9	125792	Serge Batalov	12/2014
2370	(35*10^125754-593)/9	125755	Robert Price	07/2018
2371	(32*10^125751-77)/9	125752	Robert Price	06/2018
2372	2^417704+77011	125742	Enzo Doria	05/2016
2373	(10^125706+149)/3	125706	Serge Batalov	12/2014
2374	2^417419-115309	125656	Enzo Doria	07/2015
2375	2^417300+77281	125620	Enzo Doria	05/2016
2376	2^417095-1657	125559	Yves Minet	07/2014
2377	2^416773-25	125462	Lelio R Paula	09/2015
2378	(289511#+292834)/(2^3*146417)	125444	Makoto Morimoto	10/2017
2379	(11*2^416691+1)/43	125436	Lelio R Paula	05/2014
2380	(289511#+1896)/(23^3797801939911849)	125434	Makoto Morimoto	06/2019
2381	2^416641-2*416641+1	125422	Robert Price	05/2018
2382	(21*2^416566-1)/17	125399	Lelio R Paula	05/2014
2383	2^416530+1870429	125389	Enzo Doria	05/2016
2384	(56*10^125385+691)/9	125386	Robert Price	05/2019
2385	2^416490+1875109	125376	Enzo Doria	09/2016
2386	2^416416-114929	125354	Enzo Doria	05/2015
2387	(77*10^125330-293)/9	125331	Robert Price	09/2019
2388	(172*10^125292-1)/9	125294	Serge Batalov	12/2014
2389	2^416134+1865899	125269	Enzo Doria	03/2016
2390	153^57337-152	125264	Norbert Schneider	12/2018
2391	(9*2^415992+1)/13560845	125220	Lelio R Paula	05/2014
2392	(23^91943-1)/22	125201	Robert Price	01/2012
2393	43125^27010-106	125185	Enzo Doria	08/2012
2394	(38*10^125166+349)/9	125167	Robert Price	10/2018
2395	2^415765-112603	125158	Enzo Doria	06/2014
2396	8*10^125088-13	125089	Robert Price	08/2019
2397	(25*10^125076-13)/3	125077	Robert Price	09/2019
2398	(29*10^125021-113)/3	125022	Robert Price	10/2019
2399	2^415290-113591	125015	Enzo Doria	08/2014
2400	2^415276-460919	125011	Enzo Doria	06/2015
2401	2^415259+77243	125006	Enzo Doria	05/2016
2402	2^415144-3683	124971	Yves Minet	10/2011
2403	2^414874+79	124890	Lelio R Paula	01/2015
2404	(2^414765+7)/1389	124854	Lelio R Paula	05/2014
2405	2^414618+79459	124813	Enzo Doria	06/2016
2406	(61*10^124809-1)/3	124811	Robert Price	01/2020
2407	2^414432-1846709	124757	Enzo Doria	07/2015
2408	2*10^124751-51	124752	Robert Price	04/2018
2409	(56*10^124735+367)/9	124736	Robert Price	06/2019
2410	(13*2^414274-1)/153	124708	Lelio R Paula	05/2014
2411	56*10^124656-3	124658	Robert Price	03/2020
2412	(7*10^124648+197)/3	124649	Robert Price	07/2018
2414	2^414032-5	124637	Henri Lifchitz	07/2006
2413	2^414032+1872331	124637	Enzo Doria	05/2016
2415	14120^30009-30009^14120	124533	Norbert Schneider	02/2015
2416	64^68909-63^68909	124463	Robert Price	07/2013
2417	2^413387+76253	124442	Enzo Doria	04/2016
2418	2^413352+524287	124432	Paul Underwood	09/2018
2419	287117#+391613	124424	Nicolas PALAU	01/2017
2420	(4*10^124420+83)/3	124421	Robert Price	02/2018
2421	(27*2^413207-1)/108335	124385	Lelio R Paula	05/2014
2422	(41*10^124335-383)/9	124336	Robert Price	11/2018
2423	(304*10^124329-43)/9	124331	Robert Price	02/2020
2424	2^412868-120599	124286	Paul Bourdelais	02/2012
2425	45^75145-2	124231	Lelio R Paula	08/2015
2426	2^412645-112213	124219	Enzo Doria	06/2014
2427	2^412248+74611	124100	Enzo Doria	04/2016
2428	(22*10^124096-13)/9	124097	Robert Price	06/2018
2429	2^412192-3329	124083	Yves Minet	12/2014
2430	(25*2^412191-1)/23	124082	Lelio R Paula	05/2014
2431	(25*10^124076-67)/3	124077	Robert Price	06/2019
2432	F(593689)	124074	Henri Lifchitz	01/2005
2433	(11*2^412161+1)/19	124073	Lelio R Paula	05/2014
2434	2^411884-113279	123990	Enzo Doria	07/2014
2435	(2^411832+1)/257	123972	Lelio R Paula	05/2014
