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	(151*10^154434-7)/9	154436	Robert Price	01/2020
2252	(118*10^154428+11)/3	154430	Robert Price	03/2022
2253	(14*10^154413+139)/9	154414	Robert Price	11/2021
2254	(77*10^154389-149)/9	154390	Robert Price	03/2022
2255	2^512628-114053	154317	Enzo Doria	11/2014
2256	2^512529-49783	154287	Enzo Doria	10/2015
2257	(355573#+6991)/(6991*2031599)	154285	Makoto Morimoto	06/2019
2258	2^512315-115297	154223	Enzo Doria	06/2015
2259	(47*10^154221+241)/9	154222	Robert Price	06/2022
2260	(7*10^154211+173)/9	154211	Robert Price	01/2022
2261	2^512168+79561	154178	Enzo Doria	06/2016
2262	(77*10^154175+67)/9	154176	Robert Price	12/2021
2263	(5*10^154158-311)/9	154158	Robert Price	12/2021
2264	(89*10^154103-737)/9	154104	Robert Price	01/2022
2265	4*10^154078-57	154079	Robert Price	10/2018
2266	(355049#+1859)/(111310148891*62587751)	154051	Makoto Morimoto	06/2019
2267	7*10^154038-57	154039	Robert Price	06/2020
2268	2^511658-114371	154025	Enzo Doria	02/2015
2269	(57^87719+1)/58	154022	Paul Bourdelais	11/2017
2270	2^511580-1846679	154001	Enzo Doria	07/2015
2271	(259*10^153998-1)/3	154000	Robert Price	12/2020
2272	2^511541-113713	153990	Enzo Doria	09/2014
2273	49958^32768+49957^32768	153965	Kellen Shenton	11/2020
2274	10^153935+970801	153936	Patrick De Geest	05/2021
2275	10^153935-1000001	153935	Robert Price	08/2020
2276	(16*10^153868-73)/3	153869	Robert Price	07/2020
2277	9*10^153851-67	153852	Robert Price	11/2020
2278	2^511077-112723	153850	Enzo Doria	06/2014
2279	69^83653-68^83653	153826	Robert Price	12/2013
2280	2^510963-113707	153816	Enzo Doria	09/2014
2281	(154*10^153810-1)/9	153812	Serge Batalov	12/2014
2282	(181*25^109991-75077)/8	153763	Curtis Bright	05/2015
2283	2*10^153746-3	153747	Robert Price	07/2015
2284	2^510626+1179379	153714	Enzo Doria	05/2016
2285	(7*10^153664+113)/3	153665	Robert Price	02/2018
2286	2^510420+81121	153652	Enzo Doria	07/2016
2287	(197*7^181761-1)/2	153608	Karsten Bonath	05/2017
2288	2^509894-459161	153494	Enzo Doria	05/2015
2289	(74*10^153489+673)/9	153490	Robert Price	02/2022
2290	(49*10^153484-211)/9	153485	Robert Price	06/2022
2291	2^509841+71657	153478	Enzo Doria	04/2016
2292	9*10^153446+41	153447	Robert Price	08/2020
2293	2^509533-1846723	153385	Enzo Doria	07/2015
2294	2^509468-39989	153366	Enzo Doria	09/2015
2295	70^83117-69^83117	153360	Robert Price	01/2014
2296	(7*10^153116-1)/3	153117	Robert Price	08/2022
2297	(112*10^153025-1)/3	153027	Serge Batalov	12/2014
2298	(19*10^153010+131)/3	153011	Robert Price	06/2020
2299	2^508174-1855151	152976	Enzo Doria	09/2015
2300	181^67757-2	152974	Lelio R Paula	12/2017
2301	2^508160-1864829	152972	Enzo Doria	01/2016
2302	10^152960+412563	152961	Patrick De Geest	05/2021
2303	10^152960-50000000001	152960	Robert Price	12/2020
2304	10^152960-423749	152960	Patrick De Geest	05/2021
2305	(71*10^152933-143)/9	152934	Robert Price	10/2021
2306	2^507857-1848199	152881	Enzo Doria	07/2015
2307	2^507638-115361	152815	Enzo Doria	07/2015
2308	2^507551-114025	152789	Enzo Doria	11/2014
2309	(6^196337+1)/7	152780	Paul Bourdelais	02/2010
2310	(22*10^152670-13)/9	152671	Robert Price	06/2018
2311	2^506451-22339	152457	Enzo Doria	07/2013
2312	2^505995-113185	152320	Enzo Doria	07/2014
2313	(4*10^152253+149)/9	152253	Robert Price	04/2018
