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 (> 30000)	Who ?	When ?
2251	3^229236+100	109374	Lelio R Paula	03/2017
2252	2^363268-58695	109355	Lelio R Paula	04/2017
2253	2^363191-112321	109332	Enzo Doria	06/2014
2254	2^363120+3	109311	Donovan Johnson	04/2006
2255	(10^109297-1)/9	109297	Paul Bourdelais, Harvey Dubner	04/2007
2256	2^363042-114641	109287	Enzo Doria	04/2015
2257	2^363020-112793	109280	Enzo Doria	06/2014
2258	(67607*2^362695+1)/70499	109183	Lelio R Paula	07/2014
2259	(9*2^362644+1)/5	109167	Lelio R Paula	03/2014
2260	5^156181+38	109166	Lelio R Paula	02/2017
2261	3^228750+68	109142	Lelio R Paula	03/2017
2262	(10223*2^362376+1)/9	109090	Lelio R Paula	07/2014
2263	65^60167-64^60167	109078	Robert Price	08/2013
2264	7*3^228589-2	109066	Lelio R Paula	09/2014
2265	(78557*2^362188+1)/189	109033	Lelio R Paula	07/2014
2266	2*7^129008+9	109025	Lelio R Paula	11/2014
2267	2^361957+76367	108960	Enzo Doria	05/2016
2268	2^361873-1411	108935	Yves Minet	01/2013
2269	(24737*2^361857+1)/35	108933	Lelio R Paula	07/2014
2270	13^97745-24	108883	Lelio R Paula	03/2017
2271	17^88475+8	108864	Lelio R Paula	04/2017
2272	2^361567+51	108843	Lelio R Paula	01/2012
2273	2^361563-109501	108842	Enzo Doria	04/2014
2274	12^100852+83	108838	Lelio R Paula	03/2017
2275	2^361497+767	108822	Lelio R Paula	01/2012
2276	2^361280-112349	108757	Enzo Doria	06/2014
2277	2^361271-5955	108754	Lelio R Paula	04/2017
2278	12^100757+19	108736	Lelio R Paula	03/2017
2279	14^94849-61	108710	Lelio R Paula	05/2017
2280	(19^85009-5^85009)/14	108705	Robert Price	07/2013
2281	(11*2^361027+1)/40463	108677	Lelio R Paula	03/2014
2282	2^360973+1299	108664	Lelio R Paula	04/2017
2283	2^360959-109101	108660	Enzo Doria	04/2014
2284	6*5^155454+7	108659	Lelio R Paula	11/2014
2285	10^108656+79	108657	Lelio R Paula	02/2017
2286	10^108656-50001	108656	Patrick De Geest	03/2017
2287	2^360918-35	108648	Lelio R Paula	01/2012
2288	(11*2^360886-1)/7	108638	Lelio R Paula	03/2014
2289	2^360706-458903	108584	Enzo Doria	04/2015
2290	2^360641-113185	108564	Enzo Doria	07/2014
2291	2^360618+75019	108557	Enzo Doria	04/2016
2292	3*5^155286+2	108541	Lelio R Paula	11/2014
2293	7^128422+4	108530	Lelio R Paula	11/2014
2294	7^128421-80	108529	Lelio R Paula	03/2017
2295	2^360497+53807	108521	Yves Minet	07/2010
2296	2^360366+1459	108481	Lelio R Paula	09/2011
2297	2^360364-1499	108481	Yves Minet	05/2013
2298	14^94642-23	108472	Lelio R Paula	05/2017
2299	4*10^108412+9	108413	Robert Price	05/2015
2300	2^360093-351103	108399	Enzo Doria	06/2015
2301	2^360042+723	108384	Lelio R Paula	01/2012
2302	85^56164-2	108364	Lelio R Paula	10/2013
2303	2^359937-29323	108352	Enzo Doria	07/2015
2304	2^359898-19997	108341	Enzo Doria	06/2013
2305	2*5^154948-7	108305	Lelio R Paula	11/2014
2306	10^108303+13	108304	Lelio R Paula	02/2017
2307	10^108303-207959	108303	Patrick De Geest	03/2017
2308	2^359730+753	108290	Lelio R Paula	12/2011
2309	2^359650-19797	108266	Enzo Doria	06/2013
2310	91^55259-90^55259	108255	Robert Price	07/2015
2311	3^226845+68	108233	Lelio R Paula	03/2017
2312	5^154822-12866	108216	Enzo Doria	05/2014