2436	(2^411833+2)/514	123972	Stefano Morozzi	03/2020
2437	(26*10^123970-89)/9	123971	Robert Price	06/2018
2438	2^411790-1853531	123962	Enzo Doria	08/2015
2439	(5^177337+1)/6	123953	Paul Bourdelais	11/2008
2440	2^411711-113257	123938	Enzo Doria	07/2014
2441	(23*2^411675-1)/3	123928	Lelio R Paula	05/2014
2442	(11*10^123899-179)/3	123900	Robert Price	09/2018
2443	2^411325-351103	123822	Enzo Doria	06/2015
2444	2^411052+1872481	123739	Enzo Doria	05/2016
2445	2^410997+39	123723	Lelio R Paula	05/2014
2446	(148*10^123688-1)/3	123690	Robert Price	03/2020
2447	8*10^123657+87	123658	Robert Price	10/2019
2448	155^56438+154	123618	Norbert Schneider	01/2019
2449	2^410596-39	123602	Lelio R Paula	05/2014
2450	2^410540-115079	123585	Enzo Doria	06/2015
2451	(7*10^123563+107)/3	123564	Robert Price	02/2018
2452	9*10^123549+89	123550	Robert Price	11/2019
2453	(3*2^410392-1)/9229	123537	Lelio R Paula	05/2014
2454	2^410206-113081	123485	Enzo Doria	07/2014
2455	(25*2^410192+1)/10397	123478	Lelio R Paula	04/2014
2456	2^409909-189	123395	Enzo Doria	05/2014
2457	2^409896-109043	123391	Enzo Doria	04/2014
2458	2^409890+75409	123390	Enzo Doria	04/2016
2459	133^58076-2	123345	Lelio R Paula	10/2017
2460	F(590041)	123311	Henri Lifchitz	01/2005
2461	2^409566-113501	123292	Enzo Doria	08/2014
2462	2^409533+77747	123282	Enzo Doria	05/2016
2463	2^409436-112799	123253	Enzo Doria	06/2014
2464	2^409225+1873787	123189	Enzo Doria	06/2016
2465	2^409174+73009	123174	Enzo Doria	04/2016
2466	2^409058-112685	123139	Enzo Doria	06/2014
2467	(13*10^123137-61)/3	123138	Robert Price	11/2018
2468	4*10^123113+21	123114	Robert Price	12/2018
2469	2^408778+77689	123055	Enzo Doria	05/2016
2470	2^408690-75	123028	Lelio R Paula	11/2013
2471	(29*10^122996+673)/9	122997	Robert Price	12/2018
2472	2^408574-2787341	122994	Enzo Doria	03/2016
2473	3*10^122977+37	122978	Robert Price	08/2018
2474	Phi(157825,10)	122961	Maksym Voznyy	06/2015
2475	(68*10^122933-419)/9	122934	Robert Price	07/2019
2476	(13*2^408283+1)/1665	122904	Lelio R Paula	05/2014
2477	(16*10^122871+77)/3	122872	Robert Price	03/2019
2478	(11*2^408100-1)/35	122850	Lelio R Paula	04/2014
2479	(19*10^122836-43)/3	122837	Robert Price	05/2019
2480	(2^407821-lucasV(1,2,407821)+1)/2	122767	Mike Oakes	11/2016
2481	(32*10^122733-77)/9	122734	Robert Price	06/2018
2482	(21*2^407604-1)/215	122701	Lelio R Paula	04/2014
2483	(22*10^122681+161)/3	122682	Robert Price	05/2019
2484	(21*2^407433-1)/13	122650	Lelio R Paula	04/2014
2485	(26*10^122625-131)/3	122626	Robert Price	10/2019
2486	(73*10^122592-1)/9	122593	Robert Price	01/2015
2487	(5*10^122592+91)/3	122593	Robert Price	04/2018
2488	(85*10^122585-1)/3	122587	Robert Price	02/2020
2489	2^407179-112075	122574	Enzo Doria	06/2014
2490	(21*2^407131+1)/207517523	122552	Lelio R Paula	04/2014
2491	(66^67349+1)/67	122543	Paul Bourdelais	09/2017
2492	2^407008-1867919	122522	Enzo Doria	04/2016
2493	11^117642-300	122512	Enzo Doria	10/2012
2494	(F(397700+1)^2+L(397700+1)^2)/2	122509	Henri Lifchitz	10/2017
2495	2^406949+72197	122504	Enzo Doria	04/2016
2496	(19*10^122501+149)/3	122502	Robert Price	05/2019
2497	2^406826-65	122467	Lelio R Paula	11/2013
2498	2^406821-2797363	122466	Enzo Doria	04/2016
2499	2^406758-17	122447	Lelio R Paula	11/2013
2500	(30^82883-1)/29	122427	Robert Price	12/2011

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Probable Primes Top 10000

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