26997933312 · 7001# + 7811555753

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:26997933312 · 7001# + 7811555753
Verification status (*):PRP
Official Comment (*):Consecutive primes arithmetic progression (4,d=30), ECPP
Proof-code(s): (*):x38 : Broadhurst, OpenPFGW, Primo
Decimal Digits:3020   (log10 is 3019.7771563497)
Rank (*):95734 (digit rank is 1)
Entrance Rank (*):77652
Currently on list? (*):no
Submitted:10/23/2013 00:03:08 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:116065
Status Flags:Verify
Score (*):28.7209 (normalized score 0)

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.
Consecutive Primes in Arithmetic Progression (archivable class *)
Prime on list: no, rank 7
Subcategory: "Consecutive primes in arithmetic progression (4,d=*)"
(archival tag id 217343, tag last modified 2023-07-02 12:37:20)
Arithmetic Progressions of Primes (archivable class *)
Prime on list: no, rank 193, weight 37.938733373801
Subcategory: "Arithmetic progression (4,d=*)"
(archival tag id 217344, tag last modified 2023-07-02 12:37:19)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 743
Subcategory: "ECPP"
(archival tag id 217345, tag last modified 2024-03-24 06:37:14)

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_id116065
person_id9
machineDitto P4 P4
whatprp
notesCommand: /home/ditto/client/pfgw -tc -q"26997933312*7001#+7811555753" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 26997933312*7001#+7811555753 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N+1 test using discriminant 17, base 10+sqrt(17) Calling N-1 BLS with factored part 0.29% and helper 0.23% (1.12% proof) 26997933312*7001#+7811555753 is Fermat and Lucas PRP! (2.8031s+0.0006s) [Elapsed time: 3.00 seconds]
modified2020-07-07 22:30:18
created2013-10-23 00:08:10
id161569

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