2313	(9*2^359480+1)/5	108215	Lelio R Paula	03/2014
2314	2^359454-177	108207	Lelio R Paula	12/2011
2315	6^139022-59	108181	Lelio R Paula	02/2017
2316	2^359352-179	108176	Lelio R Paula	12/2011
2317	2^359338-1858781	108172	Enzo Doria	04/2016
2318	12^100230-97	108167	Lelio R Paula	03/2017
2319	(25*2^359297-1)/137	108159	Lelio R Paula	03/2014
2320	(2^359262-509203)/9	108148	Lelio R Paula	12/2013
2321	(3^226648-8)/352715633	108131	Lelio R Paula	12/2013
2322	6^138956-59	108129	Lelio R Paula	02/2017
2323	2^359184+30285	108126	Lelio R Paula	04/2017
2324	13^97059+10	108119	Lelio R Paula	03/2017
2325	2^359137-81	108112	Lelio R Paula	12/2011
2326	(15185*2^359105-1)/567	108103	Lelio R Paula	05/2015
2327	2^359110-11655	108103	Lelio R Paula	04/2017
2328	8*6^138875+5	108067	Lelio R Paula	11/2014
2329	2^358987-216919	108066	Enzo Doria	05/2014
2330	39^67918-67918^39	108062	Norbert Schneider	02/2017
2331	2^358785-16933	108006	Enzo Doria	05/2013
2332	(2^358783+5)/33383	108000	Lelio R Paula	12/2013
2333	6^138770-77	107985	Lelio R Paula	02/2017
2334	(2^358727-1017)/94178479	107980	Lelio R Paula	12/2013
2335	10^107976+19	107977	Lelio R Paula	02/2017
2336	10^107976-202103	107976	Patrick De Geest	03/2017
2337	2^358684+75781	107975	Enzo Doria	04/2016
2338	99^54094+2	107952	Lelio R Paula	06/2013
2339	(2^358583-9)/391	107942	Lelio R Paula	12/2013
2340	2^358538+55	107931	Lelio R Paula	12/2011
2341	2^358517-109009	107925	Enzo Doria	03/2014
2342	3^226159+104	107906	Lelio R Paula	03/2017
2343	2^358310-11655	107863	Lelio R Paula	03/2017
2344	2^358275-112987	107852	Enzo Doria	07/2014
2345	2^358233-20005	107839	Enzo Doria	06/2013
2346	2^358194+175	107828	Lelio R Paula	12/2011
2347	107^53125-106	107812	Norbert Schneider	12/2016
2348	3^225922-2	107793	Lelio R Paula	10/2013
2349	12^99874-95	107783	Lelio R Paula	03/2017
2350	2^358030-171	107778	Lelio R Paula	12/2011
2351	11^103488-4170	107772	Enzo Doria	12/2012
2352	2^357911-20089	107742	Enzo Doria	06/2013
2353	2^357885+12857	107735	Yves Minet	07/2010
2354	7^127473+40	107728	Lelio R Paula	03/2017
2355	5*2^357850+9	107725	Lelio R Paula	09/2014
2356	2^357786-291191	107705	Enzo Doria	06/2015
2357	18^85798-23	107700	Lelio R Paula	04/2017
2358	2^357688-1854269	107675	Enzo Doria	09/2015
2359	2^357671-112225	107670	Enzo Doria	06/2014
2360	2^357618-21005	107654	Enzo Doria	06/2013
2361	2^357615-17505	107653	Enzo Doria	05/2013
2362	(30^72871-1)/29	107638	Robert Price	12/2011
2363	2^357521+1870217	107625	Enzo Doria	05/2016
2364	2^357477-1203	107612	Lelio R Paula	03/2017
2365	5^153894-18	107568	Lelio R Paula	02/2017
2366	2^357324-69059	107566	Enzo Doria	11/2015
2367	2^357283-869688105	107553	Lelio R Paula	01/2017
2368	2^357280-16805	107552	Enzo Doria	05/2013
2369	10^107547+481719	107548	Patrick De Geest	03/2017
2370	10^107547-47	107547	Lelio R Paula	02/2017
2371	17^87396-32	107537	Lelio R Paula	04/2017
2372	2^357081+107	107493	Lelio R Paula	12/2011
2373	2^357058-3911	107486	Yves Minet	04/2017
2374	3^225274+64	107484	Lelio R Paula	03/2017
2375	18^85619-95	107476	Lelio R Paula	04/2017
