(325569283 - 1)/32555
(Another of the Prime Pages' resources)
The Largest Known Primes Icon
  View this page in:   language help
 

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:(325569283 - 1)/32555
Verification status (*):PRP
Official Comment:Generalized repunit
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):CH2 : Wu_T, CHG, Primo, OpenPFGW
Decimal Digits:41887   (log10 is 41886.241324849)
Rank (*):48165 (digit rank is 1)
Entrance Rank (*):34052
Currently on list? (*):short
Submitted:4/22/2011 02:57:41 CDT
Last modified:4/22/2011 03:50:21 CDT
Database id:99795
Status Flags:Verify
Score (*):36.8705 (normalized score 0.0015)

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 6
Subcategory: "Generalized Repunit"
(archival tag id 213219, tag last modified 2013-05-11 04:20:32)

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.

Tom Wu writes (22 Apr 2011): 
CHG proof at 29.24% available from:
http://xenon.stanford.edu/~tjw/pp/32556_9283/index.html
24.78% of the factorization of N-1 comes from the 10378-digit helper prime Phi(4641,32556)/(9283*27847*84419168107), which was proven prime by Primo.

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_id99795
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/pfgw -o -f -q"(32556^9283-1)/32555" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
(32556^9283-1)/32555 1/1 mro=0


trial factoring to 13430677
(32556^9283-1)/32555 has no small factor.
[Elapsed time: 48.852 seconds]
modified2011-12-27 16:48:33
created2011-04-22 03:05:04
id129115

fieldvalue
prime_id99795
person_id9
machineDitto P4 P4
whatprp
notesCommand: /home/ditto/client/pfgw -tc -q"(32556^9283-1)/32555" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing (32556^9283-1)/32555 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 3+sqrt(11)
Calling N-1 BLS with factored part 0.43% and helper 0.02% (1.33% proof)
(32556^9283-1)/32555 is Fermat and Lucas PRP! (885.9712s+0.0017s)
[Elapsed time: 14.77 minutes]
modified2011-05-17 08:18:58
created2011-04-22 03:08:47
id129117

Query times: 0.0005 seconds to select prime, 0.0007 seconds to seek comments.