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	2^502769+1877567	151349	Enzo Doria	08/2016
2252	2^502576-4019	151291	Yves Minet	10/2011
2253	5*10^151257+41	151258	Robert Price	03/2019
2254	2^502290-2792501	151205	Enzo Doria	02/2016
2255	2^502181+1868417	151172	Enzo Doria	04/2016
2256	6*10^151063-77	151064	Robert Price	09/2021
2257	2^501781-1850503	151052	Enzo Doria	08/2015
2258	(5*10^151007+37)/3	151008	Robert Price	03/2018
2259	2^501627-991	151005	Yves Minet	02/2014
2260	2^501577-115333	150990	Enzo Doria	07/2015
2261	8*10^150975+3	150976	Robert Price	08/2015
2262	2^501512-113669	150971	Enzo Doria	09/2014
2263	(83*10^150908+493)/9	150909	Robert Price	12/2021
2264	2*10^150818+83	150819	Robert Price	12/2021
2265	(12^139739+1)/13	150803	Paul Bourdelais	09/2011
2266	(31^101111-1)/30	150792	Alexander Zhirkov	11/2010
2267	2^500899-500899	150786	Henri Lifchitz	04/2005
2268	2^500832+1876801	150766	Enzo Doria	07/2016
2269	(23*10^150763-59)/9	150764	Robert Price	05/2018
2270	2^500699+1884953	150726	Enzo Doria	02/2017
2271	(13*10^150675-37)/3	150676	Robert Price	01/2019
2272	(2^500527+lucasV(1,2,500527)+1)/4	150674	Mike Oakes	11/2016
2273	2^500337-71101	150617	Enzo Doria	04/2016
2274	(74*10^150616+133)/9	150617	Robert Price	06/2019
2275	4*10^150577+91	150578	Robert Price	08/2018
2276	2^500160+80071	150564	Enzo Doria	06/2016
2277	(2^500120+5)/9	150551	Lelio R Paula	12/2017
2278	(43*10^150515-421)/9	150516	Robert Price	01/2019
2279	(10^150551-1)/9/385207015049/57498437921/7808738631274081	150512	Maksym Voznyy	08/2014
2280	(10^150551-1)/1556587827131683185788921941743157225041	150512	Robert Price	07/2016
2281	2^499861-29503	150474	Enzo Doria	08/2015
2282	2^499653-113533	150411	Enzo Doria	08/2014
2283	(14*10^150391-191)/3	150392	Robert Price	10/2020
2284	2^499534-221	150375	Yves Minet	06/2012
2285	(28*10^150294+41)/3	150295	Robert Price	07/2021
2286	2^499225+49727	150282	Enzo Doria	09/2016
2287	(695*10^150274+7)/9	150276	Robert Price	12/2021
2288	2^499054-29261	150231	Enzo Doria	07/2015
2289	(844*10^150196-7)/9	150198	Robert Price	05/2021
2290	2^498907-933075	150186	Paul Bourdelais	06/2021
2291	(2^498898-7)/9	150183	Lelio R Paula	10/2015
2292	3*10^150182+17	150183	Robert Price	07/2018
2293	5*10^150175+63	150176	Robert Price	09/2020
2294	(77*10^150128+67)/9	150129	Robert Price	12/2021
2295	2^498623+1866983	150101	Enzo Doria	03/2016
2296	(25*10^150050-403)/9	150051	Robert Price	12/2020
2297	numbpart(18140942830)	150033	Serge Batalov	04/2017
2298	10^150029+4381	150030	Patrick De Geest	05/2016
2299	10^150029-41	150029	Serge Batalov	12/2014
2300	10^150000+1158603	150001	Patrick De Geest	09/2018
2301	10^150000-245703	150000	Patrick De Geest	09/2018
2302	(38*10^149999+691)/9	150000	Robert Price	10/2018
2303	2^498238-53	149985	Lelio R Paula	12/2017
2304	45728^1905+1905^45728	149984	Hans Havermann	10/2020
2305	5*10^149907+23	149908	Robert Price	03/2019
2306	39347^6442+6442^39347	149874	Hans Havermann	09/2020
2307	2^497850+81049	149868	Enzo Doria	07/2016
2308	37228^10575+10575^37228	149816	Hans Havermann	10/2020
2309	(5*2^497673+1)/2743	149812	Lelio R Paula	10/2015
2310	(5*2^497671+1)/373703	149810	Lelio R Paula	10/2015
2311	(2*10^149803-143)/3	149803	Robert Price	03/2018
2312	33845^26604+26604^33845	149763	Hans Havermann	09/2020
2313	2^497434-2784191	149743	Enzo Doria	10/2015
2314	(865*10^149737-1)/9	149739	Robert Price	04/2020
