178192 · 3712768 + 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:178192 · 3712768 + 1
Verification status (*):Proven
Official Comment:Generalized Cullen
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L2777 : Ritschel, Gcwsieve, TOPS, LLR
Decimal Digits:340083   (log10 is 340082.01337223)
Rank (*):11735 (digit rank is 1)
Entrance Rank (*):766
Currently on list? (*):no
Submitted:12/6/2011 12:30:57 CDT
Last modified:12/6/2011 15:50:23 CDT
Database id:103488
Status Flags:none
Score (*):43.3208 (normalized score 0.5575)

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 22
Subcategory: "Generalized Cullen"
(archival tag id 213747, tag last modified 2018-03-13 00:20:23)

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.

Thomas Ritschel writes (11 Sep 2014): 

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.
machineDitto P4 P4
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 178192 3 712768 1 2>&1
[Elapsed time: 9.611 seconds]
modified2011-12-27 16:48:25
created2011-12-06 12:35:01

machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -t -q"178192*3^712768+1" 2>&1
PFGW Version [GWNUM 26.5]
Primality testing 178192*3^712768+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N-1 test using base 19
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
178192*3^712768+1 is prime! (9996.6953s+0.0238s)
[Elapsed time: 2.78 hours]
modified2011-12-27 16:48:25
created2011-12-06 12:38:01

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.