(3412011311 - 1)/34119

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:(3412011311 - 1)/34119
Verification status (*):PRP
Official Comment (*):Generalized repunit
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):CH2 : Wu_T, OpenPFGW, Primo, CHG
Decimal Digits:51269   (log10 is 51268.332057152)
Rank (*):61017 (digit rank is 2)
Entrance Rank (*):32834
Currently on list? (*):short
Submitted:9/1/2011 19:53:48 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:101439
Status Flags:Verify
Score (*):37.4943 (normalized score 0.0005)

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 Repunit (archivable *)
Prime on list: yes, rank 17
Subcategory: "Generalized Repunit"
(archival tag id 213407, tag last modified 2024-02-26 02:37:04)

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.

Tom Wu writes (11 Sep 2014):  (report abuse)
CHG proof at 29.6% available at:
This proof relies on an ECPP certificate of a 12155-digit helper prime that divides N-1.

At time of posting, this prime set records for both the largest GRU (generalized repunit) prime and the largest NTG (non-trivial gigantic) prime. For more details, see the primenumbers discussion thread.

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/pfgw -o -f -q"(34120^11311-1)/34119" 2>&1 PFGW Version [GWNUM 26.5] (34120^11311-1)/34119 1/1 mro=0 trial factoring to 16679901 (34120^11311-1)/34119 has no small factor. [Elapsed time: 68.275 seconds]
modified2020-07-07 22:30:31
created2011-09-01 20:05:05

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -tc -q"(34120^11311-1)/34119" 2>&1 PFGW Version [GWNUM 26.5] Primality testing (34120^11311-1)/34119 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 13 Running N+1 test using discriminant 37, base 15+sqrt(37) Calling N-1 BLS with factored part 0.36% and helper 0.01% (1.08% proof) (34120^11311-1)/34119 is Fermat and Lucas PRP! (1436.7923s+0.0283s) [Elapsed time: 23.95 minutes]
modified2020-07-07 22:30:31
created2011-09-01 20:23:01

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