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*10^141407-27	141408	Robert Price	05/2018
2252	(214*10^141385-1)/3	141387	Robert Price	01/2021
2253	2^469630-59711	141373	Enzo Doria	10/2015
2254	(25*10^141366-331)/9	141367	Robert Price	08/2018
2255	(2^469564-3)/611	141351	Lelio R Paula	08/2015
2256	197^61601+2	141342	Lelio R Paula	08/2017
2257	2^469372-112949	141296	Enzo Doria	07/2014
2258	5*10^141294-63	141295	Robert Price	04/2021
2259	3^296115+4	141283	Tyler NeSmith	01/2021
2261	143^(2^16)+106^(2^16)	141253	Valeryi Kuryshev	02/2011
2260	143^65536+106^65536	141253	Serge Batalov	03/2018
2262	2^469198+782569	141243	Enzo Doria	10/2016
2263	2^469076-2786939	141206	Enzo Doria	11/2015
2264	2^468804+1874941	141125	Enzo Doria	06/2016
2265	2^468787+81353	141119	Enzo Doria	08/2016
2266	2^468595-350407	141062	Enzo Doria	06/2015
2267	2^468564+87855	141052	Lelio R Paula	01/2016
2268	2^468551-21987	141048	Enzo Doria	07/2013
2269	2^468523-7	141040	Lelio R Paula	08/2015
2270	(25*10^141019-13)/3	141020	Robert Price	09/2019
2271	2^468405+87855	141004	Lelio R Paula	01/2016
2272	2^467978-113051	140876	Enzo Doria	07/2014
2273	2^467780-344429	140816	Enzo Doria	07/2015
2274	9*10^140802-89	140803	Robert Price	04/2020
2275	2^467605-1855603	140764	Enzo Doria	09/2015
2276	5*10^140744-7	140745	Robert Price	09/2015
2277	(5^201359-1)/4	140744	Paul Bourdelais	12/2008
2278	2^467401-1850023	140702	Enzo Doria	08/2015
2279	(266*10^140681-17)/3	140683	Robert Price	07/2020
2280	(2^467270+78557)/23247	140658	Lelio R Paula	07/2015
2281	(29*2^467205+1)/2780517107	140635	Lelio R Paula	08/2015
2282	2^467166-1854941	140631	Enzo Doria	09/2015
2283	(203*10^140615-11)/3	140617	Robert Price	12/2020
2284	(85*10^140609+473)/9	140610	Robert Price	01/2020
2285	2^466866-1840571	140541	Enzo Doria	06/2015
2286	2^466829-459523	140530	Enzo Doria	05/2015
2287	2^466692-113213	140489	Enzo Doria	07/2014
2288	(44*10^140410-503)/9	140411	Robert Price	12/2018
2289	153^64265-2	140400	Lelio R Paula	11/2017
2290	(112*10^140357-1)/3	140359	Serge Batalov	12/2014
2291	(29*10^140337-17)/3	140338	Robert Price	09/2019
2292	2^466181-112735	140335	Enzo Doria	07/2014
2293	(5*10^140281-119)/3	140282	Robert Price	03/2018
2294	(27*2^465872+1)/691	140241	Lelio R Paula	08/2015
2295	2^465803-114817	140221	Enzo Doria	05/2015
2296	floor(Pi*10^140344)%10^140165	140165	Serge Batalov	08/2012
2297	2^465503-112735	140131	Enzo Doria	07/2014
2298	(16*10^140091+167)/3	140092	Robert Price	06/2019
2299	6^179964+179964^6-1	140040	Robert Price	04/2014
2300	(89*10^140008-179)/9	140009	Robert Price	12/2019
2301	(29*2^465077-1)/9	140003	Lelio R Paula	08/2015
2302	2^465072-344789	140001	Enzo Doria	07/2015
2303	5*10^139945+81	139946	Robert Price	03/2019
2304	2^464864-17	139939	Lelio R Paula	09/2017
2305	8*10^139920+51	139921	Robert Price	08/2019
2306	(85*10^139913-1)/3	139915	Robert Price	02/2020
2307	(17^113621+1)/18	139804	Paul Bourdelais	09/2011
2308	2*10^139800-21	139801	Robert Price	09/2020
2309	(13*10^139782+191)/3	139783	Robert Price	11/2018
2310	(19*2^464312-1)/3	139773	Lelio R Paula	08/2015
2311	(74*10^139723+133)/9	139724	Robert Price	06/2019
2312	3*10^139722+13	139723	Robert Price	07/2018
2313	77*10^139692+3	139694	Robert Price	06/2020
2314	(31*2^463970+1)/5	139670	Lelio R Paula	08/2015