2314	578^55117-577^55117	152230	Jean-Louis Charton	08/2012
2315	2^505431-505431	152150	Henri Lifchitz	04/2005
2316	(203*10^152143+1)/3	152145	Robert Price	03/2020
2317	2^505053+73097	152037	Enzo Doria	04/2016
2318	22*10^151998+3	152000	Robert Price	01/2020
2319	(238*10^151979-1)/3	151981	Robert Price	04/2020
2320	(2^504793-7)/46765	151954	Lelio R Paula	12/2017
2321	350377#+797581	151937	Nicolas PALAU	08/2017
2322	(79*10^151906-529)/9	151907	Robert Price	01/2022
2323	2^504618-343991	151906	Enzo Doria	07/2015
2324	2^504212-461939	151783	Enzo Doria	07/2015
2325	7*10^151772-41	151773	Robert Price	08/2021
2326	2^504054-2231	151736	Yves Minet	10/2011
2327	(28*10^151682+191)/3	151683	Robert Price	02/2020
2328	2^503475-933075	151562	Paul Bourdelais	06/2021
2329	2^503361-39883	151527	Enzo Doria	09/2015
2330	2^503225+382667	151486	Enzo Doria	10/2016
2331	(206*10^151483-11)/3	151485	Robert Price	02/2022
2332	(844*10^151396-7)/9	151398	Robert Price	05/2021
2333	(26*10^151391-503)/9	151392	Robert Price	07/2018
2334	2^502769+1877567	151349	Enzo Doria	08/2016
2335	2^502576-4019	151291	Yves Minet	10/2011
2336	5*10^151257+41	151258	Robert Price	03/2019
2337	2^502290-2792501	151205	Enzo Doria	02/2016
2338	2^502181+1868417	151172	Enzo Doria	04/2016
2339	6*10^151063-77	151064	Robert Price	09/2021
2340	2^501781-1850503	151052	Enzo Doria	08/2015
2341	(5*10^151007+37)/3	151008	Robert Price	03/2018
2342	2^501627-991	151005	Yves Minet	02/2014
2343	2^501577-115333	150990	Enzo Doria	07/2015
2344	8*10^150975+3	150976	Robert Price	08/2015
2345	2^501512-113669	150971	Enzo Doria	09/2014
2346	(83*10^150908+493)/9	150909	Robert Price	12/2021
2347	2*10^150818+83	150819	Robert Price	12/2021
2348	(12^139739+1)/13	150803	Paul Bourdelais	09/2011
2349	(31^101111-1)/30	150792	Alexander Zhirkov	11/2010
2350	2^500899-500899	150786	Henri Lifchitz	04/2005
2351	2^500832+1876801	150766	Enzo Doria	07/2016
2352	(23*10^150763-59)/9	150764	Robert Price	05/2018
2353	2^500699+1884953	150726	Enzo Doria	02/2017
2354	(13*10^150675-37)/3	150676	Robert Price	01/2019
2355	(2^500527+lucasV(1,2,500527)+1)/4	150674	Mike Oakes	11/2016
2356	2^500337-71101	150617	Enzo Doria	04/2016
2357	(74*10^150616+133)/9	150617	Robert Price	06/2019
2358	4*10^150577+91	150578	Robert Price	08/2018
2359	2^500160+80071	150564	Enzo Doria	06/2016
2360	(2^500120+5)/9	150551	Lelio R Paula	12/2017
2361	(43*10^150515-421)/9	150516	Robert Price	01/2019
2362	(10^150551-1)/9/385207015049/57498437921/7808738631274081	150512	Maksym Voznyy	08/2014
2363	(10^150551-1)/1556587827131683185788921941743157225041	150512	Robert Price	07/2016
2364	2^499861-29503	150474	Enzo Doria	08/2015
2365	2^499653-113533	150411	Enzo Doria	08/2014
2366	(14*10^150391-191)/3	150392	Robert Price	10/2020
2367	2^499534-221	150375	Yves Minet	06/2012
2368	(28*10^150294+41)/3	150295	Robert Price	07/2021
2369	2^499225+49727	150282	Enzo Doria	09/2016
2370	(695*10^150274+7)/9	150276	Robert Price	12/2021
2371	2^499054-29261	150231	Enzo Doria	07/2015
2372	(844*10^150196-7)/9	150198	Robert Price	05/2021
2373	2^498907-933075	150186	Paul Bourdelais	06/2021
2374	(2^498898-7)/9	150183	Lelio R Paula	10/2015
2375	3*10^150182+17	150183	Robert Price	07/2018
2376	5*10^150175+63	150176	Robert Price	09/2020
2377	32363^33292+33292^32363	150149	Norbert Schneider	07/2022
2378	(77*10^150128+67)/9	150129	Robert Price	12/2021
