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 · 10748043 + 1|
|Verification status (*):||Proven|
|Official Comment:||Divides Phi(107^48042,2)|
|Proof-code(s): (*):||gb1 : Buechel, Keller, PRP, Proth.exe|
|Decimal Digits:||97498 (log10 is 97497.9858613262)|
|Rank (*):||41456 (digit rank is 1)|
|Entrance Rank (*):||550|
|Currently on list? (*):||no|
|Submitted:||4/15/2004 16:30:31 CDT|
|Last modified:||4/15/2004 16:30:31 CDT|
|Score (*):||39.4762 (normalized score 0.0142)|
There are certain forms classed as
archivable: these prime may (at times)
remain on this list even if they do not make
the Top 5000 proper. Such primes are tracked with archival
- Divides Phi (archivable *)
- Prime on list: no, rank 65
Subcategory: "Divides Phi"
(archival tag id 188343, tag last modified 2015-03-04 06:50:26)
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||Linux P4 2.8GHz|
|notes||Command: /home/caldwell/client/pfgw -f -t -q"2*107^48043+1" 2>&1|
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 2*107^48043+1 [N-1, Brillhart-Lehmer-Selfridge]
trial factoring to 33177831
Running N-1 test using base 5
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(40960,20) to FFT(40960,19)
Reduced from FFT(40960,19) to FFT(40960,18)
Reduced from FFT(40960,18) to FFT(40960,17)
Reduced from FFT(40960,17) to FFT(40960,16)
647772 bit request FFT size=(40960,16)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
2*107^48043+1 is prime! (3400.0280s+0.0474s)
Query times: 0.0005 seconds to select prime, 0.0006 seconds to seek comments.