2376	3^225248-130	107471	Lelio R Paula	03/2017
2377	(5*2^356961+1)/143	107455	Lelio R Paula	03/2014
2378	2^356935-18085	107449	Enzo Doria	05/2013
2379	10^107409+37	107410	Lelio R Paula	02/2017
2380	10^107409-329633	107409	Patrick De Geest	03/2017
2381	2^356787-109027	107404	Enzo Doria	04/2014
2382	(2^356767+78557)/5	107397	Lelio R Paula	12/2013
2383	5^153622-42	107378	Lelio R Paula	02/2017
2384	2^356699-97305	107378	Lelio R Paula	03/2017
2385	2^356654+85	107364	Lelio R Paula	11/2011
2386	2^356641-19921	107360	Enzo Doria	06/2013
2387	2^356623-465	107355	Lelio R Paula	03/2017
2388	19^83945-92	107345	Lelio R Paula	02/2017
2389	10^107334+28149	107335	Patrick De Geest	03/2017
2390	10^107334-83	107334	Lelio R Paula	02/2017
2391	2^356518+885	107323	Lelio R Paula	03/2017
2392	(3*2^356506-1)/467	107317	Lelio R Paula	03/2014
2393	2^356442-114713	107300	Enzo Doria	04/2015
2394	2^356425+72257	107295	Enzo Doria	04/2016
2395	2^356351-112237	107273	Enzo Doria	06/2014
2396	(6^137845-11)/5	107264	Paul Bourdelais	11/2011
2397	2^356322+74539	107264	Enzo Doria	04/2016
2398	2^356274+1874479	107250	Enzo Doria	06/2016
2399	20^82422-93	107234	Lelio R Paula	02/2017
2400	2^356157-20365	107214	Enzo Doria	06/2013
2401	2^356129-18949	107206	Enzo Doria	05/2013
2402	2^356100-109587	107197	Enzo Doria	04/2014
2403	(31*2^355970+1)/5	107159	Lelio R Paula	03/2014
2404	2^355968-64875	107158	Lelio R Paula	01/2017
2405	2^355952+1870321	107153	Enzo Doria	05/2016
2406	2^355915-117	107142	Lelio R Paula	11/2011
2407	(19*2^355838-1)/15	107119	Lelio R Paula	03/2014
2408	3^224495-8	107112	Lelio R Paula	12/2013
2409	7^126691-44	107067	Lelio R Paula	03/2017
2410	4^177830-8243	107065	Mike Oakes	02/2011
2411	2^355524-21237	107024	Enzo Doria	06/2013
2412	(10223*2^355515+1)/4855	107022	Lelio R Paula	07/2014
2413	2^355494-19901	107015	Enzo Doria	06/2013
2414	2^355454-869688105	107003	Lelio R Paula	01/2017
2415	2^355366+54615	106976	Lelio R Paula	01/2017
2416	(31*2^355346-1)/1563	106969	Lelio R Paula	03/2014
2417	2^355275-19861	106949	Enzo Doria	06/2013
2418	(9179*2^355234-1)/1915	106937	Lelio R Paula	05/2015
2419	4*10^106892-3	106893	Robert Price	10/2015
2420	(66^58741+1)/67	106881	Paul Bourdelais	08/2017
2421	2^354946-3	106850	M. Frind & P. Underwood	08/2002
2422	2^354873-18693	106828	Enzo Doria	05/2013
2423	2^354828+4257	106814	Lelio R Paula	01/2017
2424	(21^80761+1)/22	106783	Paul Bourdelais	03/2010
2425	2^354640-354640+1	106758	Robert Price	10/2014
2426	2^354585+95	106741	Lelio R Paula	10/2011
2427	2^354553+189	106732	Lelio R Paula	10/2011
2428	2^354514-109031	106720	Enzo Doria	04/2014
2429	2^354509-109465	106718	Enzo Doria	04/2014
2430	(15*2^354478-1)/26983	106706	Lelio R Paula	03/2014
2431	15^90710+28	106684	Lelio R Paula	04/2017
2432	7^126237+34	106683	Lelio R Paula	03/2017
2433	2^354385-115315	106681	Enzo Doria	06/2015
2434	2^354327-19305	106664	Enzo Doria	06/2013
2435	(35*10^106649+1)/9	106650	Serge Batalov	11/2010
2436	10^106636+97	106637	Lelio R Paula	02/2017
2437	10^106636-22923	106636	Patrick De Geest	03/2017
2438	2^354220-57	106631	Lelio R Paula	10/2011
