7 · 218233956 + 1

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Description:7 · 218233956 + 1
Verification status (*):Proven
Official Comment (*):Divides Fermat F(18233954)
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L4965 : Propper, LLR
Decimal Digits:5488969   (log10 is 5488968.5407153)
Rank (*):17 (digit rank is 1)
Entrance Rank (*):17
Currently on list? (*):short
Submitted:10/1/2020 22:34:30 CDT
Last modified:10/6/2020 12:50:03 CDT
Database id:131289
Status Flags:TrialDiv
Score (*):51.8512 (normalized score 1628.857)

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.
Fermat Divisors (archivable *)
Prime on list: yes, rank 1, weight 53.797127776074
Subcategory: "Divides Fermat"
(archival tag id 225677, tag last modified 2020-10-06 12:50:08)

User comments about this prime (disclaimer):

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Lleyton Joseph writes (29 Oct 2020):  (report abuse)

7*2^18233956+1 divides GF(18233952,7), xGF(18233954,7,2), xGF(18233953,7,4), xGF(18233954,8,7), xGF(18233955,9,5), xGF(18233955,10,9), xGF(18233955,11,5), xGF(18233954,11,9), and xGF(18233955,11,10). These factors were first announced by Gary on the Mersenne Forums, at https://www.mersenneforum.org/showthread.php?p=559634#post559634.

I have confirmed them myself in a separate run.

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 (pool) 4c+4c 3.5GHz
notesCommand: /home/caldwell/clientpool/1/pfgw64 -t -q"7*2^18233956+1" 2>&1 PFGW Version [GWNUM 29.8] Primality testing 7*2^18233956+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 7*2^18233956+1 is prime! (118541.5002s+0.0077s) [Elapsed time: 32.93 hours]
modified2021-04-20 17:39:26
created2020-10-01 22:36:01

Query times: 0.0006 seconds to select prime, 0.0009 seconds to seek comments.
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