2315	10^149695-7000001	149695	Robert Price	06/2021
2316	38237^8214+8214^38237	149681	Hans Havermann	09/2020
2317	(23*10^149655+19)/3	149656	Robert Price	07/2019
2318	2^497068-113579	149633	Enzo Doria	08/2014
2319	2^497037+73727	149624	Enzo Doria	04/2016
2320	11*10^149618+3	149620	Robert Price	07/2021
2321	34942^19067+19067^34942	149562	Hans Havermann	09/2020
2322	33696^27449+27449^33696	149561	Hans Havermann	09/2020
2323	2^496773+77747	149544	Enzo Doria	05/2016
2324	(7*10^149483-493)/9	149483	Robert Price	04/2021
2325	(206*10^149459+7)/3	149461	Robert Price	07/2020
2326	34589^20940+20940^34589	149459	Hans Havermann	09/2020
2327	2^496477-113485	149455	Enzo Doria	08/2014
2328	((10^74703-1)10000/9+7481)10^74703+(10^74703-1)/9	149410	Hans Havermann	09/2019
2329	2^496270-49451	149393	Enzo Doria	10/2015
2330	2^496238-1865081	149383	Enzo Doria	01/2016
2331	33831^26030+26030^33831	149380	Hans Havermann	09/2020
2332	34131^23780+23780^34131	149365	Hans Havermann	09/2020
2333	(5*10^149335-53)/3	149336	Robert Price	09/2020
2334	2^495968-1853699	149302	Enzo Doria	09/2015
2335	2^495935-4117	149292	Yves Minet	02/2018
2336	35816^14709+14709^35816	149267	Hans Havermann	09/2020
2337	(10^149264+7)/191/2683/80557	149254	Alfred Reich	07/2021
2338	2^495712-396765	149225	Enzo Doria	07/2013
2339	(21*2^495676-1)/4835	149211	Lelio R Paula	10/2015
2340	2^495420+1880701	149137	Enzo Doria	10/2016
2341	2^495337-1847293	149112	Enzo Doria	07/2015
2342	(2^495193-7)/5	149068	Lelio R Paula	10/2015
2343	2^495163+111546435	149059	Paul Bourdelais	10/2021
2344	33282^30097+30097^33282	149055	Hans Havermann	09/2020
2345	37384^9705+9705^37384	149050	Hans Havermann	09/2020
2346	34808^19143+19143^34808	149049	Hans Havermann	09/2020
2347	413^56963-412^56963	149013	Jean-Louis Charton	08/2012
2348	47^89113-46^89113	149006	Robert Price	10/2012
2349	2^494916+87855	148985	Lelio R Paula	01/2016
2350	6*10^148982+73	148983	Robert Price	04/2019
2351	10^148934+1530019	148935	Patrick De Geest	02/2021
2352	10^148934-1000000001	148934	Robert Price	11/2020
2353	10^148934-512057	148934	Patrick De Geest	02/2021
2354	39000^6571+6571^39000	148888	Hans Havermann	10/2020
2355	2^494586-2791991	148886	Enzo Doria	02/2016
2356	8*10^148860-3	148861	Ray Chandler	04/2011
2357	38262^7769+7769^38262	148854	Hans Havermann	10/2020
2358	10^148816-500001	148816	Robert Price	03/2022
2359	(53*10^148811-287)/9	148812	Robert Price	02/2022
2360	2^494333-286183	148810	Enzo Doria	06/2015
2361	2^494144-264119	148753	Enzo Doria	05/2014
2362	6*10^148734+47	148735	Robert Price	06/2022
2363	36502^11823+11823^36502	148663	Hans Havermann	11/2020
2364	(5*2^493838-1)/3721	148658	Lelio R Paula	10/2015
2365	64239^206+206^64239	148641	Hans Havermann	10/2020
2366	(23*2^493761-1)/555	148636	Lelio R Paula	10/2015
2367	(23*10^148627-137)/3	148628	Robert Price	08/2021
2368	(151*10^148601-1)/3	148603	Robert Price	03/2020
2369	2^493636+82081	148600	Enzo Doria	09/2016
2370	((((((((((((((34251^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2	148593	Serge Batalov	07/2016
2371	177487#+(519643#)/(177487#)	148558	Makoto Morimoto	11/2017
2372	(2*10^148460-23)/3	148460	Robert Price	04/2018
2373	(28*10^148445+101)/3	148446	Robert Price	09/2020
2374	36203^12556+12556^36203	148391	Hans Havermann	10/2020
2375	33912^23749+23749^33912	148387	Hans Havermann	10/2020
2376	(8*10^148328+1)/9	148328	Serge Batalov	05/2010
