21749869755 · 2184515 - 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.

Description:21749869755 · 2184515 - 1
Verification status (*):Proven
Official Comment (*):Sophie Germain (p)
Proof-code(s): (*):L3494 : Batalov, NewPGen, LLR
Decimal Digits:55555   (log10 is 55554.8871066)
Rank (*):53881 (digit rank is 2)
Entrance Rank (*):53847
Currently on list? (*):short
Submitted:9/9/2021 03:41:47 CDT
Last modified:9/9/2021 04:37:34 CDT
Database id:132699
Status Flags:TrialDiv
Score (*):37.7421 (normalized score 0.0012)

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.
Sophie Germain (p) (archivable *)
Prime on list: yes, rank 9
Subcategory: "Sophie Germain (p)"
(archival tag id 226293, tag last modified 2021-09-09 06:37:37)

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_id132699
person_id9
machineUsing: Xeon (pool) 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/clientpool/1/pfgw64 -tp -q"21749869755*2^184515-1" 2>&1
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing 21749869755*2^184515-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling Brillhart-Lehmer-Selfridge with factored part 99.98%


21749869755*2^184515-1 is prime! (54.0896s+0.0002s)
[Elapsed time: 54.00 seconds]
modified2021-09-09 03:46:55
created2021-09-09 03:46:01
id178411

Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.