
At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes. This prime's information:
field (help)  value 
Description:  75707404^{65536} + 1 
Verification status (*):  Proven 
Official Comment:  Generalized Fermat 
Proofcode(s): (*):  L4530 : Reynolds1, GFNSvCUDA, GeneFer, AthGFNSieve, PrimeGrid, LLR 
Decimal Digits:  516368 (log_{10} is 516367.211201905) 
Rank (*):  2912 (digit rank is 1) 
Entrance Rank (*):  2550 
Currently on list? (*):  yes 
Submitted:  2/4/2020 13:42:25 CDT 
Last modified:  2/4/2020 16:50:13 CDT 
Database id:  130371 
Status Flags:  TrialDiv 
Score (*):  44.604 (normalized score 1.5252) 

Archival tags:
There are certain forms classed as
archivable: these prime may (at times)
remain on this list even if they do not make
the Top 5000 proper. Such primes are tracked with archival
tags.
 Generalized Fermat (archivable *)
 Prime on list: no, rank 557
Subcategory: "Generalized Fermat"
(archival tag id 223721, tag last modified 20200528 04:50:22)
Verification data:
The Top 5000 Primes is a list for proven primes only. In order to maintain the
integrity of this list, we seek to verify the primality of all submissions.
We are currently unable to check all proofs (ECPP, KP, ...), but we will at least trial
divide and PRP
check every entry before it is included in the list.
field  value 
prime_id  130371 
person_id  9 
machine  Using: Xeon 4c+4c 3.5GHz 
what  prime 
notes  Command: /home/caldwell/client/pfgw/pfgw64 t q"75707404^65536+1" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 75707404^65536+1 [N1, BrillhartLehmerSelfridge] F: 75707404^65536+1 65536/5427909 (trial factor to 195731976) F: 75707404^65536+1 133120/5427909 (trial factor to 195731976) F: 75707404^65536+1 202752/5427909 (trial factor to 195731976) F: 75707404^65536+1 274432/5427909 (trial factor to 195731976) F: 75707404^65536+1 346112/5427909 (trial factor to 195731976) F: 75707404^65536+1 417792/5427909 (trial factor to 195731976) F: 75707404^65536+1 489472/5427909 (trial factor to 195731976) F: 75707404^65536+1 561152/5427909 (trial factor to 195731976)
Running N1 test using base 3 Calling BrillhartLehmerSelfridge with factored part 92.36%
75707404^65536+1 is prime! (9506.9193s+0.0091s) [Elapsed time: 2.64 hours]

modified  20200204 16:29:29 
created  20200204 13:51:01 
id  176058 

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.
