77 · 25422903 + 1

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly.  This list is the most important PrimePages database: 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:

Description:77 · 25422903 + 1
Verification status (*):Proven
Official Comment (*):Divides GF(5422902,12)
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):A2 : Propper, Srsieve, PRST
Decimal Digits:1632459   (log10 is 1632458.3530669)
Rank (*):460 (digit rank is 1)
Entrance Rank (*):460
Currently on list? (*):short
Submitted:7/6/2024 19:46:35 UTC
Last modified:7/9/2024 23:37:22 UTC
Database id:138278
Status Flags:none
Score (*):48.1362 (normalized score 22.3004)

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 Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 8, weight 52.480011457625
Subcategory: "Divides GF(*,12)"
(archival tag id 229588, tag last modified 2024-07-09 23:37:26)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

Gary B. Gostin writes (9 Jul 2024):  (report abuse)
Divides GF(5422902,12) and xGF(5422900,9,8)

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.
fieldvalue
prime_id138278
person_id9
machineUsing: Digital Ocean Droplet
whatprime
notesCommand: /var/www/clientpool/1/pfgw64 -V -f -t -q"77*2^5422903+1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 77*2^5422903+1 [N-1, Brillhart-Lehmer-Selfridge]
trial


Running N-1 test using base 3
Special modular reduction using all-complex AVX-512 FFT length 336K, Pass1=896, Pass2=384, clm=1 on 77*2^5422903+1
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%


77*2^5422903+1 is prime! (9424.6788s+0.0027s)
[Elapsed time: 2.62 hours]
modified2024-07-07 03:21:23
created2024-07-07 00:44:16
id184120

Query times: 0.0003 seconds to select prime, 0.0003 seconds to seek comments.
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