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	10^148934-512057	148934	Patrick De Geest	02/2021
2252	39000^6571+6571^39000	148888	Hans Havermann	10/2020
2253	2^494586-2791991	148886	Enzo Doria	02/2016
2254	8*10^148860-3	148861	Ray Chandler	04/2011
2255	38262^7769+7769^38262	148854	Hans Havermann	10/2020
2256	2^494333-286183	148810	Enzo Doria	06/2015
2257	2^494144-264119	148753	Enzo Doria	05/2014
2258	36502^11823+11823^36502	148663	Hans Havermann	11/2020
2259	(5*2^493838-1)/3721	148658	Lelio R Paula	10/2015
2260	64239^206+206^64239	148641	Hans Havermann	10/2020
2261	(23*2^493761-1)/555	148636	Lelio R Paula	10/2015
2262	(23*10^148627-137)/3	148628	Robert Price	08/2021
2263	(151*10^148601-1)/3	148603	Robert Price	03/2020
2264	2^493636+82081	148600	Enzo Doria	09/2016
2265	((((((((((((((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
2266	177487#+(519643#)/(177487#)	148558	Makoto Morimoto	11/2017
2267	(2*10^148460-23)/3	148460	Robert Price	04/2018
2268	(28*10^148445+101)/3	148446	Robert Price	09/2020
2269	36203^12556+12556^36203	148391	Hans Havermann	10/2020
2270	33912^23749+23749^33912	148387	Hans Havermann	10/2020
2271	(8*10^148328+1)/9	148328	Serge Batalov	05/2010
2272	34294^21117+21117^34294	148309	Hans Havermann	10/2020
2273	(71*10^148306-539)/9	148307	Robert Price	07/2019
2274	38042^7875+7875^38042	148222	Hans Havermann	10/2020
2275	5^211959-12874	148153	Enzo Doria	05/2014
2276	34142^21831+21831^34142	148145	Hans Havermann	10/2020
2277	10^148112+34059	148113	Patrick De Geest	05/2021
2278	10^148112-70000001	148112	Robert Price	03/2021
2279	10^148112-106593	148112	Patrick De Geest	05/2021
2280	36303^12016+12016^36303	148108	Hans Havermann	10/2020
2281	(16*10^148071+41)/3	148072	Robert Price	03/2019
2282	187^65175-2	148068	Lelio R Paula	11/2017
2283	2^491851+1871453	148062	Enzo Doria	05/2016
2284	(68*10^148060-257)/9	148061	Robert Price	07/2019
2285	(151*10^148020-1)/3	148022	Robert Price	03/2020
2286	39153^6032+6032^39153	148017	Hans Havermann	10/2020
2287	36798^10507+10507^36798	147983	Hans Havermann	12/2020
2288	(26*10^147973-23)/3	147974	Robert Price	12/2019
2289	2^491521-1865323	147963	Enzo Doria	02/2016
2290	(2^491476+7)/71	147948	Lelio R Paula	10/2015
2291	2*10^147928+47	147929	Robert Price	12/2021
2292	2^491391-7807	147924	Lelio R Paula	01/2013
2293	39736^5279+5279^39736	147920	Hans Havermann	11/2020
2294	2^491370-113297	147918	Enzo Doria	07/2014
2295	(32760^32760+32759^32759)/95546586737133567708319	147900	Robert Price	07/2016
2296	44368^2155+2155^44368	147899	Hans Havermann	12/2020
2297	(17*10^147890+79)/3	147891	Robert Price	04/2019
2298	94*10^147871-3	147873	Robert Price	05/2020
2299	10^147843+620967	147844	Patrick De Geest	05/2021
2300	10^147843-50000000001	147843	Robert Price	12/2020
2301	10^147843-182891	147843	Patrick De Geest	05/2021
2302	35805^13346+13346^35805	147709	Hans Havermann	11/2020
2303	2^490672+255255	147707	Paul Bourdelais	10/2021
2304	2^490660-17	147704	Lelio R Paula	12/2017
2305	(229*10^147699-1)/3	147701	Robert Price	07/2020
2306	40656^4289+4289^40656	147678	Hans Havermann	11/2020
2307	2^490550+1179439	147671	Enzo Doria	06/2016
2308	(23*10^147649-59)/9	147650	Robert Price	05/2018
2309	2^490303+2793653	147596	Enzo Doria	03/2016
2310	2^490266+255255	147585	Paul Bourdelais	10/2021
2311	199^64181-2	147543	Lelio R Paula	11/2017
