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:||2209 · 2524186 + 1|
|Verification status (*):||Proven|
|Official Comment:||Generalized Fermat|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||L1180 : Morris1, PSieve, Srsieve, PrimeGrid, LLR|
|Decimal Digits:||157800 (log10 is 157799.05350284)|
|Rank (*):||31705 (digit rank is 1)|
|Entrance Rank (*):||4737|
|Currently on list? (*):||no|
|Submitted:||7/9/2010 14:36:48 CDT|
|Last modified:||7/10/2010 08:20:03 CDT|
|Removed (*):||7/27/2010 14:43:34 CDT|
|Score (*):||40.959 (normalized score 0.0516)|
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
- Generalized Fermat (archivable *)
- Prime on list: no, rank 907
Subcategory: "Generalized Fermat"
(archival tag id 210725, tag last modified 2019-01-15 02:20:26)
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||RedHat P4 P4|
|notes||Command: /home/caldwell/client/TrialDiv/TrialDiv -q 2209 2 524186 1 2>&1|
[Elapsed time: 9.714 seconds]
|machine||RedHat P4 P4|
|notes||Command: /home/caldwell/client/pfgw -t -q"2209*2^524186+1" 2>&1|
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 2209*2^524186+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(65536,20) to FFT(65536,19)
Reduced from FFT(65536,19) to FFT(65536,18)
Reduced from FFT(65536,18) to FFT(65536,17)
Reduced from FFT(65536,17) to FFT(65536,16)
1048404 bit request FFT size=(65536,16)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
2209*2^524186+1 is prime! (1424.9400s+0.0000s)
[Elapsed time: 23.92 minutes]
Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.