121152729080 · 7019#/1729 + 19

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.

Description:121152729080 · 7019#/1729 + 19
Verification status (*):PRP
Official Comment (*):Consecutive primes arithmetic progression (4,d=6), ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c92 : Lamprecht, Luhn, Primo
Decimal Digits:3025   (log10 is 3024.8835431189)
Rank (*):91974 (digit rank is 1)
Entrance Rank (*):88018
Currently on list? (*):short
Submitted:10/14/2019 01:27:53 CDT
Last modified:10/14/2019 10:50:02 CDT
Database id:130027
Status Flags:Verify, TrialDiv
Score (*):28.7262 (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 3
Subcategory: "Consecutive primes in arithmetic progression (4,d=*)"
(archival tag id 223574, tag last modified 2021-11-02 18:37:44)
Arithmetic Progressions of Primes (archivable class *)
Prime on list: no, rank 188, weight 37.945682543797
Subcategory: "Arithmetic progression (4,d=*)"
(archival tag id 223575, tag last modified 2022-06-09 19:37:16)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 656
Subcategory: "ECPP"
(archival tag id 223576, tag last modified 2022-06-26 16:37:20)

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.

Norman Luhn writes (14 Oct 2019):  (report abuse)
Certificate

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_id130027
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprp
notesCommand: /home/caldwell/client/pfgw/pfgw64 -tc -q"121152729080*7019#/1729+19" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 121152729080*7019#/1729+19 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N-1 test using base 3 Running N+1 test using discriminant 19, base 129+sqrt(19) Calling N+1 BLS with factored part 0.04% and helper 0.02% (0.15% proof) 121152729080*7019#/1729+19 is Fermat and Lucas PRP! (0.6091s+0.0004s) [Elapsed time: 1.00 seconds]
modified2020-07-07 17:30:10
created2019-10-14 01:31:03
id175714

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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