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	2^527644-1856999	158837	Enzo Doria	10/2015
2252	(37200^37199-37198^37199)/(2^37199)	158822	Henri Lifchitz	06/2013
2253	2^527573-1863253	158816	Enzo Doria	12/2015
2254	2^527553-23401	158810	Enzo Doria	08/2013
2255	(49*10^158783+437)/9	158784	Robert Price	09/2021
2256	10^158755+310207	158756	Patrick De Geest	08/2021
2257	10^158755-50001	158755	Robert Price	08/2020
2258	(61*10^158748-619)/9	158749	Robert Price	03/2022
2259	11^152420-210	158730	Enzo Doria	09/2012
2260	(13*10^158694+401)/9	158695	Robert Price	01/2018
2261	2^527052-69059	158659	Enzo Doria	11/2015
2262	2^526849-113233	158598	Enzo Doria	07/2014
2263	(2^526763-lucasV(1,2,526763)+1)/2	158572	Mike Oakes	11/2016
2264	(299*10^158544-17)/3	158546	Robert Price	04/2020
2265	2^526658-3551	158540	Yves Minet	03/2017
2266	7*10^158465-11	158466	Robert Price	06/2019
2267	2^526375-23115	158455	Enzo Doria	08/2013
2268	(77*10^158407-293)/9	158408	Robert Price	09/2019
2269	2^526028-112793	158351	Enzo Doria	07/2014
2270	(229*10^158339-1)/3	158341	Robert Price	07/2020
2271	2^525690-9221	158249	Lelio R Paula	01/2013
2272	2*10^158242-7	158243	Robert Price	10/2015
2273	2^525667-525667^2	158242	Henri Lifchitz	12/2017
2274	(56*10^158230+187)/9	158231	Robert Price	10/2021
2275	10^158209-7000000001	158209	Robert Price	12/2021
2276	2^525186-1857431	158097	Enzo Doria	10/2015
2277	2^524515-23245	157895	Enzo Doria	08/2013
2278	2^524499-109087	157890	Enzo Doria	04/2014
2279	2^18067*(2^506221+1)-1	157827	Makoto Morimoto	05/2014
2280	2^524288+189093	157827	Makoto Morimoto	01/2016
2281	2^524288-164073	157827	Matthias Baur	03/2020
2282	(2^(2^19)-9333)/(1923463121331973)	157814	Makoto Morimoto	09/2017
2283	(10^157792+359)/9	157792	Serge Batalov	12/2014
2284	2^524154+25	157787	Stefano Morozzi	04/2021
2285	2^523924+1876591	157717	Enzo Doria	07/2016
2286	(17*10^157705+67)/3	157706	Robert Price	01/2019
2287	(46^94841+1)/47	157696	Robert Price	01/2014
2288	2^523774+77839	157672	Enzo Doria	05/2016
2289	2^523587+2799143	157616	Enzo Doria	04/2016
2290	2^523371+1872113	157551	Enzo Doria	05/2016
2291	8*10^157477+27	157478	Robert Price	09/2021
2292	(8*10^157368+49)/3	157369	Robert Price	05/2020
2293	(82*10^157319+449)/9	157320	Robert Price	11/2019
2294	2^522535-351457	157299	Enzo Doria	07/2015
2295	2^522226+2799079	157206	Enzo Doria	04/2016
2296	(134*10^157191-11)/3	157193	Robert Price	01/2022
2297	2^522134-1849451	157178	Enzo Doria	08/2015
2298	9*10^157152+71	157153	Robert Price	08/2020
2299	4*10^157150+93	157151	Robert Price	08/2018
2300	2^521401-29593	156958	Enzo Doria	08/2015
2301	7*10^156956+87	156957	Robert Price	07/2019
2302	2^521348-23397	156942	Enzo Doria	08/2013
2303	10^156902+34509	156903	Patrick De Geest	08/2021
2305	10^156902-80000001	156902	Robert Price	04/2021
2304	10^156902-69789	156902	Patrick De Geest	08/2021
2306	(98^78797+1)/99	156901	Paul Bourdelais	12/2017
2307	65^86522+64	156857	Lelio R Paula	04/2016
2308	8^173687-7^173687	156855	Jean-Louis Charton	09/2004
2309	2^520977-1858183	156830	Enzo Doria	10/2015
2310	(8*10^156718-101)/3	156719	Robert Price	08/2018
2311	(10^156640+7)/53	156639	Alfred Reich	07/2021
2312	2^520314-1849481	156631	Enzo Doria	08/2015
2313	(16*10^156563-637)/9	156564	Robert Price	09/2022
