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	2^624008+1874941	187846	Enzo Doria	06/2016
2252	2^623870+78679	187804	Enzo Doria	05/2016
2253	2^623714-114035	187757	Enzo Doria	11/2014
2254	2^623651-1834251	187738	Enzo Doria	07/2015
2255	(7*10^187645+53)/3	187646	Robert Price	05/2018
2256	21650^43269+43269^21650	187591	Norbert Schneider	02/2023
2257	2^623146+1879609	187586	Enzo Doria	09/2016
2258	(401*10^187512+13)/9	187514	Robert Price	09/2021
2259	(5*10^187471+91)/3	187472	Robert Price	04/2018
2260	2^622500+81931	187392	Enzo Doria	08/2016
2261	(13*10^187382-157)/9	187383	Robert Price	05/2021
2262	2^622300-1861739	187331	Enzo Doria	12/2015
2263	(22*10^187317-91)/3	187318	Robert Price	02/2022
2264	(38*10^187281+349)/9	187282	Robert Price	10/2018
2265	2^622052+76771	187257	Enzo Doria	05/2016
2266	2^622005-24091	187243	Enzo Doria	08/2013
2267	7*10^187205-57	187206	Robert Price	06/2020
2268	2^621879-351787	187205	Enzo Doria	07/2015
2269	(5*10^187168-53)/3	187169	Robert Price	09/2020
2270	(23*10^187164-143)/3	187165	Robert Price	12/2019
2271	2^621700+79411	187151	Enzo Doria	06/2016
2272	2^621597+39	187120	Jon Grantham	08/2023
2273	(7*10^187101+131)/3	187102	Robert Price	06/2020
2274	(2*10^187062-71)/3	187062	Robert Price	12/2017
2275	2^620929-113203	186919	Enzo Doria	07/2014
2276	10^186842+168223	186843	Patrick De Geest	07/2018
2277	10^186842-8001	186842	Robert Price	03/2018
2278	2^620347-1777	186744	Lelio R Paula	07/2013
2279	(11*10^186659+133)/9	186660	Robert Price	04/2022
2280	11^179143-4170	186559	Enzo Doria	12/2012
2281	(5^266863+1)/6	186529	Paul Bourdelais	07/2010
2282	2*10^186517+33	186518	Robert Price	11/2021
2283	2^619297-2792353	186427	Enzo Doria	02/2016
2284	(49*10^186409+383)/9	186410	Robert Price	04/2019
2285	2^618940-460139	186320	Enzo Doria	06/2015
2286	2^618046+74179	186051	Enzo Doria	04/2016
2287	3*10^186019+11	186020	Robert Price	07/2018
2288	(16*10^185978-19)/3	185979	Robert Price	02/2019
2289	(22*10^185950-7)/3	185951	Robert Price	12/2022
2290	2*10^185930-3	185931	Robert Price	07/2015
2291	(82^97151+1)/83	185928	Paul Bourdelais	10/2017
2292	4*10^185905+91	185906	Robert Price	08/2018
2293	(34*10^185902-601)/9	185903	Robert Price	07/2022
2294	(19*10^185873+131)/3	185874	Robert Price	06/2020
2295	(37*10^185811+377)/9	185812	Robert Price	11/2018
2296	2^617250+9385	185811	Lelio R Paula	07/2013
2297	2^617130+9	185775	Stefano Morozzi	05/2021
2298	39^116749+2	185756	Robert Price	04/2015
2299	2^616924-39719	185713	Enzo Doria	09/2015
2300	2^616712+1867621	185649	Enzo Doria	04/2016
2301	(3^388897+2^388897)/5	185551	Jean-Louis Charton	09/2011
2302	8*10^185529-67	185530	Robert Price	08/2019
2303	(5*10^185520-11)/3	185521	Tyler Busby	02/2023
2304	5*2^616124+3	185473	Jon Grantham	07/2023
2305	2^615916+26791	185410	Enzo Doria	12/2023
2306	4*10^185355+9	185356	Robert Price	05/2015
2307	(16*10^185347+89)/3	185348	Robert Price	03/2021
2308	2^615622+76639	185321	Enzo Doria	05/2016
2309	2^615591+1879223	185312	Enzo Doria	08/2016
2310	2^615587+217013	185311	Enzo Doria	12/2023
2311	2^615503+1876643	185285	Enzo Doria	07/2016
2312	5^265007-4^265007	185232	Jean-Louis Charton	02/2013
2314	(4*10^185221-91)/3	185222	Robert Price	03/2018
2313	(7*10^185221+131)/3	185222	Robert Price	06/2020
