2733014524288 + 1
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GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits)

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:2733014524288 + 1
Verification status (*):Proven
Official Comment:Generalized Fermat
Unofficial Comments:This prime has 2 user comments below.
Proof-code(s): (*):L4929 : Givoni, GFNSvCUDA, GeneFer, AthGFNSieve, PrimeGrid, LLR
Decimal Digits:3374655   (log10 is 3374654.08560479)
Rank (*):27 (digit rank is 1)
Entrance Rank (*):26
Currently on list? (*):short
Submitted:3/19/2019 09:59:54 CDT
Last modified:3/23/2019 12:21:32 CDT
Database id:126324
Status Flags:TrialDiv
Score (*):50.3616 (normalized score 586.6842)

Archival tags:

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 tags.
Generalized Fermat (archivable *)
Prime on list: yes, rank 4
Subcategory: "Generalized Fermat"
(archival tag id 220184, tag last modified 2019-04-18 08:20:02)

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.

PrimeGrid writes (19 Mar 2019): 
./sllr64 -v
LLR Program - Version 3.8.21, using Gwnum Library Version 28.14
./sllr64 -d -t4 -q2733014^524288+1
Base factorized as : 2*1366507
Base prime factor(s) taken : 1366507
Starting N-1 prime test of 2733014^524288+1
Using generic reduction FMA3 FFT length 1152K, Pass1=384, Pass2=3K, 4 threads, a = 3
2733014^524288+1 may be prime, trying to compute gcd's 3^((N-1)/1366507)-1 is coprime to N!
2733014^524288+1 is prime! (3374655 decimal digits) Time : 96196.850 sec.

PrimeGrid writes (9 Apr 2019): 
For more details, please 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.
fieldvalue
prime_id126324
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/client/pfgw/pfgw64 -t -q"2733014^524288+1" 2>&1
PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11]
Primality testing 2733014^524288+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 95.32%


2733014^524288+1 is prime! (354030.6938s+0.1329s)
[Elapsed time: 4.10 days]
modified2019-03-23 12:21:32
created2019-03-19 10:01:01
id172003

Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.