163 · 21374474 + 1
(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:163 · 21374474 + 1
Verification status (*):Proven
Official Comment:
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L2933 : Winkler1, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:413761   (log10 is 413760.11444786)
Rank (*):3831 (digit rank is 1)
Entrance Rank (*):393
Currently on list? (*):yes
Submitted:1/27/2012 10:59:14 CDT
Last modified:1/27/2012 13:57:39 CDT
Database id:104075
Status Flags:none
Score (*):43.9234 (normalized score 1.2007)

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.

Timothy Winkler writes (11 Sep 2014): 
Divides xGF(1374472,7,5)

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_id104075
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 163 2 1374474 1 2>&1
[Elapsed time: 10.278 seconds]
modified2012-02-19 19:07:47
created2012-01-27 11:05:01
id137739

fieldvalue
prime_id104075
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/pfgw -t -q"163*2^1374474+1" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing 163*2^1374474+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
163*2^1374474+1 is prime! (4414.1769s+0.0015s)
[Elapsed time: 73.57 minutes]
modified2012-02-19 19:07:47
created2012-01-27 11:41:42
id137741

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