2312	32849^30958+30958^32849	147518	Hans Havermann	11/2020
2313	2^489871-286987	147466	Enzo Doria	07/2015
2314	2^489864-351899	147464	Enzo Doria	07/2015
2315	175^65724-2	147422	Lelio R Paula	11/2017
2316	2^489712+1874851	147419	Enzo Doria	06/2016
2317	34473^18830+18830^34473	147367	Hans Havermann	11/2020
2318	63^81896-2	147359	Lelio R Paula	10/2017
2319	34580^18237+18237^34580	147344	Hans Havermann	11/2020
2320	(11*10^147313-107)/3	147314	Robert Price	09/2018
2321	2^489305-59815	147296	Enzo Doria	10/2015
2322	(2^489280-7)/6381	147285	Lelio R Paula	09/2015
2323	2*10^147264-61	147265	Robert Price	10/2021
2324	2*10^147260+29	147261	Robert Price	02/2021
2325	33556^24457+24457^33556	147258	Hans Havermann	11/2020
2326	2^489125+80357	147242	Enzo Doria	06/2016
2327	32835^30452+30452^32835	147220	Hans Havermann	12/2020
2328	(19*10^147213-97)/3	147214	Robert Price	10/2021
2329	(148*10^147139-1)/3	147141	Robert Price	03/2020
2330	34338^19255+19255^34338	147123	Hans Havermann	11/2020
2331	2^488648-112799	147098	Enzo Doria	07/2014
2332	2^488627-350317	147092	Enzo Doria	06/2015
2333	33432^25075+25075^33432	147076	Hans Havermann	12/2020
2334	(2^488441-1)/(61543567*30051203516986199)	147012	Dario Alpern	12/2014
2335	2^488280-2165	146987	Yves Minet	07/2014
2336	2^488278+45	146987	Lelio R Paula	12/2017
2337	2^487927-39	146881	Lelio R Paula	12/2017
2338	(7*10^146860-13)/3	146861	Robert Price	07/2018
2339	(26*10^146856-77)/3	146857	Robert Price	11/2019
2340	32948^28611+28611^32948	146834	Hans Havermann	11/2020
2341	42596^2799+2799^42596	146829	Hans Havermann	12/2020
2342	2^487726-1863341	146821	Enzo Doria	12/2015
2343	43838^2229+2229^43838	146775	Hans Havermann	11/2020
2344	35005^15594+15594^35005	146775	Hans Havermann	11/2020
2345	(167*10^146764+7)/3	146766	Robert Price	04/2021
2346	(59*10^146738+157)/9	146739	Robert Price	12/2021
2347	((10^73362-1)10000/9+6701)10^73362+(10^73362-1)/9	146728	Hans Havermann	09/2019
2348	32963^28234+28234^32963	146711	Hans Havermann	12/2020
2349	(22*10^146661-19)/3	146662	Robert Price	04/2019
2350	33958^20825+20825^33958	146651	Hans Havermann	12/2020
2351	2^487121-39523	146639	Enzo Doria	09/2015
2352	61063^252+252^61063	146637	Hans Havermann	12/2020
2353	(7*2^486967+1)/39	146591	Lelio R Paula	09/2015
2354	34099^19900+19900^34099	146587	Hans Havermann	11/2020
2355	2^486893-79	146570	Yves Minet	09/2017
2356	36818^9567+9567^36818	146565	Hans Havermann	12/2020
2357	2^486840+1879141	146554	Enzo Doria	08/2016
2358	2^486774-87	146534	Lelio R Paula	12/2017
2359	38655^6176+6176^38655	146530	Hans Havermann	11/2020
2360	8*10^146522-81	146523	Robert Price	02/2021
2361	32820^29059+29059^32820	146485	Hans Havermann	12/2020
2362	37261^8530+8530^37261	146472	Hans Havermann	12/2020
2363	66953^154+154^66953	146462	Hans Havermann	12/2020
2364	96^73877-95^73877	146445	Robert Price	10/2015
2365	8*10^146421+81	146422	Robert Price	08/2019
2366	33153^26090+26090^33153	146420	Hans Havermann	11/2020
2367	(52^85259+1)/53	146304	Paul Bourdelais	09/2017
2368	179^64935+2	146290	Lelio R Paula	10/2017
2369	32595^30758+30758^32595	146285	Hans Havermann	11/2020
2370	34972^15157+15157^34972	146205	Hans Havermann	12/2020
2371	(19*10^146181-49)/3	146182	Robert Price	05/2019
2372	2^485531-114621	146160	Enzo Doria	05/2015
2373	2^485473-933075	146142	Paul Bourdelais	06/2021
2374	(2^485461-9)/4249	146135	Lelio R Paula	09/2015