2314	(13*10^156522+89)/3	156523	Robert Price	09/2018
2315	(2^(6*86654+1)-5)/3	156513	Kevin Acres	12/2013
2316	(2^519925-5)/3	156513	Stefano Morozzi	08/2022
2317	(4*10^156501+119)/3	156502	Robert Price	12/2021
2318	(83*10^156476-101)/9	156477	Robert Price	08/2021
2319	3*10^156435-97	156436	Robert Price	07/2018
2320	(8*10^156371-77)/3	156372	Robert Price	07/2018
2321	53^90679-52^90679	156356	Robert Price	01/2013
2322	(418*10^156309-31)/9	156311	Robert Price	05/2022
2323	2^519106-59141	156267	Enzo Doria	10/2015
2324	2^519053+6077	156251	Enzo Doria	02/2016
2325	2^518968-1860989	156225	Enzo Doria	11/2015
2326	(25*10^156221-7)/9	156222	Robert Price	05/2018
2327	2^518931-2782297	156214	Enzo Doria	09/2015
2328	2^518608-2939	156117	Yves Minet	09/2014
2329	10*27^109005+697	156027	Curtis Bright	05/2015
2330	(49*10^155933-319)/9	155934	Robert Price	10/2021
2331	2^517967-113485	155924	Enzo Doria	08/2014
2332	(103*10^155904+17)/3	155906	Robert Price	08/2020
2333	(8*10^155887-719)/9	155887	Robert Price	03/2021
2334	4*10^155853-39	155854	Robert Price	09/2020
2335	2^517698+4429	155843	Lelio R Paula	01/2013
2336	2^517543-113257	155796	Enzo Doria	07/2014
2337	(14*10^155740-143)/3	155741	Robert Price	11/2018
2338	31^104309-30^104309	155563	Henri Lifchitz	08/2013
2339	2^516742-39851	155555	Enzo Doria	09/2015
2340	(22*10^155543+47)/3	155544	Robert Price	06/2021
2341	(19*10^155504+131)/3	155505	Robert Price	06/2020
2342	7*10^155496+61	155497	Robert Price	08/2019
2343	2^516440+1878421	155464	Enzo Doria	08/2016
2344	2^515863-1867237	155291	Enzo Doria	03/2016
2345	2^515786-461861	155268	Enzo Doria	07/2015
2346	2^515644-113247	155225	Enzo Doria	07/2014
2347	(7*10^155203+107)/3	155204	Robert Price	02/2018
2348	10^155163+206871	155164	Patrick De Geest	05/2021
2349	10^155163-40001	155163	Robert Price	01/2021
2350	(17*10^155133-89)/9	155134	Robert Price	07/2018
2351	2^515227-114997	155099	Enzo Doria	06/2015
2353	EPrime(155025)	155025	Eric W. Weisstein	10/2010
2352	(14*10^155024-221)/9	155025	Robert Price	04/2018
2354	(4*10^155022+173)/3	155023	Robert Price	02/2018
2355	(266*10^154897+1)/3	154899	Robert Price	04/2020
2356	(115*10^154869-1)/3	154871	Serge Batalov	12/2014
2357	(86*10^154853-221)/9	154854	Robert Price	09/2019
2358	2^514361+78167	154839	Enzo Doria	05/2016
2359	2^514281-115033	154815	Enzo Doria	06/2015
2360	2^514194-3311	154788	Yves Minet	12/2014
2361	(14*10^154773+37)/3	154774	Robert Price	12/2018
2362	(16*10^154748+131)/3	154749	Robert Price	03/2022
2363	6*10^154742-31	154743	Robert Price	07/2020
2364	(14*10^154645+139)/9	154646	Robert Price	11/2021
2365	5*10^154618-79	154619	Robert Price	03/2021
2366	(167*10^154595+1)/3	154597	Robert Price	04/2021
2367	2^513437+1879337	154560	Enzo Doria	09/2016
2368	2^513306-113201	154521	Enzo Doria	07/2014
2369	(10^154494-13)/3	154494	Robert Price	12/2017
2370	2^513042-113787	154442	Enzo Doria	09/2014
2371	(151*10^154434-7)/9	154436	Robert Price	01/2020
2372	(118*10^154428+11)/3	154430	Robert Price	03/2022
2373	(14*10^154413+139)/9	154414	Robert Price	11/2021
2374	(77*10^154389-149)/9	154390	Robert Price	03/2022
2375	2^512628-114053	154317	Enzo Doria	11/2014
2376	2^512529-49783	154287	Enzo Doria	10/2015
2377	(355573#+6991)/(6991*2031599)	154285	Makoto Morimoto	06/2019
