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:
|Description:||2 · 263140989 + 1|
|Verification status (*):||Proven|
|Official Comment:||Divides Phi(263^140989,2)|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||g424 : Broadhurst, NewPGen, OpenPFGW, Proth.exe|
|Decimal Digits:||341188 (log10 is 341187.44205382)|
|Rank (*):||11334 (digit rank is 1)|
|Entrance Rank (*):||358|
|Currently on list? (*):||short|
|Submitted:||3/4/2011 10:04:55 CDT|
|Last modified:||3/4/2011 11:20:22 CDT|
|Score (*):||43.3308 (normalized score 0.5937)|
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
- Divides Phi (archivable *)
- Prime on list: yes, rank 18
Subcategory: "Divides Phi"
(archival tag id 213156, tag last modified 2017-06-27 10:50:20)
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.
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.
|machine||Ditto P4 P4|
|notes||Command: /home/ditto/client/TrialDiv/TrialDiv -q 2 263 140989 1 2>&1|
[Elapsed time: 9.206 seconds]
|machine||Ditto P4 P4|
|notes||Command: /home/ditto/client/pfgw -t -q"2*263^140989+1" 2>&1|
PFGW Version 220.127.116.11BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing 2*263^140989+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
2*263^140989+1 is prime! (3751.2673s+0.0239s)
[Elapsed time: 62.53 minutes]
Query times: 0.0011 seconds to select prime, 0.0008 seconds to seek comments.