2379	2^498623+1866983	150101	Enzo Doria	03/2016
2380	(25*10^150050-403)/9	150051	Robert Price	12/2020
2381	numbpart(18140942830)	150033	Serge Batalov	04/2017
2382	10^150029+4381	150030	Patrick De Geest	05/2016
2383	10^150029-41	150029	Serge Batalov	12/2014
2384	10^150000+1158603	150001	Patrick De Geest	09/2018
2385	10^150000-245703	150000	Patrick De Geest	09/2018
2386	(38*10^149999+691)/9	150000	Robert Price	10/2018
2387	2^498238-53	149985	Lelio R Paula	12/2017
2388	45728^1905+1905^45728	149984	Hans Havermann	10/2020
2389	5*10^149907+23	149908	Robert Price	03/2019
2390	39347^6442+6442^39347	149874	Hans Havermann	09/2020
2391	2^497850+81049	149868	Enzo Doria	07/2016
2392	37228^10575+10575^37228	149816	Hans Havermann	10/2020
2393	(5*2^497673+1)/2743	149812	Lelio R Paula	10/2015
2394	(5*2^497671+1)/373703	149810	Lelio R Paula	10/2015
2395	(2*10^149803-143)/3	149803	Robert Price	03/2018
2396	33845^26604+26604^33845	149763	Hans Havermann	09/2020
2397	2^497434-2784191	149743	Enzo Doria	10/2015
2398	(865*10^149737-1)/9	149739	Robert Price	04/2020
2399	10^149695-7000001	149695	Robert Price	06/2021
2400	38237^8214+8214^38237	149681	Hans Havermann	09/2020
2401	(23*10^149655+19)/3	149656	Robert Price	07/2019
2402	2^497068-113579	149633	Enzo Doria	08/2014
2403	2^497037+73727	149624	Enzo Doria	04/2016
2404	11*10^149618+3	149620	Robert Price	07/2021
2405	34942^19067+19067^34942	149562	Hans Havermann	09/2020
2406	33696^27449+27449^33696	149561	Hans Havermann	09/2020
2407	2^496773+77747	149544	Enzo Doria	05/2016
2408	(7*10^149483-493)/9	149483	Robert Price	04/2021
2409	(206*10^149459+7)/3	149461	Robert Price	07/2020
2410	34589^20940+20940^34589	149459	Hans Havermann	09/2020
2411	2^496477-113485	149455	Enzo Doria	08/2014
2412	((10^74703-1)10000/9+7481)10^74703+(10^74703-1)/9	149410	Hans Havermann	09/2019
2413	2^496270-49451	149393	Enzo Doria	10/2015
2414	2^496238-1865081	149383	Enzo Doria	01/2016
2415	33831^26030+26030^33831	149380	Hans Havermann	09/2020
2416	34131^23780+23780^34131	149365	Hans Havermann	09/2020
2417	(5*10^149335-53)/3	149336	Robert Price	09/2020
2418	2^495968-1853699	149302	Enzo Doria	09/2015
2419	2^495935-4117	149292	Yves Minet	02/2018
2420	35816^14709+14709^35816	149267	Hans Havermann	09/2020
2421	(10^149264+7)/191/2683/80557	149254	Alfred Reich	07/2021
2422	10^149240-40000001	149240	Robert Price	07/2022
2423	2^495712-396765	149225	Enzo Doria	07/2013
2424	(21*2^495676-1)/4835	149211	Lelio R Paula	10/2015
2425	2^495420+1880701	149137	Enzo Doria	10/2016
2426	2^495337-1847293	149112	Enzo Doria	07/2015
2427	(2^495193-7)/5	149068	Lelio R Paula	10/2015
2428	2^495163+111546435	149059	Paul Bourdelais	10/2021
2429	33282^30097+30097^33282	149055	Hans Havermann	09/2020
2430	37384^9705+9705^37384	149050	Hans Havermann	09/2020
2431	34808^19143+19143^34808	149049	Hans Havermann	09/2020
2432	413^56963-412^56963	149013	Jean-Louis Charton	08/2012
2433	47^89113-46^89113	149006	Robert Price	10/2012
2434	2^494916+87855	148985	Lelio R Paula	01/2016
2435	6*10^148982+73	148983	Robert Price	04/2019
2436	10^148934+1530019	148935	Patrick De Geest	02/2021
2437	10^148934-1000000001	148934	Robert Price	11/2020
2438	10^148934-512057	148934	Patrick De Geest	02/2021
2439	39000^6571+6571^39000	148888	Hans Havermann	10/2020
2440	2^494586-2791991	148886	Enzo Doria	02/2016
