2746496109133 · 3001# + 27011

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:2746496109133 · 3001# + 27011
Verification status (*):PRP
Official Comment (*):Consecutive primes arithmetic progression (5,d=30), ECPP
Proof-code(s): (*):c97 : Lamprecht, Luhn, APSieve, OpenPFGW, Primo
Decimal Digits:1290   (log10 is 1289.4234696606)
Rank (*):113724 (digit rank is 8)
Entrance Rank (*):108745
Currently on list? (*):short
Submitted:10/9/2021 15:27:14 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:132815
Status Flags:Verify
Score (*):26.0668 (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: yes, rank 4
Subcategory: "Consecutive primes in arithmetic progression (5,d=*)"
(archival tag id 226338, tag last modified 2023-03-11 15:53:59)
Arithmetic Progressions of Primes (archivable class *)
Prime on list: no, rank 694, weight 38.388886771661
Subcategory: "Arithmetic progression (5,d=*)"
(archival tag id 226339, tag last modified 2023-03-11 15:53:59)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 1034
Subcategory: "ECPP"
(archival tag id 226340, 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_id132815
person_id9
machineUsing: Xeon (pool) 4c+4c 3.5GHz
whatprp
notesCommand: /home/caldwell/clientpool/1/pfgw64 -tc -q"2746496109133*3001#+27011" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 2746496109133*3001#+27011 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 7, base 2+sqrt(7) Calling N-1 BLS with factored part 0.68% and helper 0.30% (2.36% proof) 2746496109133*3001#+27011 is Fermat and Lucas PRP! (0.0993s+0.0002s) [Elapsed time: 0.00 seconds]
modified2022-07-11 18:21:46
created2021-10-09 15:36:03
id178528

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