2315	(62*10^185216-413)/9	185217	Robert Price	09/2021
2316	(232*10^185180+17)/3	185182	Robert Price	04/2021
2317	56*10^185139-3	185141	Robert Price	03/2020
2318	(28*10^185105+47)/3	185106	Robert Price	02/2021
2319	2^614783-2790097	185069	Enzo Doria	12/2015
2320	2^614745-29323	185057	Enzo Doria	07/2015
2321	(((((((((((2^3+3)^3+30)^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+66768)^3+300840	185052	Serge Batalov	07/2013
2322	(49*10^184993-67)/9	184994	Robert Price	03/2019
2323	(5*10^184954-191)/3	184955	Robert Price	05/2021
2324	(14*10^184950+211)/9	184951	Robert Price	04/2018
2325	2^614360+215221	184941	Enzo Doria	11/2023
2326	2^614315+81353	184928	Enzo Doria	08/2016
2327	2^614294-1849961	184921	Enzo Doria	08/2015
2328	2^614266+1877809	184913	Enzo Doria	08/2016
2329	(185*10^184878-11)/3	184880	Robert Price	10/2020
2330	91*10^184867-9	184869	Robert Price	06/2021
2331	39803^40170-40170^39803	184779	Norbert Schneider	05/2024
2332	(14789^44521-1)/(14789^211-1)	184770	Ryan Propper	11/2023
2333	(85*10^184768+77)/9	184769	Robert Price	07/2022
2334	2^613715-1860727	184747	Enzo Doria	11/2015
2335	(4*10^184730+89)/3	184731	Robert Price	08/2021
2336	2*10^184723+41	184724	Robert Price	05/2018
2337	(49*10^184703+293)/9	184704	Robert Price	03/2021
2338	2^613487-349987	184678	Enzo Doria	07/2015
2339	(95^93377+1)/96	184672	Paul Bourdelais	11/2017
2340	14^161089-161089^14	184629	Serge Batalov	05/2016
2341	40008^40109-40109^40008	184588	Norbert Schneider	05/2024
2342	2^613033-114621	184542	Enzo Doria	05/2015
2343	3*2^612759+5	184460	Jon Grantham	07/2023
2344	2^612587+213413	184408	Enzo Doria	09/2023
2345	(9^193247+1)/10	184404	Paul Bourdelais	02/2010
2346	2^612424+212341	184358	Enzo Doria	08/2023
2347	2^612341-1604809	184334	Enzo Doria	05/2015
2348	(11*10^184308-161)/3	184309	Robert Price	11/2021
2349	(2^611999-1)/18464214225958267477777390354183	184199	Dario Alpern	06/2017
2350	(14*10^184150+37)/3	184151	Robert Price	12/2018
2351	2^611731-4837	184150	Yves Minet	08/2018
2352	3*10^184124-7	184125	Robert Price	08/2015
2353	2^611644+29371	184124	Enzo Doria	02/2024
2354	9*10^184122-11	184123	Mischa Rodermond	04/2023
2355	2^611628-24537	184119	Enzo Doria	08/2013
2356	3*10^184110+13	184111	Robert Price	07/2018
2357	(14280^44521-1)/(14280^211-1)	184097	Ryan Propper	11/2023
2358	(194*10^184093+1)/3	184095	Robert Price	01/2022
2359	2^611460+71881	184068	Enzo Doria	04/2016
2360	4*10^184004-63	184005	Robert Price	10/2018
2361	2^611111+84083	183963	Boyan Hu	05/2024
2362	2^610982-1867301	183924	Enzo Doria	03/2016
2363	(10^183917+1)/11/9952852373	183906	Alfred Reich	02/2024
2364	3*10^183872-49	183873	Robert Price	07/2018
2365	2^610597+1178897	183809	Enzo Doria	05/2016
2366	(8*10^183773-269)/9	183773	Robert Price	09/2021
2367	(65*10^183768-29)/9	183769	Robert Price	01/2021
2368	(17*10^183764+31)/3	183765	Robert Price	01/2019
2369	(28*10^183760-1)/9	183761	Serge Batalov	10/2014
2370	2^610401+1277	183750	Lelio R Paula	07/2013
2371	2^610356-1849019	183736	Enzo Doria	08/2015
2372	(63^102103+1)/64	183717	Paul Bourdelais	10/2017
2373	23*10^183710-7	183712	Robert Price	02/2020
2374	(2^610289+1)/(3*528882550291)	183704	Gord Palameta	08/2018
2375	(4*10^183659+149)/9	183659	Robert Price	04/2018