2315	(18203^(2^15)+(18201)^(2^15))/2	139597	Robert Price	05/2018
2316	2^463633-2788423	139568	Enzo Doria	11/2015
2317	2^463271-109501	139459	Enzo Doria	04/2014
2318	(5*10^139457+79)/3	139458	Robert Price	03/2018
2319	2^463237-99	139449	Lelio R Paula	09/2017
2320	(49*10^139442+383)/9	139443	Robert Price	04/2019
2321	(7*10^139417-547)/9	139417	Robert Price	01/2018
2322	(10^139398+191)/3	139398	Robert Price	02/2018
2323	2^463019+79463	139383	Enzo Doria	06/2016
2324	3^292129-112756	139381	Enzo Doria	07/2014
2325	(15*2^462951+1)/527	139361	Lelio R Paula	08/2015
2326	2^462855-1865707	139334	Enzo Doria	02/2016
2327	(86*10^139315+121)/9	139316	Robert Price	08/2019
2328	2^462786-292043	139313	Enzo Doria	08/2015
2329	(26*10^139289+1)/9	139290	Serge Batalov	05/2010
2330	(17*10^139239+67)/3	139240	Robert Price	01/2019
2331	2^462238-935	139148	Yves Minet	02/2014
2332	(109*10^139100-7)/3	139102	Robert Price	03/2021
2333	2^461228+1870441	138844	Enzo Doria	05/2016
2334	2^461204-113675	138837	Enzo Doria	08/2014
2335	(2^461139-7)/47	138815	Lelio R Paula	08/2015
2336	(17*10^138812-521)/9	138813	Robert Price	04/2018
2337	3*10^138811-11	138812	Robert Price	07/2018
2338	(28*10^138768+173)/3	138769	Robert Price	12/2019
2339	(17*2^460963+1)/124051613	138757	Lelio R Paula	08/2015
2340	(379*10^138737-1)/9	138739	Robert Price	02/2020
2341	(43*10^138648+101)/9	138649	Robert Price	11/2018
2342	2^460567-113541	138645	Enzo Doria	08/2014
2343	7*10^138604+3	138605	Robert Price	08/2015
2344	2^460330+69	138574	Lelio R Paula	09/2017
2345	(17*10^138569-77)/3	138570	Robert Price	08/2019
2346	(16*10^138545+89)/3	138546	Robert Price	03/2021
2347	6*10^138520-37	138521	Robert Price	02/2021
2348	2^460078-69581	138498	Enzo Doria	12/2015
2349	2^459768+1531	138404	Lelio R Paula	06/2012
2350	(266*10^138328-17)/3	138330	Robert Price	07/2020
2351	2^459343-113611	138277	Enzo Doria	08/2014
2352	(28*10^138240+113)/3	138241	Robert Price	03/2020
2353	2^459199+1874393	138233	Enzo Doria	06/2016
2354	2^459063-345307	138192	Enzo Doria	06/2015
2355	2*10^138162-43	138163	Robert Price	04/2018
2356	2^458927-112747	138151	Enzo Doria	06/2014
2357	2^458927-69217	138151	Enzo Doria	11/2015
2358	555555*2^458524+1513	138036	Darren Bedwell	08/2009
2359	2^458465+2^32+1	138012	T. D. Noe	06/2007
2360	2^458321-113053	137969	Enzo Doria	07/2014
2361	2^458298+79459	137962	Enzo Doria	06/2016
2362	2^458248-21815	137947	Enzo Doria	07/2013
2363	2^458194+1876549	137931	Enzo Doria	07/2016
2364	(318259#+325270)/(2^2511*2957)	137907	Makoto Morimoto	10/2017
2365	(318259#+2625)/(3^257^5*22965193)	137899	Makoto Morimoto	06/2019
2366	2^457937+57	137853	Lelio R Paula	09/2017
2367	(8*10^137845+13)/3	137846	Robert Price	06/2018
2368	2^457822+105	137819	Donovan Johnson	06/2006
2369	2^457754-113711	137798	Enzo Doria	09/2014
2370	11^132315-360	137792	Enzo Doria	09/2012
2371	2^457347-37	137676	Lelio R Paula	09/2017
2372	2^457322-2786393	137668	Enzo Doria	10/2015
2373	gcd(Phi(699340,10),(10^34967+1)^3(10^34967+1+10^17484)-(10^69934+10^34967)(10^17484-1)+10^104901)	137664	Serge Batalov	04/2015
2374	2^457240-59939	137643	Enzo Doria	10/2015
2375	(856*10^137633-1)/9	137635	Robert Price	03/2020
2376	2^457120-21575	137607	Enzo Doria	07/2013