2375	2^485389+81887	146117	Enzo Doria	08/2016
2376	32554^30773+30773^32554	146108	Hans Havermann	11/2020
2377	(10^146063+71)/9	146063	Serge Batalov	07/2015
2378	2*10^146051-63	146052	Robert Price	01/2022
2379	(2^485119+7)/2745	146032	Lelio R Paula	09/2015
2380	(22*10^146029+257)/9	146030	Robert Price	06/2018
2381	7*10^145982-53	145983	Robert Price	06/2020
2382	2^484743+1872923	145923	Enzo Doria	05/2016
2383	33140^25287+25287^33140	145913	Hans Havermann	01/2021
2384	37875^7112+7112^37875	145895	Hans Havermann	01/2021
2385	32862^27473+27473^32862	145872	Hans Havermann	01/2021
2386	32836^27587+27587^32836	145815	Hans Havermann	01/2021
2387	2^484341+1879157	145802	Enzo Doria	08/2016
2388	2*10^145784-91	145785	Robert Price	04/2020
2389	2^484271-51	145781	Lelio R Paula	11/2017
2390	70^78989-69^78989	145743	Robert Price	01/2014
2391	51^85334+2	145714	Robert Price	07/2015
2392	2^483886-1857101	145665	Enzo Doria	10/2015
2393	33350^23307+23307^33350	145656	Hans Havermann	01/2021
2394	(19*10^145585+131)/3	145586	Robert Price	06/2020
2395	2^483563-1863457	145567	Enzo Doria	12/2015
2396	2^483516-1861409	145553	Enzo Doria	11/2015
2397	2^483384-115019	145514	Enzo Doria	06/2015
2398	(259*10^145501-1)/3	145503	Robert Price	12/2020
2399	(19*10^145499-61)/3	145500	Robert Price	05/2019
2400	2^483302-3221	145489	Lelio R Paula	12/2012
2401	(23*10^145463+61)/3	145464	Robert Price	01/2022
2402	35523^12434+12434^35523	145453	Hans Havermann	01/2021
2403	2^483046+1874029	145412	Enzo Doria	06/2016
2404	2^482991-2789317	145395	Enzo Doria	12/2015
2405	2^482978-2789711	145391	Enzo Doria	12/2015
2406	2^482966-2789711	145388	Enzo Doria	12/2015
2407	2^482817-1858843	145343	Enzo Doria	10/2015
2408	2^482751-113635	145323	Enzo Doria	08/2014
2409	2^482705-459763	145309	Enzo Doria	05/2015
2410	(4^241306+11)/3	145281	Robert Price	03/2017
2411	(238*10^145276-1)/3	145278	Robert Price	04/2020
2412	(19*2^482534+1)/7	145258	Lelio R Paula	09/2015
2413	53^84239-52^84239	145252	Robert Price	01/2013
2414	47952^1067+1067^47952	145207	Hans Havermann	01/2021
2415	(2^482333+5)/9287	145193	Lelio R Paula	09/2015
2416	2^482087+72623	145123	Enzo Doria	04/2016
2417	2^482016-286565	145102	Enzo Doria	07/2015
2418	(19*10^145093+101)/3	145094	Robert Price	09/2019
2419	2^481956+121	145084	Stefano Morozzi	04/2021
2420	2^481840+15	145049	Robert Price	09/2015
2421	2^481801-481801	145037	Henri Lifchitz	03/2005
2422	2^481775+1869083	145029	Enzo Doria	05/2016
2423	29^99167+2	145022	Ray Chandler	08/2011
2424	2^481663+1875653	144996	Enzo Doria	07/2016
2425	8*10^144977+27	144978	Robert Price	09/2021
2426	36486^9379+9379^36486	144929	Hans Havermann	12/2020
2427	35111^13378+13378^35111	144882	Hans Havermann	01/2021
2428	2^481149-459073	144841	Enzo Doria	05/2015
2429	34619^15246+15246^34619	144817	Hans Havermann	01/2021
2430	2^481045-113215	144809	Enzo Doria	07/2014
2431	(64*10^144797+287)/9	144798	Robert Price	04/2019
2432	2^480859-113695	144753	Enzo Doria	09/2014
2433	(106*10^144744+17)/3	144746	Robert Price	04/2021
2434	2^480766-2787191	144725	Enzo Doria	11/2015
2435	(21*27^101106-151)/26	144720	Curtis Bright	05/2015
2436	2^480678+1874239	144699	Enzo Doria	06/2016
2437	(8*10^144683+1)/9	144683	Serge Batalov	05/2010
2438	L(692147)	144651	Henri Lifchitz	10/2008
2439	(76*10^144648+77)/9	144649	Robert Price	10/2019
