The nth Prime Page
will now find any of the first 2,623,557,157,654,233 primes or
) for x
up to 100,000,000,000,000,000.
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 · 31086112 + 1|
|Verification status (*):||Proven|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||p199 : Broadhurst, NewPGen, OpenPFGW|
|Decimal Digits:||518208 (log10 is 518207.42123608)|
|Rank (*):||1396 (digit rank is 1)|
|Entrance Rank (*):||91|
|Currently on list? (*):||yes|
|Submitted:||2/13/2010 17:00:24 CDT|
|Last modified:||2/14/2010 09:20:21 CDT|
|Score (*):||44.6149 (normalized score 2.4261)|
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 3 1086112 1 2>&1|
[Elapsed time: 9.533 seconds]
|machine||Ditto P4 P4|
|notes||Command: /home/ditto/client/pfgw -t -q"2*3^1086112+1" 2>&1|
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 2*3^1086112+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(229376,19) to FFT(229376,18)
Reduced from FFT(229376,18) to FFT(229376,17)
Reduced from FFT(229376,17) to FFT(229376,16)
3442904 bit request FFT size=(229376,16)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
2*3^1086112+1 is prime! (56982.9327s+0.1376s)
[Elapsed time: 15.83 hours]
Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.