720128166480 · 2621# + 1

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.

This prime's information:

Description:720128166480 · 2621# + 1
Verification status (*):Proven
Official Comment (*):Cunningham chain 2nd kind (16p-15)
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p199 : Broadhurst, NewPGen, OpenPFGW
Decimal Digits:1117   (log10 is 1116.4832685798)
Rank (*):122274 (digit rank is 44)
Entrance Rank (*):81632
Currently on list? (*):no
Submitted:7/28/2010 07:02:45 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:93846
Status Flags:none
Score (*):25.6166 (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.
Cunningham Chains (2nd kind) (archivable class *)
Prime on list: no, rank 6, weight 46.163769636511
Subcategory: "Cunningham chain 2nd kind (16p-15)"
(archival tag id 212877, tag last modified 2023-03-11 15:53:59)

User comments about this prime (disclaimer):

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David Broadhurst writes (11 Sep 2014):  (report abuse)
comment

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_id93846
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/pfgw -t -q"720128166480*2621#+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 720128166480*2621#+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2633 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(448,22) to FFT(448,21) Reduced from FFT(448,21) to FFT(448,20) Reduced from FFT(448,20) to FFT(448,19) Reduced from FFT(448,19) to FFT(448,18) Reduced from FFT(448,18) to FFT(448,17) 7426 bit request FFT size=(448,17) Running N-1 test using base 2659 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(448,22) to FFT(448,21) Reduced from FFT(448,21) to FFT(448,20) Reduced from FFT(448,20) to FFT(448,19) Reduced from FFT(448,19) to FFT(448,18) Reduced from FFT(448,18) to FFT(448,17) 7426 bit request FFT size=(448,17) Calling Brillhart-Lehmer-Selfridge with factored part 33.36% 720128166480*2621#+1 is prime! (1.0900s+0.0000s) [Elapsed time: 1.00 seconds]
modified2020-07-07 22:30:34
created2010-07-28 07:08:26
id117028

fieldvalue
prime_id93846
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 720128166480 2621 # 1 2>&1 [Elapsed time: 155.464 seconds]
modified2020-07-07 22:30:34
created2010-07-28 08:45:30
id117075

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