174885 · 98174885 + 1
(Another of the Prime Pages' resources)
The Largest Known Primes Icon
  View this page in:   language help

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:174885 · 98174885 + 1
Verification status (*):Proven
Official Comment:Generalized Cullen
Proof-code(s): (*):g157 : Loeh, Proth.exe
Decimal Digits:348241   (log10 is 348240.81500004)
Rank (*):11254 (digit rank is 1)
Entrance Rank (*):1212
Currently on list? (*):no
Submitted:8/26/2012 06:48:07 CDT
Last modified:8/26/2012 08:20:55 CDT
Database id:108952
Status Flags:none
Score (*):43.3937 (normalized score 0.6055)

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 Cullen (archivable *)
Prime on list: no, rank 21
Subcategory: "Generalized Cullen"
(archival tag id 214464, tag last modified 2018-03-13 00:20:23)

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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 174885 98 174885 1 2>&1
[Elapsed time: 9.251 seconds]
modified2012-09-15 19:04:20
created2012-08-26 06:52:02

machineRedHat Virtual STEM Server
notesCommand: /home/caldwell/client/pfgw -t -q"174885*98^174885+1" 2>&1
PFGW Version [GWNUM 25.14]
Primality testing 174885*98^174885+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 13
Calling Brillhart-Lehmer-Selfridge with factored part 84.88%
174885*98^174885+1 is prime! (4335.9648s+0.0677s)
[Elapsed time: 72.28 minutes]
modified2012-09-15 19:04:20
created2012-08-26 06:52:38

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