3 · 1000008458192 + 3 · 1000008454096 + 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:3 · 1000008458192 + 3 · 1000008454096 + 1
Verification status (*):Proven
Official Comment:
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p97 : Andersen, OpenPFGW
Decimal Digits:65537   (log10 is 65536.507184034)
Rank (*):41544 (digit rank is 2)
Entrance Rank (*):4688
Currently on list? (*):no
Submitted:1/7/2006 21:45:26 CDT
Last modified:1/7/2006 23:21:31 CDT
Removed (*):2/14/2006 06:13:49 CDT
Database id:76705
Status Flags:none
Score (*):38.2517 (normalized score 0.0053)

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.

Jens Kruse Andersen writes (11 Sep 2014): 
Cuban prime (difference between successive cubes):
(x+1)3-x3 for x = 1000008454096.

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_id76705
person_id9
machineLinux P4 2.8GHz
whattrial_divided
notesCommand: /home/caldwell/client/pfgw -o -f -q"3*100000845^8192+3*100000845^4096+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
trial factoring to 21696196
3*100000845^8192+3*100000845^4096+1 has no small factor.
[Elapsed time: 145.374 seconds]
modified2006-01-18 12:45:08
created2006-01-07 21:52:00
id82385

fieldvalue
prime_id76705
person_id9
machineLinux P4 2.8GHz
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"3*100000845^8192+3*100000845^4096+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 3*100000845^8192+3*100000845^4096+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(28672,20) to FFT(28672,19)
Reduced from FFT(28672,19) to FFT(28672,18)
Reduced from FFT(28672,18) to FFT(28672,17)
Reduced from FFT(28672,17) to FFT(28672,16)
435424 bit request FFT size=(28672,16)
Running N-1 test using base 7
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(28672,20) to FFT(28672,19)
Reduced from FFT(28672,19) to FFT(28672,18)
Reduced from FFT(28672,18) to FFT(28672,17)
Reduced from FFT(28672,17) to FFT(28672,16)
435424 bit request FFT size=(28672,16)
Running N-1 test using base 13
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(28672,20) to FFT(28672,19)
Reduced from FFT(28672,19) to FFT(28672,18)
Reduced from FFT(28672,18) to FFT(28672,17)
Reduced from FFT(28672,17) to FFT(28672,16)
435424 bit request FFT size=(28672,16)
Running N-1 test using base 17
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(28672,20) to FFT(28672,19)
Reduced from FFT(28672,19) to FFT(28672,18)
Reduced from FFT(28672,18) to FFT(28672,17)
Reduced from FFT(28672,17) to FFT(28672,16)
435424 bit request FFT size=(28672,16)
Calling Brillhart-Lehmer-Selfridge with factored part 40.35%
3*100000845^8192+3*100000845^4096+1 is prime! (-1773.7773s+0.0100s)
[Elapsed time: 5310 seconds]
modified2006-01-18 12:45:08
created2006-01-07 21:53:01
id82386

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