(154912973 - 1)/1548
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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:(154912973 - 1)/1548
Verification status (*):PRP
Official Comment:Generalized repunit
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p170 : Wu_T, Primo, OpenPFGW
Decimal Digits:41382   (log10 is 41381.347271634)
Rank (*):49470 (digit rank is 1)
Entrance Rank (*):31493
Currently on list? (*):short
Submitted:12/12/2010 12:55:04 CDT
Last modified:12/12/2010 13:50:21 CDT
Database id:96872
Status Flags:Verify
Score (*):36.8331 (normalized score 0.0012)

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 Repunit (archivable *)
Prime on list: yes, rank 8
Subcategory: "Generalized Repunit"
(archival tag id 213016, tag last modified 2014-10-17 06:20:33)

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.

Tom Wu writes (11 Sep 2014): 
The BLS primality proof for this number can be found at:
http://xenon.stanford.edu/~tjw/pp/1549_12973/index.html
This primality proof relies on the gigantic 12903-digit helper prime Phi(12972,1549)/(12973*2568457) which was proven prime by Primo 3.0.8 and has its own database entry.

For more information, see the announcement in the primeform group.

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_id96872
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/pfgw -o -f -q"(1549^12973-1)/1548" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
trial factoring to 13257035
(1549^12973-1)/1548 has no small factor.
[Elapsed time: 44.319 seconds]
modified2011-12-27 16:48:35
created2010-12-12 13:05:06
id123133

fieldvalue
prime_id96872
person_id9
machineDitto P4 P4
whatprp
notesCommand: /home/ditto/client/pfgw -tc -q"(1549^12973-1)/1548" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing (1549^12973-1)/1548 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(16384,20) to FFT(16384,19)
Reduced from FFT(16384,19) to FFT(16384,18)
Reduced from FFT(16384,18) to FFT(16384,17)
274940 bit request FFT size=(16384,17)
Running N+1 test using discriminant 17, base 3+sqrt(17)
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(16384,20) to FFT(16384,19)
Reduced from FFT(16384,19) to FFT(16384,18)
Reduced from FFT(16384,18) to FFT(16384,17)
274948 bit request FFT size=(16384,17)
Calling N-1 BLS with factored part 0.25% and helper 0.02% (0.79% proof)
(1549^12973-1)/1548 is Fermat and Lucas PRP! (764.8700s+0.0100s)
[Elapsed time: 12.80 minutes]
modified2011-01-18 10:15:30
created2010-12-12 13:09:19
id123135

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.