10590941048576 + 1

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly.  This list is the most important PrimePages database: 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:10590941048576 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Unofficial Comments:This prime has 2 user comments below.
Proof-code(s): (*):L4720 : Gahan, GFNSvCUDA, GeneFer, AthGFNSieve, PrimeGrid, LLR
Decimal Digits:6317602   (log10 is 6317601.7263155)
Rank (*):19 (digit rank is 1)
Entrance Rank (*):13
Currently on list? (*):short
Submitted:11/4/2018 10:01:24 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:125753
Status Flags:none
Score (*):52.2815 (normalized score 1412.6531)

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 3
Subcategory: "Generalized Fermat"
(archival tag id 219944, tag last modified 2023-03-11 15:53:59)

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 (4 Nov 2018):  (report abuse)
>cllr64 -d -t4 -oNextFFTifNearLimit=1 -oDiskWriteTime=1 -q"1059094^1048576+1"
Base factorized as : 2*529547
Base prime factor(s) taken : 529547
Starting N-1 prime test of 1059094^1048576+1
Using generic reduction FMA3 FFT length 2240K, Pass1=448, Pass2=5K, 4 threads, a = 3
1059094^1048576+1 may be prime, trying to compute gcd's
3^((N-1)/529547)-1 is coprime to N!
1059094^1048576+1 is prime! (6317602 decimal digits) Time : 366869.443 sec.
>cllr64 -v
LLR Program - Version 3.8.21, using Gwnum Library Version 28.14

PrimeGrid writes (5 Nov 2018):  (report abuse)
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.
machineUsing: Xeon (pool) 4c+4c 3.5GHz
notesCommand: /home/caldwell/clientpool/1/pfgw64 -t -q"1059094^1048576+1" 2>&1 PFGW Version [GWNUM 27.11] Primality testing 1059094^1048576+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 95.00% 1059094^1048576+1 is prime! (1616899.0806s+0.0845s) [Elapsed time: 18.71 days]
modified2020-07-07 22:30:14
created2018-11-04 10:30:11

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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