2378	2^512315-115297	154223	Enzo Doria	06/2015
2379	(47*10^154221+241)/9	154222	Robert Price	06/2022
2380	(7*10^154211+173)/9	154211	Robert Price	01/2022
2381	2^512168+79561	154178	Enzo Doria	06/2016
2382	(77*10^154175+67)/9	154176	Robert Price	12/2021
2383	(5*10^154158-311)/9	154158	Robert Price	12/2021
2384	(89*10^154103-737)/9	154104	Robert Price	01/2022
2385	4*10^154078-57	154079	Robert Price	10/2018
2386	(355049#+1859)/(111310148891*62587751)	154051	Makoto Morimoto	06/2019
2387	7*10^154038-57	154039	Robert Price	06/2020
2388	2^511658-114371	154025	Enzo Doria	02/2015
2389	(57^87719+1)/58	154022	Paul Bourdelais	11/2017
2390	2^511580-1846679	154001	Enzo Doria	07/2015
2391	(259*10^153998-1)/3	154000	Robert Price	12/2020
2392	2^511541-113713	153990	Enzo Doria	09/2014
2393	49958^32768+49957^32768	153965	Kellen Shenton	11/2020
2394	10^153935+970801	153936	Patrick De Geest	05/2021
2395	10^153935-1000001	153935	Robert Price	08/2020
2396	(16*10^153868-73)/3	153869	Robert Price	07/2020
2397	9*10^153851-67	153852	Robert Price	11/2020
2398	2^511077-112723	153850	Enzo Doria	06/2014
2399	69^83653-68^83653	153826	Robert Price	12/2013
2400	2^510963-113707	153816	Enzo Doria	09/2014
2401	(154*10^153810-1)/9	153812	Serge Batalov	12/2014
2402	(181*25^109991-75077)/8	153763	Curtis Bright	05/2015
2403	2*10^153746-3	153747	Robert Price	07/2015
2404	2^510626+1179379	153714	Enzo Doria	05/2016
2405	(7*10^153664+113)/3	153665	Robert Price	02/2018
2406	2^510420+81121	153652	Enzo Doria	07/2016
2407	(197*7^181761-1)/2	153608	Karsten Bonath	05/2017
2408	2^509894-459161	153494	Enzo Doria	05/2015
2409	(74*10^153489+673)/9	153490	Robert Price	02/2022
2410	(49*10^153484-211)/9	153485	Robert Price	06/2022
2411	2^509841+71657	153478	Enzo Doria	04/2016
2412	9*10^153446+41	153447	Robert Price	08/2020
2413	2^509533-1846723	153385	Enzo Doria	07/2015
2414	2^509468-39989	153366	Enzo Doria	09/2015
2415	70^83117-69^83117	153360	Robert Price	01/2014
2416	(7*10^153116-1)/3	153117	Robert Price	08/2022
2417	(112*10^153025-1)/3	153027	Serge Batalov	12/2014
2418	(19*10^153010+131)/3	153011	Robert Price	06/2020
2419	2^508174-1855151	152976	Enzo Doria	09/2015
2420	181^67757-2	152974	Lelio R Paula	12/2017
2421	2^508160-1864829	152972	Enzo Doria	01/2016
2422	10^152960+412563	152961	Patrick De Geest	05/2021
2423	10^152960-50000000001	152960	Robert Price	12/2020
2424	10^152960-423749	152960	Patrick De Geest	05/2021
2425	(71*10^152933-143)/9	152934	Robert Price	10/2021
2426	2^507857-1848199	152881	Enzo Doria	07/2015
2427	2^507638-115361	152815	Enzo Doria	07/2015
2428	2^507551-114025	152789	Enzo Doria	11/2014
2429	(6^196337+1)/7	152780	Paul Bourdelais	02/2010
2430	(22*10^152670-13)/9	152671	Robert Price	06/2018
2431	2^506451-22339	152457	Enzo Doria	07/2013
2432	2^505995-113185	152320	Enzo Doria	07/2014
2433	(8*10^152260-17)/9	152260	Serge Batalov	11/2022
2434	(4*10^152253+149)/9	152253	Robert Price	04/2018
2435	578^55117-577^55117	152230	Jean-Louis Charton	08/2012
2436	2^505431-505431	152150	Henri Lifchitz	04/2005
2437	(203*10^152143+1)/3	152145	Robert Price	03/2020
2438	2^505053+73097	152037	Enzo Doria	04/2016
2439	22*10^151998+3	152000	Robert Price	01/2020
2440	(238*10^151979-1)/3	151981	Robert Price	04/2020
