103289324131072 + 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:103289324131072 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Proof-code(s): (*):L5044 : Bergelt, GFNSvCUDA, GeneFer, AthGFNSieve, PrimeGrid, LLR
Decimal Digits:1050419   (log10 is 1050418.273989)
Rank (*):640 (digit rank is 1)
Entrance Rank (*):510
Currently on list? (*):short
Submitted:2/7/2022 18:09:09 CDT
Last modified:2/7/2022 21:37:09 CDT
Database id:133398
Status Flags:TrialDiv
Score (*):46.7839 (normalized score 8.7158)

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 144
Subcategory: "Generalized Fermat"
(archival tag id 226788, tag last modified 2022-08-13 21:37:10)

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_id133398
person_id9
machineUsing: Dual Intel Xeon Gold 5222 CPUs 3.8GHz
whatprime
notesCommand: /home/caldwell/clientpool/1/pfgw64 -t -q"103289324^131072+1" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 103289324^131072+1 [N-1, Brillhart-Lehmer-Selfridge] F: 103289324^131072+1 86016/11059377 (trial factor to 415512617) F: 103289324^131072+1 174080/11059377 (trial factor to 415512617) F: 103289324^131072+1 262144/11059377 (trial factor to 415512617) F: 103289324^131072+1 350208/11059377 (trial factor to 415512617) F: 103289324^131072+1 438272/11059377 (trial factor to 415512617) F: 103289324^131072+1 526336/11059377 (trial factor to 415512617) F: 103289324^131072+1 614400/11059377 (trial factor to 415512617) F: 103289324^131072+1 702464/11059377 (trial factor to 415512617) F: 103289324^131072+1 790528/11059377 (trial factor to 415512617) Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 92.49% 103289324^131072+1 is prime! (11446.2757s+0.0081s) [Elapsed time: 3.18 hours]
modified2022-07-11 13:21:45
created2022-02-07 18:16:01
id179120

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.