1288726869465789 · 234567 - 5

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:1288726869465789 · 234567 - 5
Verification status (*):PRP
Official Comment (*):ECPP, Triplet (1)
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c58 : Kaiser1, NewPGen, OpenPFGW, Primo
Decimal Digits:10421   (log10 is 10420.814021)
Rank (*):76012 (digit rank is 3)
Entrance Rank (*):66586
Currently on list? (*):short
Submitted:4/16/2014 14:45:41 CDT
Last modified:4/16/2014 15:52:10 CDT
Database id:117633
Status Flags:Verify, TrialDiv
Score (*):32.5678 (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.
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 188
Subcategory: "ECPP"
(archival tag id 217672, tag last modified 2020-11-23 19:50:21)
Triplet (archivable class *)
Prime on list: yes, rank 5
Subcategory: "Triplet (1)"
(archival tag id 217673, tag last modified 2019-04-23 14:20:12)

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.

Peter Kaiser writes (11 Sep 2014):  (report abuse)
Certificate can be found here: http://factordb.com/cert.php?id=1100000000601145752

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_id117633
person_id9
machineDitto P4 P4
whatprp
notesCommand: /home/ditto/client/pfgw -tc -q"1288726869465789*2^34567-5" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 1288726869465789*2^34567-5 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 5, base 1+sqrt(5) Calling N+1 BLS with factored part 0.11% and helper 0.05% (0.38% proof) 1288726869465789*2^34567-5 is Fermat and Lucas PRP! (87.1941s+0.0004s) [Elapsed time: 87.00 seconds]
modified2020-07-07 17:30:17
created2014-04-16 15:24:50
id163174

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