2377	(11*2^456978+1)/15	137564	Lelio R Paula	07/2015
2378	(7*25^98399+10613)/12	137556	Curtis Bright	05/2015
2379	419^52446+52446^419	137525	Norbert Schneider	11/2020
2380	2^456796-113513	137510	Enzo Doria	08/2014
2381	(7*2^456655+1)/39	137467	Lelio R Paula	07/2015
2382	2^456503-114361	137422	Enzo Doria	01/2015
2383	(11*2^456387+1)/19	137386	Lelio R Paula	07/2015
2384	(71*10^137250+1)/9	137251	Serge Batalov	05/2010
2385	2^455922+76249	137247	Enzo Doria	05/2016
2386	14^119741-119741^14	137239	Serge Batalov	04/2016
2387	(19*2^455760+1)/3455	137196	Lelio R Paula	07/2015
2389	124^(2^16)+57^(2^16)	137195	Valeryi Kuryshev	02/2011
2388	124^65536+57^65536	137195	Serge Batalov	03/2018
2390	2^455689+72677	137177	Enzo Doria	04/2016
2391	(17948!)^2+Prime(17948)	137118	Robert Price	08/2014
2392	(37^87421-1)/36	137093	Robert Price	03/2012
2393	2^455323-57	137066	Lelio R Paula	09/2017
2394	(73*17^111333-9)/16	136991	Curtis Bright	05/2015
2395	2^455025-112723	136977	Enzo Doria	06/2014
2396	66*10^136894+7	136896	Robert Price	07/2020
2397	2^454675-1777	136871	Yves Minet	10/2011
2398	3*10^136829+29	136830	Robert Price	05/2018
2399	4*10^136813-57	136814	Robert Price	10/2018
2400	(6092*28^94536-143)/9	136812	Curtis Bright	05/2015
2401	2^454348-53	136773	Lelio R Paula	09/2017
2402	31^91680-2	136729	Lelio R Paula	05/2017
2403	2^454199-113697	136728	Enzo Doria	09/2014
2404	7*10^136716+69	136717	Robert Price	07/2019
2405	6*10^136692+53	136693	Robert Price	05/2020
2406	(13*10^136687+47)/3	136688	Robert Price	10/2018
2407	2^453935-2791357	136649	Enzo Doria	01/2016
2408	2^453906-69131	136640	Enzo Doria	11/2015
2409	2^453791+1873913	136605	Enzo Doria	06/2016
2410	(21*2^453740-1)/2735	136588	Lelio R Paula	07/2015
2411	580^49413+49413^580	136550	Norbert Schneider	02/2019
2412	2^453503-2788297	136519	Enzo Doria	11/2015
2413	34989^7958+7958^34989	136486	Hans Havermann	12/2020
2414	31007^25158+25158^31007	136452	Hans Havermann	11/2020
2415	2^453267-113827	136447	Enzo Doria	09/2014
2416	32234^17085+17085^32234	136435	Hans Havermann	12/2020
2417	2^453102+1877629	136398	Enzo Doria	08/2016
2418	31016^24981+24981^31016	136397	Hans Havermann	12/2020
2419	(62*10^136384-791)/9	136385	Robert Price	06/2019
2420	34171^9798+9798^34171	136382	Hans Havermann	12/2020
2421	32756^14541+14541^32756	136350	Hans Havermann	11/2020
2422	32205^17086+17086^32205	136313	Hans Havermann	12/2020
2423	(25*10^136303+161)/3	136304	Robert Price	09/2019
2424	35337^7196+7196^35337	136299	Hans Havermann	12/2020
2425	(182*10^136291+1)/3	136293	Robert Price	02/2020
2426	23*10^136225-7	136227	Robert Price	02/2020
2427	L(651821)	136223	Henri Lifchitz	09/2008
2428	2^452460+77701	136205	Enzo Doria	05/2016
2429	2^452440-114755	136199	Enzo Doria	04/2015
2430	32286^16489+16489^32286	136157	Hans Havermann	11/2020
2431	(47*10^136141+493)/9	136142	Robert Price	03/2019
2432	40392^2339+2339^40392	136082	Hans Havermann	12/2020
2433	2*10^136057-43	136058	Robert Price	04/2018
2434	(2^451956-5)/181	136051	Lelio R Paula	07/2015
2435	2^451947-22165	136050	Enzo Doria	07/2013
2436	2^451787-21805	136002	Enzo Doria	07/2013
2437	2^451734-112817	135986	Enzo Doria	06/2014
2438	(11*2^451714+1)/75	135979	Lelio R Paula	07/2015
2439	2^451705-21879	135977	Enzo Doria	07/2013
