Phi(3, 10137747) + (137 · 10137748 + 731 · 10129293) · (108454 - 1)/999
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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:Phi(3, 10137747) + (137 · 10137748 + 731 · 10129293) · (108454 - 1)/999
Verification status (*):Proven
Official Comment:Palindrome
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p44 : Broadhurst, OpenPFGW
Decimal Digits:275495   (log10 is 275494)
Rank (*):14971 (digit rank is 1)
Entrance Rank (*):1813
Currently on list? (*):short
Submitted:1/13/2012 16:17:11 CDT
Last modified:1/13/2012 23:50:23 CDT
Database id:103926
Status Flags:none
Score (*):42.6733 (normalized score 0.3376)

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.
Palindrome (archivable *)
Prime on list: yes, rank 8
Subcategory: "Palindrome"
(archival tag id 213781, tag last modified 2014-11-16 14:50:32)

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.

David Broadhurst writes (11 Sep 2014): 
1 (0)_{129292} (137)_{2818} 1 (731)_{2818} (0)_{129292} 1

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_id103926
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/pfgw -o -f -q"Phi(3,10^137747)+(137*10^137748+731*10^129293)*(10^8454-1)/999" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Phi(3,10^137747)....*(10^8454-1)/999 1/1 mro=0


trial factoring to 100402909
Phi(3,10^137747)+(137*10^137748+731*10^129293)*(10^8454-1)/999 has no small factor.
[Elapsed time: 2130.580 seconds]
modified2012-02-19 19:07:48
created2012-01-13 16:18:01
id137441

fieldvalue
prime_id103926
person_id9
machineRedHat Virtual STEM Server
whatprime
notesCommand: /home/caldwell/client/pfgw -tc -q"Phi(3,10^137747)+(137*10^137748+731*10^129293)*(10^8454-1)/999" 2>&1
PFGW Version 3.3.4.20100405.x86_Stable [GWNUM 25.14]
Primality testing Phi(3,10^137747)+(137*10^137748+731*10^129293)*(10^8454-1)/999 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N-1 test using base 13
Running N+1 test using discriminant 19, base 14+sqrt(19)
Calling N-1 BLS with factored part 46.94% and helper 0.00% (140.81% proof)
Phi(3,10^137747)+(137*10^137748+731*10^129293)*(10^8454-1)/999 is prime! (25362.1632s+0.1884s)
[Elapsed time: 7.05 hours]
modified2012-02-19 19:07:48
created2012-01-13 16:29:59
id137442

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