87 · 24297718 + 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:87 · 24297718 + 1
Verification status (*):Proven
Official Comment (*):[none]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L4965 : Propper, LLR
Decimal Digits:1293744   (log10 is 1293743.9704243)
Rank (*):743 (digit rank is 1)
Entrance Rank (*):475
Currently on list? (*):yes
Submitted:7/28/2023 20:52:46 UTC
Last modified:7/28/2023 23:37:18 UTC
Database id:136305
Status Flags:none
Score (*):47.423 (normalized score 9.7547)

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.

Gary B. Gostin writes (29 Jul 2023):  (report abuse)
Divides xGF(4297717,9,7)

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_id136305
person_id9
machineUsing: Digital Ocean Droplet
whatprime
notesCommand: /var/www/clientpool/1/pfgw64 -V -f -t -q"87*2^4297718+1" 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 87*2^4297718+1 [N-1, Brillhart-Lehmer-Selfridge]
trial


Running N-1 test using base 7
Special modular reduction using all-complex FMA3 FFT length 256K, Pass1=128, Pass2=2K, clm=2 on 87*2^4297718+1
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%


87*2^4297718+1 is prime! (9013.8959s+0.0019s)
[Elapsed time: 2.50 hours]
modified2023-07-28 23:23:15
created2023-07-28 20:53:01
id182136

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