3534827 - 3267414 + 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:3534827 - 3267414 + 1
Verification status (*):Proven
Official Comment (*):Generalized unique
Unofficial Comments:This prime has 2 user comments below.
Proof-code(s): (*):x28 : Iskra
Decimal Digits:255178   (log10 is 255177.32929795)
Rank (*):29471 (digit rank is 1)
Entrance Rank (*):128
Currently on list? (*):no
Submitted:11/28/2005 13:28:52 UTC
Last modified:3/31/2024 19:30:52 UTC
Database id:76301
Status Flags:none
Score (*):42.4377 (normalized score 0.0255)

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 Unique (archivable *)
Prime on list: no, rank 168
Subcategory: "Generalized Unique"
(archival tag id 224225, tag last modified 2026-01-09 22:37:30)

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.

Boris Iskra writes (11 Sep 2014):  (report abuse)
Eisenstein Mersenne Norm

Chris Caldwell writes (11 Sep 2014):  (report abuse)
This prime may also be written: 3^534827-3^267414+1

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_id76301
person_id9
machineLinux P4 2.8GHz
whatprime
notesCommand: /home/caldwell/client/pfgw -f -t -q"3^534827-3^267414+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 3^534827-3^267414+1 [N-1, Brillhart-Lehmer-Selfridge] trial factoring to 92543938 Running N-1 test using base 2 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(114688,20) to FFT(114688,19) Reduced from FFT(114688,19) to FFT(114688,18) Reduced from FFT(114688,18) to FFT(114688,17) Reduced from FFT(114688,17) to FFT(114688,16) 1695370 bit request FFT size=(114688,16) Calling Brillhart-Lehmer-Selfridge with factored part 50.00% 3^534827-3^267414+1 is prime! (19211.2786s+0.2041s) [Elapsed time: 19212 seconds]
modified2020-07-07 22:30:43
created2005-11-28 13:53:00
id81506

Query times: 0.0011 seconds to select prime, 0.0018 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.