728192 + 438192

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:728192 + 438192
Verification status (*):PRP
Official Comment (*):ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c60 : Lemsafer, Primo
Decimal Digits:15216   (log10 is 15215.267810765)
Rank (*):70308 (digit rank is 1)
Entrance Rank (*):55911
Currently on list? (*):no
Submitted:10/16/2012 00:05:50 CDT
Last modified:10/16/2012 00:20:30 CDT
Database id:109871
Status Flags:Verify
Score (*):33.7402 (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 67
Subcategory: "ECPP"
(archival tag id 214599, tag last modified 2020-09-27 14:50:25)

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.

Youcef Lemsafer writes (11 Sep 2014):  (report abuse)
Certificate available from here

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.
machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -tc -q"72^8192+43^8192" 2>&1 PFGW Version [GWNUM 26.5] Primality testing 72^8192+43^8192 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Running N+1 test using discriminant 13, base 10+sqrt(13) Calling N+1 BLS with factored part 0.07% and helper 0.03% (0.24% proof) 72^8192+43^8192 is Fermat and Lucas PRP! (89.6369s+0.0007s) [Elapsed time: 90.00 seconds]
modified2020-07-07 17:30:23
created2012-10-16 00:08:01

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -o -f -q"72^8192+43^8192" 2>&1 PFGW Version [GWNUM 26.5] 72^8192+43^8192 1/1 mro=0 trial factoring to 4520445 72^8192+43^8192 has no small factor. [Elapsed time: 5.979 seconds]
modified2020-07-07 17:30:23
created2012-10-16 00:18:02

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.
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