2440	32672^26721+26721^32672	144635	Hans Havermann	01/2021
2441	2^480417+35	144620	Robert Price	11/2015
2442	2^480296-59879	144584	Enzo Doria	10/2015
2443	33157^22878+22878^33157	144546	Hans Havermann	12/2020
2444	45494^1497+1497^45494	144454	Hans Havermann	12/2020
2445	2^479844+3	144448	Donovan Johnson	06/2006
2446	33442^20803+20803^33442	144407	Hans Havermann	01/2021
2447	(27*2^479642+1)/733	144386	Lelio R Paula	08/2015
2448	44917^1638+1638^44917	144378	Hans Havermann	12/2020
2449	(21*2^479605-1)/11	144376	Lelio R Paula	09/2015
2450	(56*10^144336+583)/9	144337	Robert Price	08/2021
2451	2^479348-2792219	144299	Enzo Doria	02/2016
2452	3^302389-6242	144277	Enzo Doria	05/2014
2453	33778^18641+18641^33778	144248	Hans Havermann	01/2021
2454	2*10^144220-3	144221	Robert Price	07/2015
2455	2^478904-109109	144165	Enzo Doria	04/2014
2456	43698^1987+1987^43698	144125	Hans Havermann	12/2020
2457	36128^9723+9723^36128	144072	Hans Havermann	01/2021
2458	32817^24518+24518^32817	144050	Hans Havermann	12/2020
2459	34295^15828+15828^34295	144020	Hans Havermann	01/2021
2460	2^478337-115333	143994	Enzo Doria	07/2015
2461	(7*2^478330-1)/3	143993	Lelio R Paula	08/2015
2462	88^74047-87^74047	143984	Robert Price	05/2015
2463	33242^21441+21441^33242	143980	Hans Havermann	01/2021
2464	(19*10^143963+467)/9	143964	Robert Price	02/2018
2465	(71^77761+1)/72	143954	Paul Bourdelais	09/2017
2466	33490^19859+19859^33490	143939	Hans Havermann	01/2021
2467	(853*10^143931-7)/9	143933	Robert Price	07/2021
2468	2^478088+27	143919	Robert Price	11/2015
2469	7*10^143857-93	143858	Robert Price	08/2020
2470	3*10^143844+61	143845	Robert Price	09/2020
2471	41358^3005+3005^41358	143837	Hans Havermann	01/2021
2472	2^477475-22071	143735	Enzo Doria	07/2013
2473	2^477417-22123	143717	Enzo Doria	07/2013
2474	2^477359-3577	143700	Yves Minet	03/2017
2475	39435^4402+4402^39435	143688	Hans Havermann	01/2021
2476	(14*10^143662-71)/3	143663	Robert Price	12/2018
2477	6^184614+5	143658	Paul Bourdelais	01/2021
2478	46371^1252+1252^46371	143640	Hans Havermann	12/2020
2479	34975^12748+12748^34975	143588	Hans Havermann	01/2021
2480	2^476936-396765	143573	Enzo Doria	07/2013
2481	2^476888-2791229	143558	Enzo Doria	01/2016
2482	2^476868-1859939	143552	Enzo Doria	11/2015
2483	40807^3294+3294^40807	143548	Hans Havermann	12/2020
2484	755^49878+49878^755	143547	Norbert Schneider	04/2019
2485	(19^112247-4^112247)/15	143536	Robert Price	03/2021
2486	35561^10872+10872^35561	143536	Hans Havermann	06/2021
2487	37637^6492+6492^37637	143487	Hans Havermann	05/2021
2488	61567^214+214^61567	143477	Hans Havermann	05/2021
2489	2^476558-113627	143459	Enzo Doria	08/2014
2490	2^476478-45	143435	Lelio R Paula	11/2017
2491	36380^8757+8757^36380	143423	Hans Havermann	06/2021
2492	32510^25707+25707^32510	143371	Hans Havermann	05/2021
2493	8*10^143361+17	143362	Robert Price	07/2021
2494	(2^475854+9)/73	143245	Lelio R Paula	08/2015
2495	2^475813-113239	143234	Enzo Doria	07/2014
2496	32218^27849+27849^32218	143203	Hans Havermann	04/2021
2497	2^475624-114059	143178	Enzo Doria	11/2014
2498	(11*2^475553-7)/15	143156	Renaud Lifchitz	03/2011
2499	2^475480-2786129	143134	Enzo Doria	10/2015
2500	33912^16621+16621^33912	143131	Hans Havermann	05/2021

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Probable Primes Top 10000

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