2376	(4*10^183657+41)/9	183657	Serge Batalov	11/2022
2377	7*10^183596+39	183597	Robert Price	01/2023
2378	2^609846-1834251	183582	Enzo Doria	07/2015
2379	10^183546+1547323	183547	Patrick De Geest	02/2021
2381	10^183546-800000001	183546	Robert Price	09/2020
2380	10^183546-584297	183546	Patrick De Geest	02/2021
2382	7*10^183511+39	183512	Robert Price	01/2023
2383	(23*10^183477-71)/3	183478	Robert Price	07/2020
2384	11^176176-240	183469	Enzo Doria	11/2012
2385	(41^113749+1)/42	183451	Paul Bourdelais	11/2017
2386	6*10^183429+53	183430	Robert Price	05/2020
2387	(28*10^183403+191)/3	183404	Robert Price	02/2020
2388	(101^91463+1)/102	183320	Paul Bourdelais	11/2017
2389	2^608965-113989	183317	Enzo Doria	10/2014
2390	A005165(43592)	183312	Serge Batalov	07/2017
2391	(61*10^183294+119)/9	183295	Robert Price	05/2019
2392	2^608814-461261	183272	Enzo Doria	06/2015
2393	(163*10^183227-1)/9	183229	Serge Batalov	12/2014
2394	2^608541-608541^2	183190	Henri Lifchitz	02/2018
2395	2^608293+143807	183115	Enzo Doria	10/2016
2396	2^608164-462419	183076	Enzo Doria	08/2015
2397	2^607950-1862303	183012	Enzo Doria	12/2015
2398	5*3^383376+2^383376	182918	Jon Grantham	08/2023
2399	(46*10^182896+683)/9	182897	Robert Price	03/2019
2400	(2*10^182787+73)/3	182787	Robert Price	09/2020
2401	2^607101+1871987	182756	Enzo Doria	05/2016
2402	2^606869-69175	182686	Enzo Doria	11/2015
2403	8*10^182671+71	182672	Robert Price	05/2022
2404	(23*10^182666-71)/3	182667	Robert Price	07/2020
2405	3*10^182614-11	182615	Robert Price	07/2018
2406	2^606560-357	182593	Enzo Doria	05/2014
2407	66*10^182420+7	182422	Robert Price	07/2020
2408	2^605687+1866983	182330	Enzo Doria	03/2016
2409	2^605655-114445	182321	Enzo Doria	02/2015
2410	94*10^182291-3	182293	Robert Price	05/2020
2411	(20^140053+1)/21	182212	Paul Bourdelais	04/2010
2412	(14*10^182177-221)/9	182178	Robert Price	04/2018
2413	2^605174-112751	182176	Enzo Doria	06/2014
2414	(905^61609-1)/904	182154	Anonymous	05/2024
2415	2^604761+1874507	182052	Enzo Doria	06/2016
2416	2^604705+1871957	182035	Enzo Doria	05/2016
2417	(14*10^182000+229)/9	182001	Robert Price	03/2018
2418	(10^181996+41)/3	181996	Robert Price	12/2017
2419	(17*10^181979+91)/9	181980	Robert Price	02/2022
2420	(5*10^181950-101)/3	181951	Robert Price	04/2018
2421	2^603915+75233	181797	Enzo Doria	04/2016
2422	39470^39537+39537^39470	181723	Norbert Schneider	12/2022
2423	(10^181710+7)/563747/2019847	181698	Alfred Reich	08/2021
2424	7*10^181594-57	181595	Robert Price	06/2020
2425	8*10^181580+29	181581	Robert Price	11/2021
2426	(83*10^181544+61)/9	181545	Serge Batalov	01/2023
2427	(2*10^181457+7)/9	181457	Rytis Slatkevicius	01/2023
2428	3*10^181445+23	181446	Robert Price	03/2022
2429	(194*10^181369-11)/3	181371	Robert Price	09/2020
2430	11^174145-360	181354	Enzo Doria	10/2012
2431	2^602351-396765	181326	Enzo Doria	08/2013
2432	6*10^181306+17	181307	Robert Price	04/2019
2433	(353^71143-1)/352	181254	Anonymous	04/2024
2434	(286*10^181220-1)/3	181222	Robert Price	11/2020
2435	2^601957-113833	181208	Enzo Doria	09/2014
2436	66^99581-65^99581	181193	Robert Price	09/2013
2437	10^181182+383973	181183	Patrick De Geest	04/2016
2438	10^181182-21	181182	Serge Batalov	12/2014
2439	(797*10^181171-41)/9	181173	Robert Price	04/2022
