2733014524288 + 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: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 3374654.0856048)
Rank (*):111 (digit rank is 1)
Entrance Rank (*):26
Currently on list? (*):short
Submitted:3/19/2019 14:59:54 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:126324
Status Flags:none
Score (*):50.3616 (normalized score 212.1178)

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: no, rank 21
Subcategory: "Generalized Fermat"
(archival tag id 220184, tag last modified 2024-04-19 01:37:21)

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):  (report abuse)
./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 (10 Apr 2019):  (report abuse)
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.
machineUsing: Xeon 4c+4c 3.5GHz
notesCommand: /home/caldwell/client/pfgw/pfgw64 -t -q"2733014^524288+1" 2>&1 PFGW Version [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]
modified2020-07-07 22:30:13
created2019-03-19 15:01:01

Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
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