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:||2618163402417 · 21290001 - 1|
|Verification status (*):||Proven|
|Official Comment:||Sophie Germain (2p+1)|
|Unofficial Comments:||This prime has 2 user comments below.|
|Proof-code(s): (*):||L927 : Brown1, TwinGen, PrimeGrid, LLR|
|Decimal Digits:||388342 (log10 is 388341.41343328)|
|Rank (*):||6847 (digit rank is 1)|
|Entrance Rank (*):||3742|
|Currently on list? (*):||short|
|Submitted:||2/29/2016 08:11:16 CDT|
|Last modified:||2/29/2016 09:24:37 CDT|
|Score (*):||43.7286 (normalized score 0.7583)|
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
- Sophie Germain (2p+1) (archivable *)
- Prime on list: yes, rank 1
Subcategory: "Sophie Germain (2p+1)"
(archival tag id 218235, tag last modified 2016-02-29 09:24:40)
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||Using: Xeon 4c+4c 3.5GHz|
|notes||Command: /home/caldwell/client/llr.pl 2618163402417*2^1290001-1 2>&1|
Starting Lucas Lehmer Riesel prime test of 2618163402417*2^1290001-1
Using zero-padded AVX FFT length 128K, Pass1=128, Pass2=1K
V1 = 3 ; Computing U0...
V1 = 3 ; Computing U0...done.Starting Lucas-Lehmer loop...
2618163402417*2^1290001-1 is prime! (388342 decimal digits) Time : 776.757 sec.
[Elapsed time: 12.95 minutes]
Query times: 0.0005 seconds to select prime, 0.0007 seconds to seek comments.