2440	2^601722+74209	181137	Enzo Doria	08/2023
2441	(5*10^181127-29)/3	181128	Robert Price	03/2018
2442	2^601521-29143	181076	Enzo Doria	07/2015
2443	2^601442-2797811	181053	Enzo Doria	04/2016
2444	44*10^181029+3	181031	Robert Price	04/2020
2445	5*10^180992-9	180993	Robert Price	05/2015
2446	10^180979+79477	180980	Patrick De Geest	04/2016
2447	10^180979+107739	180980	Patrick De Geest	04/2016
2448	10^180979-11	180979	Serge Batalov	12/2014
2449	2^601023-113851	180926	Enzo Doria	10/2014
2450	(23*10^180862-143)/3	180863	Robert Price	12/2019
2451	3*10^180852+29	180853	Robert Price	05/2018
2452	(277*10^180782-7)/9	180784	Robert Price	02/2022
2453	2^600412+29851	180743	Enzo Doria	03/2024
2454	(8*10^180725-629)/9	180725	Robert Price	01/2022
2455	(79*10^180710-1)/3	180712	Robert Price	02/2020
2456	2^600300-1852559	180709	Enzo Doria	08/2015
2457	(2*10^180706-77)/3	180706	Robert Price	02/2021
2458	(156^82393-1)/155	180696	Anonymous	06/2024
2459	(10^180689+71)/9	180689	Serge Batalov	07/2015
2460	2^600209+76487	180681	Enzo Doria	05/2016
2461	2^599999+378461	180618	Norman Luhn	09/2023
2462	(8*10^180536-269)/9	180536	Robert Price	09/2021
2463	2^599702-369885	180529	Enzo Doria	11/2013
2464	Tau(643^11688)	180524	Nik Lygeros / Olivier Rozier	05/2015
2465	(2951*29^123418-3)/4	180490	Curtis Bright	05/2015
2466	(29*10^180432-17)/3	180433	Robert Price	09/2019
2467	4*10^180360+93	180361	Robert Price	08/2018
2468	2^599035+219323	180328	Enzo Doria	03/2024
2469	2^598942+80779	180300	Enzo Doria	07/2016
2470	(38*10^180296+403)/9	180297	Robert Price	10/2018
2471	(85*10^180241+77)/9	180242	Robert Price	07/2022
2472	2^598591-1844797	180194	Enzo Doria	06/2015
2473	(100^90089+1)/101	180176	Paul Bourdelais	08/2017
2474	2^598301+28517	180107	Enzo Doria	01/2024
2475	(29*10^180072+691)/9	180073	Robert Price	08/2021
2476	(59*10^180038+157)/9	180039	Robert Price	12/2021
2477	95*10^180019-9	180021	Robert Price	01/2022
2478	6*10^179970+91	179971	Robert Price	05/2019
2479	(4*10^179963-79)/3	179964	Robert Price	02/2018
2480	(403*10^179944-43)/9	179946	Robert Price	06/2021
2481	Gamma-Prime(179849)	179849	Eric W. Weisstein	06/2011
2482	2^597424-1859729	179843	Enzo Doria	11/2015
2483	Phi(180683,10)	179760	Maksym Voznyy	09/2015
2484	(10^180683-1)*9/(10^643-1)/(10^281-1)	179760	Robert Price	07/2016
2485	(3^376657-2^376657)/22301107657	179701	Mike Oakes	04/2017
2486	(29*10^179697+223)/9	179698	Robert Price	09/2018
2487	2^596884+73	179680	Stefano Morozzi	04/2021
2488	(11*10^179679+13)/3	179680	Robert Price	03/2022
2489	(68*10^179656+7)/3	179658	Robert Price	01/2020
2490	(10^179643+173)/3	179643	Robert Price	05/2021
2491	2^596690-461261	179622	Enzo Doria	07/2015
2492	2^596684-113939	179620	Enzo Doria	10/2014
2493	2^596642+39	179608	Jon Grantham	08/2023
2494	2*10^179602+63	179603	Robert Price	05/2018
2495	32262^39815-39815^32262	179514	Frank Doornink	02/2024
2496	(25*10^179488-403)/9	179489	Robert Price	01/2021
2497	7*10^179460+99	179461	Robert Price	05/2021
2498	2^596127+74333	179453	Enzo Doria	07/2023
2499	3^375887-112696	179344	Enzo Doria	07/2014
2500	4*10^179265-71	179266	Robert Price	12/2018

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Probable Primes Top 10000

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