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:||26997933312 · 7001# + 7811555753|
|Verification status (*):||PRP|
|Official Comment:||Consecutive primes arithmetic progression (4,d=30), ECPP|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||x38 : Broadhurst, Primo, OpenPFGW|
|Decimal Digits:||3020 (log10 is 3019.7771563497)|
|Rank (*):||85229 (digit rank is 1)|
|Entrance Rank (*):||77652|
|Currently on list? (*):||short|
|Submitted:||10/22/2013 19:03:08 CDT|
|Last modified:||10/22/2013 19:20:33 CDT|
|Status Flags:||Verify, TrialDiv|
|Score (*):||28.7209 (normalized score 0)|
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
- Consecutive Primes in Arithmetic Progression (archivable class *)
- Prime on list: yes, rank 3
Subcategory: "Consecutive primes in arithmetic progression (4,d=*)"
(archival tag id 217343, tag last modified 2013-10-25 14:50:55)
- Arithmetic Progressions of Primes (archivable class *)
- Prime on list: no, rank 59, weight 37.9387333738008
Subcategory: "Arithmetic progression (4,d=*)"
(archival tag id 217344, tag last modified 2017-08-19 13:50:02)
- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 552
(archival tag id 217345, tag last modified 2017-10-19 05:50:25)
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/pfgw -tc -q"26997933312*7001#+7811555753" 2>&1|
PFGW Version 126.96.36.199BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing 26997933312*7001#+7811555753 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 17, base 10+sqrt(17)
Calling N-1 BLS with factored part 0.29% and helper 0.23% (1.12% proof)
26997933312*7001#+7811555753 is Fermat and Lucas PRP! (2.8031s+0.0006s)
[Elapsed time: 3.00 seconds]
Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.