27 · 25213635 + 1
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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:

field (help)value
Description:27 · 25213635 + 1
Verification status (*):Proven
Official Comment:
Unofficial Comments:This prime has 3 user comments below.
Proof-code(s): (*):L3760 : Okazaki, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:1569462   (log10 is 1569461.95280734)
Rank (*):100 (digit rank is 1)
Entrance Rank (*):38
Currently on list? (*):short
Submitted:3/12/2015 14:14:22 CDT
Last modified:3/15/2015 06:30:43 CDT
Database id:119539
Status Flags:TrialDiv
Score (*):48.0155 (normalized score 60.5367)

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.

Serge Batalov writes (15 Mar 2015): 
The correct factor data is:
27*2^5213635+1 is a Factor of GF(5213633,8)/F5213633 co-factor, and of xGF(5213634,7,6)

Hiroyuki Okazaki writes (15 Mar 2015): 
Divides xGF(5213634,7,6)!!!! xGF(5213603,0,8)!!!!

PrimeGrid writes (27 Nov 2016): 
For more details, see the Official Announcement.

Verification data:

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.
machineUsing: Xeon 4c+4c 3.5GHz
notesCommand: /home/caldwell/client/pfgw/pfgw64 -t -q"27*2^5213635+1" 2>&1
PFGW Version [GWNUM 27.11]
Primality testing 27*2^5213635+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%

27*2^5213635+1 is prime! (9569.5310s+0.0016s)
[Elapsed time: 2.66 hours]
modified2015-04-20 07:32:09
created2015-03-12 14:21:01

Query times: 0.0004 seconds to select prime, 0.0011 seconds to seek comments.