2441	8*10^148860-3	148861	Ray Chandler	04/2011
2442	38262^7769+7769^38262	148854	Hans Havermann	10/2020
2443	10^148816-500001	148816	Robert Price	03/2022
2444	(53*10^148811-287)/9	148812	Robert Price	02/2022
2445	2^494333-286183	148810	Enzo Doria	06/2015
2446	2^494144-264119	148753	Enzo Doria	05/2014
2447	6*10^148734+47	148735	Robert Price	06/2022
2448	36502^11823+11823^36502	148663	Hans Havermann	11/2020
2449	(5*2^493838-1)/3721	148658	Lelio R Paula	10/2015
2450	64239^206+206^64239	148641	Hans Havermann	10/2020
2451	(23*2^493761-1)/555	148636	Lelio R Paula	10/2015
2452	(23*10^148627-137)/3	148628	Robert Price	08/2021
2453	(151*10^148601-1)/3	148603	Robert Price	03/2020
2454	2^493636+82081	148600	Enzo Doria	09/2016
2455	((((((((((((((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
2456	177487#+(519643#)/(177487#)	148558	Makoto Morimoto	11/2017
2457	(2*10^148460-23)/3	148460	Robert Price	04/2018
2458	(28*10^148445+101)/3	148446	Robert Price	09/2020
2459	36203^12556+12556^36203	148391	Hans Havermann	10/2020
2460	33912^23749+23749^33912	148387	Hans Havermann	10/2020
2461	(8*10^148328+1)/9	148328	Serge Batalov	05/2010
2462	34294^21117+21117^34294	148309	Hans Havermann	10/2020
2463	(71*10^148306-539)/9	148307	Robert Price	07/2019
2464	38042^7875+7875^38042	148222	Hans Havermann	10/2020
2465	5^211959-12874	148153	Enzo Doria	05/2014
2466	34142^21831+21831^34142	148145	Hans Havermann	10/2020
2467	10^148112+34059	148113	Patrick De Geest	05/2021
2468	10^148112-70000001	148112	Robert Price	03/2021
2469	10^148112-106593	148112	Patrick De Geest	05/2021
2470	36303^12016+12016^36303	148108	Hans Havermann	10/2020
2471	(77*10^148089-149)/9	148090	Robert Price	03/2022
2472	(16*10^148071+41)/3	148072	Robert Price	03/2019
2473	187^65175-2	148068	Lelio R Paula	11/2017
2474	2^491851+1871453	148062	Enzo Doria	05/2016
2475	(68*10^148060-257)/9	148061	Robert Price	07/2019
2476	(151*10^148020-1)/3	148022	Robert Price	03/2020
2477	39153^6032+6032^39153	148017	Hans Havermann	10/2020
2478	36798^10507+10507^36798	147983	Hans Havermann	12/2020
2479	(26*10^147973-23)/3	147974	Robert Price	12/2019
2480	2^491521-1865323	147963	Enzo Doria	02/2016
2481	(2^491476+7)/71	147948	Lelio R Paula	10/2015
2482	2*10^147928+47	147929	Robert Price	12/2021
2483	2^491391-7807	147924	Lelio R Paula	01/2013
2484	39736^5279+5279^39736	147920	Hans Havermann	11/2020
2485	2^491370-113297	147918	Enzo Doria	07/2014
2486	(32760^32760+32759^32759)/95546586737133567708319	147900	Robert Price	07/2016
2487	44368^2155+2155^44368	147899	Hans Havermann	12/2020
2488	(17*10^147890+79)/3	147891	Robert Price	04/2019
2489	94*10^147871-3	147873	Robert Price	05/2020
2490	10^147843+620967	147844	Patrick De Geest	05/2021
2491	10^147843-50000000001	147843	Robert Price	12/2020
2492	10^147843-182891	147843	Patrick De Geest	05/2021
2493	35805^13346+13346^35805	147709	Hans Havermann	11/2020
2494	2^490672+255255	147707	Paul Bourdelais	10/2021
2495	2^490660-17	147704	Lelio R Paula	12/2017
2496	(229*10^147699-1)/3	147701	Robert Price	07/2020
2497	40656^4289+4289^40656	147678	Hans Havermann	11/2020
2498	2^490550+1179439	147671	Enzo Doria	06/2016
2499	(23*10^147649-59)/9	147650	Robert Price	05/2018
2500	2^490303+2793653	147596	Enzo Doria	03/2016

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