2440	2^451560-112349	135934	Enzo Doria	06/2014
2441	2^451530+45	135925	Lelio R Paula	08/2017
2442	31622^19875+19875^31622	135922	Hans Havermann	11/2020
2443	(25*10^135906-73)/3	135907	Robert Price	09/2019
2444	2^451450-21743	135900	Enzo Doria	07/2013
2445	35218^7199+7199^35218	135846	Hans Havermann	11/2020
2446	35661^6446+6446^35661	135844	Hans Havermann	11/2020
2447	31869^18248+18248^31869	135801	Hans Havermann	12/2020
2448	2^450805+65	135706	Lelio R Paula	08/2017
2449	30761^25728+25728^30761	135669	Hans Havermann	12/2020
2450	2*10^135663+69	135664	Robert Price	06/2020
2451	33962^9867+9867^33962	135651	Hans Havermann	11/2020
2452	34474^8605+8605^34474	135647	Hans Havermann	11/2020
2453	34501^8508+8508^34501	135583	Hans Havermann	12/2020
2454	35487^6614+6614^35487	135577	Hans Havermann	12/2020
2455	(13725^32768+1)/131074	135573	Lelio R Paula	03/2012
2456	(313007#+121876)/(230469424867)	135559	Makoto Morimoto	08/2020
2457	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
2458	40387^2260+2260^40387	135463	Hans Havermann	12/2020
2459	2^449944-113247	135447	Enzo Doria	07/2014
2460	2^449770-113247	135395	Enzo Doria	07/2014
2461	2^449637-21471	135355	Enzo Doria	07/2013
2462	2^449571-75	135335	Lelio R Paula	08/2017
2463	(14*10^135301-53)/3	135302	Robert Price	12/2018
2464	(3*2^449494+1)/61340334013	135301	Lelio R Paula	07/2015
2465	(13*10^135279+437)/9	135280	Robert Price	04/2018
2466	2^449330-35	135262	Lelio R Paula	08/2017
2467	(19*2^449325+1)/9	135261	Lelio R Paula	07/2015
2468	(13*10^135184-43)/3	135185	Robert Price	11/2018
2469	2^449049-115309	135178	Enzo Doria	07/2015
2470	(10^135174+191)/3	135174	Robert Price	02/2018
2471	2^449030-15	135172	Lelio R Paula	08/2017
2472	(27*2^448936-1)/11	135144	Lelio R Paula	07/2015
2473	32221^15586+15586^32221	135095	Hans Havermann	12/2020
2474	2^448762-351401	135091	Enzo Doria	07/2015
2475	2*10^135083-43	135084	Robert Price	04/2018
2476	31357^20278+20278^31357	135056	Hans Havermann	12/2020
2477	32242^15445+15445^32242	135055	Hans Havermann	12/2020
2478	k(198476)	135054	Robert Price	07/2020
2479	32461^14470+14470^32461	135053	Hans Havermann	12/2020
2480	31353^20288+20288^31353	135045	Hans Havermann	12/2020
2481	5*10^135019+77	135020	Robert Price	12/2018
2482	(10^135011+719)/9	135011	Serge Batalov	12/2014
2483	(197*10^134978+7)/3	134980	Robert Price	12/2020
2484	2^448386-2786261	134978	Enzo Doria	03/2016
2485	(73*10^134939+143)/9	134940	Robert Price	07/2019
2486	33957^9392+9392^33957	134903	Hans Havermann	12/2020
2487	2^448113-113949	134896	Enzo Doria	11/2014
2488	30958^22755+22755^30958	134887	Hans Havermann	12/2020
2489	2^447888-2786639	134828	Enzo Doria	03/2016
2490	2^447870-396765	134823	Enzo Doria	07/2013
2491	2^447766-21791	134791	Enzo Doria	07/2013
2492	(19*10^134786-49)/3	134787	Robert Price	05/2019
2493	Phi(202173,10)/10064306514895399941409	134758	Makoto Kamada	05/2019
2494	(23*2^447647+1)/155	134755	Lelio R Paula	07/2015
2495	2^447552-1019	134727	Yves Minet	02/2014
2496	(2*10^134720-41)/3	134720	Robert Price	02/2018
2497	2^447437-113569	134692	Enzo Doria	08/2014
2498	2^447426-65	134689	Lelio R Paula	08/2017
2499	2^447357-2797573	134668	Enzo Doria	04/2016
2500	2^447278+93	134645	Lelio R Paula	08/2017

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