2377	34294^21117+21117^34294	148309	Hans Havermann	10/2020
2378	(71*10^148306-539)/9	148307	Robert Price	07/2019
2379	38042^7875+7875^38042	148222	Hans Havermann	10/2020
2380	5^211959-12874	148153	Enzo Doria	05/2014
2381	34142^21831+21831^34142	148145	Hans Havermann	10/2020
2382	10^148112+34059	148113	Patrick De Geest	05/2021
2383	10^148112-70000001	148112	Robert Price	03/2021
2384	10^148112-106593	148112	Patrick De Geest	05/2021
2385	36303^12016+12016^36303	148108	Hans Havermann	10/2020
2386	(77*10^148089-149)/9	148090	Robert Price	03/2022
2387	(16*10^148071+41)/3	148072	Robert Price	03/2019
2388	187^65175-2	148068	Lelio R Paula	11/2017
2389	2^491851+1871453	148062	Enzo Doria	05/2016
2390	(68*10^148060-257)/9	148061	Robert Price	07/2019
2391	(151*10^148020-1)/3	148022	Robert Price	03/2020
2392	39153^6032+6032^39153	148017	Hans Havermann	10/2020
2393	36798^10507+10507^36798	147983	Hans Havermann	12/2020
2394	(26*10^147973-23)/3	147974	Robert Price	12/2019
2395	2^491521-1865323	147963	Enzo Doria	02/2016
2396	(2^491476+7)/71	147948	Lelio R Paula	10/2015
2397	2*10^147928+47	147929	Robert Price	12/2021
2398	2^491391-7807	147924	Lelio R Paula	01/2013
2399	39736^5279+5279^39736	147920	Hans Havermann	11/2020
2400	2^491370-113297	147918	Enzo Doria	07/2014
2401	(32760^32760+32759^32759)/95546586737133567708319	147900	Robert Price	07/2016
2402	44368^2155+2155^44368	147899	Hans Havermann	12/2020
2403	(17*10^147890+79)/3	147891	Robert Price	04/2019
2404	94*10^147871-3	147873	Robert Price	05/2020
2405	10^147843+620967	147844	Patrick De Geest	05/2021
2406	10^147843-50000000001	147843	Robert Price	12/2020
2407	10^147843-182891	147843	Patrick De Geest	05/2021
2408	35805^13346+13346^35805	147709	Hans Havermann	11/2020
2409	2^490672+255255	147707	Paul Bourdelais	10/2021
2410	2^490660-17	147704	Lelio R Paula	12/2017
2411	(229*10^147699-1)/3	147701	Robert Price	07/2020
2412	40656^4289+4289^40656	147678	Hans Havermann	11/2020
2413	2^490550+1179439	147671	Enzo Doria	06/2016
2414	(23*10^147649-59)/9	147650	Robert Price	05/2018
2415	2^490303+2793653	147596	Enzo Doria	03/2016
2416	2^490266+255255	147585	Paul Bourdelais	10/2021
2417	199^64181-2	147543	Lelio R Paula	11/2017
2418	32849^30958+30958^32849	147518	Hans Havermann	11/2020
2419	2^489871-286987	147466	Enzo Doria	07/2015
2420	2^489864-351899	147464	Enzo Doria	07/2015
2421	175^65724-2	147422	Lelio R Paula	11/2017
2422	2^489712+1874851	147419	Enzo Doria	06/2016
2423	34473^18830+18830^34473	147367	Hans Havermann	11/2020
2424	63^81896-2	147359	Lelio R Paula	10/2017
2425	34580^18237+18237^34580	147344	Hans Havermann	11/2020
2426	(11*10^147313-107)/3	147314	Robert Price	09/2018
2427	(397*10^147310+17)/9	147312	Robert Price	03/2022
2428	2^489305-59815	147296	Enzo Doria	10/2015
2429	(2^489280-7)/6381	147285	Lelio R Paula	09/2015
2430	2*10^147264-61	147265	Robert Price	10/2021
2431	2*10^147260+29	147261	Robert Price	02/2021
2432	33556^24457+24457^33556	147258	Hans Havermann	11/2020
2433	2^489125+80357	147242	Enzo Doria	06/2016
2434	32835^30452+30452^32835	147220	Hans Havermann	12/2020
2435	(19*10^147213-97)/3	147214	Robert Price	10/2021
2436	(148*10^147139-1)/3	147141	Robert Price	03/2020
2437	34338^19255+19255^34338	147123	Hans Havermann	11/2020
2438	2^488648-112799	147098	Enzo Doria	07/2014
2439	2^488627-350317	147092	Enzo Doria	06/2015
2440	33432^25075+25075^33432	147076	Hans Havermann	12/2020
