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:
|Verification status (*):||PRP|
|Official Comment:||Euler irregular, ECPP|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||c8 : Water, Broadhurst, Primo|
|Decimal Digits:||9516 (log10 is 9515.9812816038)|
|Rank (*):||74153 (digit rank is 1)|
|Entrance Rank (*):||67840|
|Currently on list? (*):||short|
|Submitted:||6/21/2014 13:10:51 CDT|
|Last modified:||6/21/2014 13:51:39 CDT|
|Blob database id:||327|
|Status Flags:||Verify, TrialDiv|
|Score (*):||32.2863 (normalized score 0)|
(from blob table id=327)
[This prime has a pre-calculated decimal expansion (linked blob)]
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
- Euler Irregular primes (archivable *)
- Prime on list: yes, rank 2
Subcategory: "Euler Irregular primes"
(archival tag id 217725, tag last modified 2018-03-14 05:50:22)
- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 181
(archival tag id 217726, tag last modified 2018-06-17 18:50:23)
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||WinXP Dual Core 2.6GHz 64-bit Laptop|
|notes||Command: pfgw64.exe -tc p_118067.txt 2>&1|
PFGW Version 126.96.36.199BIT.20130210.Win_Dev [GWNUM 27.8]
Primality testing 9578149333...8683176273 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 10+sqrt(13)
Calling N-1 BLS with factored part 0.11% and helper 0.03% (0.35% proof)
9578149333...8683176273 is Fermat and Lucas PRP! (26.6857s+0.1862s)
[Elapsed time: 27 seconds]
Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.