2439	2^354157-17041	106612	Enzo Doria	05/2013
2440	12^98778+73	106600	Lelio R Paula	02/2017
2441	2^354064+1870651	106584	Enzo Doria	05/2016
2442	2^353992-57	106563	Lelio R Paula	10/2011
2443	2^353832-1853849	106515	Enzo Doria	09/2015
2444	(7^126037-1)/6	106513	Paul Bourdelais	09/2008
2445	2^353794-18453	106503	Enzo Doria	05/2013
2446	2^353728+7695	106483	Lelio R Paula	01/2017
2447	2^353672-303	106466	Yves Minet	02/2012
2448	6^136811+101	106460	Lelio R Paula	02/2017
2449	2^353641+1871981	106457	Enzo Doria	05/2016
2450	2^353553+54615	106431	Lelio R Paula	01/2017
2451	2^353544-18897	106428	Enzo Doria	05/2013
2452	6^136729-133	106396	Lelio R Paula	02/2017
2453	2^353418+1605	106390	Lelio R Paula	01/2017
2454	2^353387+65	106381	Lelio R Paula	10/2011
2455	2^353372+74311	106376	Enzo Doria	04/2016
2456	2^353344-3693	106368	Yves Minet	03/2017
2457	2^353277-20089	106347	Enzo Doria	06/2013
2458	2^353275+72173	106347	Enzo Doria	04/2016
2459	2^353268-17705	106345	Enzo Doria	05/2013
2460	2^353267-19857	106344	Enzo Doria	06/2013
2461	222748^3+3^222748	106278	Anatoly F. Selevich	12/2010
2462	(9179*2^353019-1)/9	106273	Lelio R Paula	05/2015
2463	2^353025+72257	106272	Enzo Doria	04/2016
2465	2^352932-20345	106244	Enzo Doria	06/2013
2464	(2^353011-3)/745325861246794515484535	106244	Lelio R Paula	12/2013
2466	2^352883-187	106229	Lelio R Paula	10/2011
2467	20^81649-19^81649	106228	Jean-Louis Charton	03/2011
2468	2^352814-131	106208	Lelio R Paula	10/2011
2469	2^352752+73951	106189	Enzo Doria	04/2016
2470	6^136434+5	106167	Lelio R Paula	11/2014
2471	7*5^151872-8	106155	Lelio R Paula	11/2014
2472	2^352601-1604809	106144	Enzo Doria	05/2015
2473	12^98353-43	106141	Lelio R Paula	02/2017
2474	2^352585-18901	106139	Enzo Doria	05/2013
2475	(2^352554-3)/193	106128	Lelio R Paula	12/2013
2476	2^352540+15015	106126	Lelio R Paula	01/2017
2477	2^352524-3149	106121	Yves Minet	10/2014
2478	2^352486-1858781	106109	Enzo Doria	04/2016
2479	2^352444+12705	106097	Lelio R Paula	01/2017
2480	2^352228-18953	106032	Enzo Doria	05/2013
2481	2^352107+1872533	105995	Enzo Doria	05/2016
2482	2^352066-2591	105983	Yves Minet	07/2014
2483	2^352030+715	105972	Lelio R Paula	10/2011
2484	9*6^136176-5	105967	Lelio R Paula	11/2014
2485	155^48377+2	105962	Lelio R Paula	08/2013
2486	2^351865+1869707	105922	Enzo Doria	05/2016
2487	2^351831+23	105912	Lelio R Paula	10/2011
2488	9*2^351784-5	105899	Lelio R Paula	09/2014
2489	2^351671-112387	105864	Enzo Doria	06/2014
2490	2^351669-109501	105863	Enzo Doria	04/2014
2491	2^351644+74731	105856	Enzo Doria	04/2016
2492	13^95025-42	105853	Lelio R Paula	12/2016
2493	2^351599+15015	105842	Lelio R Paula	01/2017
2494	19^82763+90	105834	Lelio R Paula	01/2017
2495	(9179*2^351540-1)/221	105826	Lelio R Paula	05/2015
2496	20^81329-51	105812	Lelio R Paula	01/2017
2497	2^351483+28425	105807	Lelio R Paula	01/2017
2498	15^89960+86	105802	Lelio R Paula	02/2017
2499	2^351460-17289	105801	Enzo Doria	05/2013
2500	19^82735+22	105798	Lelio R Paula	01/2017

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PRP Records

Probable Primes Top 10000

(181746 PRPs in the top)