2441	(2^504793-7)/46765	151954	Lelio R Paula	12/2017
2442	350377#+797581	151937	Nicolas PALAU	08/2017
2443	(79*10^151906-529)/9	151907	Robert Price	01/2022
2444	2^504618-343991	151906	Enzo Doria	07/2015
2445	2^504212-461939	151783	Enzo Doria	07/2015
2446	7*10^151772-41	151773	Robert Price	08/2021
2447	2^504054-2231	151736	Yves Minet	10/2011
2448	(28*10^151682+191)/3	151683	Robert Price	02/2020
2449	2^503475-933075	151562	Paul Bourdelais	06/2021
2450	2^503361-39883	151527	Enzo Doria	09/2015
2451	2^503225+382667	151486	Enzo Doria	10/2016
2452	(206*10^151483-11)/3	151485	Robert Price	02/2022
2453	(844*10^151396-7)/9	151398	Robert Price	05/2021
2454	(26*10^151391-503)/9	151392	Robert Price	07/2018
2455	2^502769+1877567	151349	Enzo Doria	08/2016
2456	2^502576-4019	151291	Yves Minet	10/2011
2457	5*10^151257+41	151258	Robert Price	03/2019
2458	2^502290-2792501	151205	Enzo Doria	02/2016
2459	2^502181+1868417	151172	Enzo Doria	04/2016
2460	6*10^151063-77	151064	Robert Price	09/2021
2461	2^501781-1850503	151052	Enzo Doria	08/2015
2462	(5*10^151007+37)/3	151008	Robert Price	03/2018
2463	2^501627-991	151005	Yves Minet	02/2014
2464	2^501577-115333	150990	Enzo Doria	07/2015
2465	8*10^150975+3	150976	Robert Price	08/2015
2466	2^501512-113669	150971	Enzo Doria	09/2014
2467	(83*10^150908+493)/9	150909	Robert Price	12/2021
2468	2*10^150818+83	150819	Robert Price	12/2021
2469	(12^139739+1)/13	150803	Paul Bourdelais	09/2011
2470	(31^101111-1)/30	150792	Alexander Zhirkov	11/2010
2471	2^500899-500899	150786	Henri Lifchitz	04/2005
2472	2^500832+1876801	150766	Enzo Doria	07/2016
2473	(23*10^150763-59)/9	150764	Robert Price	05/2018
2474	2^500699+1884953	150726	Enzo Doria	02/2017
2475	(13*10^150675-37)/3	150676	Robert Price	01/2019
2476	(2^500527+lucasV(1,2,500527)+1)/4	150674	Mike Oakes	11/2016
2477	2^500337-71101	150617	Enzo Doria	04/2016
2478	(74*10^150616+133)/9	150617	Robert Price	06/2019
2479	(2*10^150612-17)/3	150612	Serge Batalov	11/2022
2480	4*10^150577+91	150578	Robert Price	08/2018
2481	2^500160+80071	150564	Enzo Doria	06/2016
2482	(2^500120+5)/9	150551	Lelio R Paula	12/2017
2483	(43*10^150515-421)/9	150516	Robert Price	01/2019
2484	(10^150551-1)/9/385207015049/57498437921/7808738631274081	150512	Maksym Voznyy	08/2014
2485	(10^150551-1)/1556587827131683185788921941743157225041	150512	Robert Price	07/2016
2486	2^499861-29503	150474	Enzo Doria	08/2015
2487	2^499653-113533	150411	Enzo Doria	08/2014
2488	(14*10^150391-191)/3	150392	Robert Price	10/2020
2489	2^499534-221	150375	Yves Minet	06/2012
2490	(28*10^150294+41)/3	150295	Robert Price	07/2021
2491	2^499225+49727	150282	Enzo Doria	09/2016
2492	(695*10^150274+7)/9	150276	Robert Price	12/2021
2493	2^499054-29261	150231	Enzo Doria	07/2015
2494	(844*10^150196-7)/9	150198	Robert Price	05/2021
2495	2^498907-933075	150186	Paul Bourdelais	06/2021
2496	(2^498898-7)/9	150183	Lelio R Paula	10/2015
2497	3*10^150182+17	150183	Robert Price	07/2018
2498	5*10^150175+63	150176	Robert Price	09/2020
2499	32363^33292+33292^32363	150149	Norbert Schneider	07/2022
2500	(77*10^150128+67)/9	150129	Robert Price	12/2021

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Probable Primes Top 10000

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