2788032524288 + 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:2788032524288 + 1
Verification status (*):Proven
Official Comment:Generalized Fermat
Unofficial Comments:This prime has 2 user comments below.
Proof-code(s): (*):L4584 : Goforth, GFNSvCUDA, GeneFer, AthGFNSieve, PrimeGrid, LLR
Decimal Digits:3379193   (log10 is 3379192.26891521)
Rank (*):30 (digit rank is 1)
Entrance Rank (*):26
Currently on list? (*):short
Submitted:4/18/2019 07:32:29 CDT
Last modified:4/22/2019 13:12:27 CDT
Database id:126397
Status Flags:TrialDiv
Score (*):50.3657 (normalized score 558.9877)

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 220221, tag last modified 2019-07-04 01:20:18)

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 (18 Apr 2019): 
cllr64 -v
LLR Program - Version 3.8.21, using Gwnum Library Version 28.14
cllr64 -d -t4 -oNextFFTifNearLimit=1 -oDiskWriteTime=1 -q"2788032^524288+1"
Base factorized as : 2^6*3*13*1117
Base prime factor(s) taken : 13, 1117
Current FFT beeing too near the limit, next FFT length is forced...
Starting N-1 prime test of 2788032^524288+1
Using generic reduction FMA3 FFT length 1200K, Pass1=320, Pass2=3840, 4 threads, a = 3
2788032^524288+1 may be prime, trying to compute gcd's
3^((N-1)/1117)-1 is coprime to N!
3^((N-1)/13)-1 is coprime to N!
2788032^524288+1 is prime! (3379193 decimal digits) Time : 90210.492 sec.

PrimeGrid writes (26 Apr 2019): 
For more information, 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_id126397
person_id9
machineUsing: Xeon (pool) 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/clientpool/1/pfgw64 -t -q"2788032^524288+1" 2>&1
PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11]
Primality testing 2788032^524288+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Calling Brillhart-Lehmer-Selfridge with factored part 47.29%


2788032^524288+1 is prime! (365965.4203s+0.0385s)
[Elapsed time: 4.24 days]
modified2019-04-22 13:12:27
created2019-04-18 07:33:02
id172080

Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.