1669 · 2531990 + 1
(Another of the Prime Pages' resources)
The Largest Known Primes Icon
  View this page in:   language help
GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits)

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:1669 · 2531990 + 1
Verification status (*):Proven
Official Comment:
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L1135 : Frith, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:160149   (log10 is 160148.16984962)
Rank (*):32137 (digit rank is 1)
Entrance Rank (*):4593
Currently on list? (*):no
Submitted:7/27/2010 14:54:45 CDT
Last modified:7/27/2010 17:13:20 CDT
Removed (*):8/17/2010 10:44:44 CDT
Database id:93776
Status Flags:none
Score (*):41.0045 (normalized score 0.0475)

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.

Michael Frith writes (11 Sep 2014): 
Divides xGF(531989,10,9)

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.
machineDitto P4 P4
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 1669 2 531990 1 2>&1
[Elapsed time: 9.482 seconds]
modified2011-12-27 16:48:38
created2010-07-27 15:05:01

machineWinXP Dual Core 2.6GHz Laptop
notesCommand: pfgw.exe -n -t -q"1669*2^531990+1" 2>&1
PFGW Version 20030811.Win_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Running N-1 test using base 3
N-1: 1669*2^5Primality testing 1669*2^531990+1 [N-1, Brillhart-Lehmer-Selfridge]
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
1669*2^531990+1 is prime! (952.0262s+0.0052s)
31990+1[Elapsed time: 952 seconds]
modified2011-12-27 16:48:38
created2010-07-27 16:08:29

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.