2389335 + 297837 + 1
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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:2389335 + 297837 + 1
Verification status (*):PRP
Official Comment:
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):x32 : Renze, Broadhurst, OpenPFGW
Decimal Digits:117202   (log10 is 117201.513361836)
Rank (*):36977 (digit rank is 1)
Entrance Rank (*):976
Currently on list? (*):no
Submitted:3/5/2006 19:19:59 CDT
Last modified:3/5/2006 20:53:02 CDT
Removed (*):4/28/2009 15:26:39 CDT
Database id:77228
Status Flags:Verify
Score (*):40.0432 (normalized score 0.0218)

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): 
This prime has been subjected to deep scrutiny, which will, we hope, continue. Please see the comments attached to the proving code, x32, and in the GP source file, T389335.gp, in what we claim to be the proof of http://physics.open.ac.uk/~dbroadhu/cert/T389335.zip

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.
machineLinux P4 2.8GHz
notesCommand: /home/caldwell/client/pfgw -o -f -q"2^389335+2^97837+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
trial factoring to 40384465
2^389335+2^97837+1 has no small factor.
[Elapsed time: 395.039 seconds]
modified2006-03-10 10:52:00
created2006-03-05 19:22:01

machineLinux P4 2.8GHz
notesCommand: /home/caldwell/client/pfgw -t -q"2^389335+2^97837+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 2^389335+2^97837+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(49152,20) to FFT(49152,19)
Reduced from FFT(49152,19) to FFT(49152,18)
Reduced from FFT(49152,18) to FFT(49152,17)
Reduced from FFT(49152,17) to FFT(49152,16)
778680 bit request FFT size=(49152,16)
Calling Brillhart-Lehmer-Selfridge with factored part 25.16%
2^389335+2^97837+1 is PRP! (-1884.3273s+0.0000s)
[Elapsed time: 5401 seconds]
modified2006-03-10 10:52:00
created2006-03-05 19:23:01

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