# 15 · 21276177 + 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.

Description: 15 · 21276177 + 1 Proven Divides GF(1276174,3), GF(1276174,10) This prime has 1 user comment below. g279 : Cooper, NewPGen, PRP, Proth.exe 384169   (log10 is 384168.73286773) 14255 (digit rank is 1) 71 short 2/15/2006 03:28:29 CDT 2/18/2006 21:50:20 CDT 77070 none 43.6954 (normalized score 0.4071)

#### 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.
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 15, weight 46.403534196924
Subcategory: "Divides GF(*,10)"
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: no, rank 23, weight 46.403534196924
Subcategory: "Divides GF(*,3)"

Curtis Cooper writes (11 Sep 2014):  (report abuse)
 15*2^1276177+1 is a Factor of GF(1276174,3) 15*2^1276177+1 is a Factor of xGF(1276175,5,4) 15*2^1276177+1 is a Factor of GF(1276175,8) 15*2^1276177+1 is a Factor of xGF(1276175,8,3) 15*2^1276177+1 is a Factor of xGF(1276175,9,8) 15*2^1276177+1 is a Factor of GF(1276174,10) 15*2^1276177+1 is a Factor of xGF(1276173,10,3) 15*2^1276177+1 is a Factor of xGF(1276174,10,9) 15*2^1276177+1 is a Factor of xGF(1276175,12,5)

#### 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_id77070
person_id9
machineLinux P4 2.8GHz
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 15 2 1276177 1 2>&1 [Elapsed time: 13.880 seconds]
modified2020-07-07 17:30:42
created2006-02-15 03:52:00
id83132

fieldvalue
prime_id77070
person_id9
machineLinux P4 2.8GHz
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"15*2^1276177+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 15*2^1276177+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(163840,20) to FFT(163840,19) Reduced from FFT(163840,19) to FFT(163840,18) Reduced from FFT(163840,18) to FFT(163840,17) Reduced from FFT(163840,17) to FFT(163840,16) 2552370 bit request FFT size=(163840,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 15*2^1276177+1 is prime! (27312.9832s+0.0352s) [Elapsed time: 27313 seconds]
modified2020-07-07 17:30:42
created2006-02-15 03:53:01
id83133

Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.