275690740456281 · 233501 + 5
(Another of the Prime Pages' resources)
The Largest Known Primes Icon
  View this page in:   language help

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: 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:

field (help)value
Description:275690740456281 · 233501 + 5
Verification status (*):PRP
Official Comment:Triplet (3)
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c88 : Kaiser1, PolySieve, Primo
Decimal Digits:10100   (log10 is 10099.246306919)
Rank (*):73556 (digit rank is 4)
Entrance Rank (*):73543
Currently on list? (*):no
Submitted:7/11/2018 11:24:48 CDT
Last modified:7/11/2018 11:50:22 CDT
Database id:125449
Status Flags:Verify, TrialDiv
Score (*):32.4707 (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.
Triplet (archivable class *)
Prime on list: no, rank 6
Subcategory: "Triplet (3)"
(archival tag id 219818, tag last modified 2018-07-16 09:50:23)

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 Jul 2018): 
Certificate: http://www.factordb.com/index.php?id=1100000001156179203

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.
machineUsing: Xeon 4c+4c 3.5GHz
notesCommand: /home/caldwell/client/pfgw/pfgw64 -tc -q"275690740456281*2^33501+5" 2>&1
PFGW Version [GWNUM 27.11]
Primality testing 275690740456281*2^33501+5 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N+1 test using discriminant 5, base 4+sqrt(5)
Calling N+1 BLS with factored part 0.06% and helper 0.04% (0.23% proof)

275690740456281*2^33501+5 is Fermat and Lucas PRP! (8.3019s+0.0003s)
[Elapsed time: 9.00 seconds]
modified2018-07-11 11:31:10
created2018-07-11 11:31:01

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