2441	(2^488441-1)/(61543567*30051203516986199)	147012	Dario Alpern	12/2014
2442	2^488280-2165	146987	Yves Minet	07/2014
2443	2^488278+45	146987	Lelio R Paula	12/2017
2444	2^487927-39	146881	Lelio R Paula	12/2017
2445	(7*10^146860-13)/3	146861	Robert Price	07/2018
2446	(26*10^146856-77)/3	146857	Robert Price	11/2019
2447	32948^28611+28611^32948	146834	Hans Havermann	11/2020
2448	42596^2799+2799^42596	146829	Hans Havermann	12/2020
2449	2^487726-1863341	146821	Enzo Doria	12/2015
2450	43838^2229+2229^43838	146775	Hans Havermann	11/2020
2451	35005^15594+15594^35005	146775	Hans Havermann	11/2020
2452	(167*10^146764+7)/3	146766	Robert Price	04/2021
2453	53^85114+85114	146761	Kellen Shenton	05/2022
2454	(59*10^146738+157)/9	146739	Robert Price	12/2021
2455	((10^73362-1)10000/9+6701)10^73362+(10^73362-1)/9	146728	Hans Havermann	09/2019
2456	32963^28234+28234^32963	146711	Hans Havermann	12/2020
2457	(22*10^146661-19)/3	146662	Robert Price	04/2019
2458	33958^20825+20825^33958	146651	Hans Havermann	12/2020
2459	2^487121-39523	146639	Enzo Doria	09/2015
2460	61063^252+252^61063	146637	Hans Havermann	12/2020
2461	(7*2^486967+1)/39	146591	Lelio R Paula	09/2015
2462	34099^19900+19900^34099	146587	Hans Havermann	11/2020
2463	2^486893-79	146570	Yves Minet	09/2017
2464	36818^9567+9567^36818	146565	Hans Havermann	12/2020
2465	2^486840+1879141	146554	Enzo Doria	08/2016
2466	2^486774-87	146534	Lelio R Paula	12/2017
2467	38655^6176+6176^38655	146530	Hans Havermann	11/2020
2468	8*10^146522-81	146523	Robert Price	02/2021
2469	32820^29059+29059^32820	146485	Hans Havermann	12/2020
2470	37261^8530+8530^37261	146472	Hans Havermann	12/2020
2471	66953^154+154^66953	146462	Hans Havermann	12/2020
2472	96^73877-95^73877	146445	Robert Price	10/2015
2473	8*10^146421+81	146422	Robert Price	08/2019
2474	33153^26090+26090^33153	146420	Hans Havermann	11/2020
2475	(52^85259+1)/53	146304	Paul Bourdelais	09/2017
2476	179^64935+2	146290	Lelio R Paula	10/2017
2477	32595^30758+30758^32595	146285	Hans Havermann	11/2020
2478	34972^15157+15157^34972	146205	Hans Havermann	12/2020
2479	(16*10^146200+131)/3	146201	Robert Price	03/2022
2480	(19*10^146181-49)/3	146182	Robert Price	05/2019
2481	2^485531-114621	146160	Enzo Doria	05/2015
2482	2^485473-933075	146142	Paul Bourdelais	06/2021
2483	(2^485461-9)/4249	146135	Lelio R Paula	09/2015
2484	2^485389+81887	146117	Enzo Doria	08/2016
2485	32554^30773+30773^32554	146108	Hans Havermann	11/2020
2486	(10^146063+71)/9	146063	Serge Batalov	07/2015
2487	2*10^146051-63	146052	Robert Price	01/2022
2488	(2^485119+7)/2745	146032	Lelio R Paula	09/2015
2489	(22*10^146029+257)/9	146030	Robert Price	06/2018
2490	7*10^145982-53	145983	Robert Price	06/2020
2491	2^484743+1872923	145923	Enzo Doria	05/2016
2492	33140^25287+25287^33140	145913	Hans Havermann	01/2021
2493	37875^7112+7112^37875	145895	Hans Havermann	01/2021
2494	32862^27473+27473^32862	145872	Hans Havermann	01/2021
2495	32836^27587+27587^32836	145815	Hans Havermann	01/2021
2496	2^484341+1879157	145802	Enzo Doria	08/2016
2497	2*10^145784-91	145785	Robert Price	04/2020
2498	2^484271-51	145781	Lelio R Paula	11/2017
2499	(188*10^145750-11)/3	145752	Robert Price	02/2022
2500	70^78989-69^78989	145743	Robert Price	01/2014

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Probable Primes Top 10000

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