8319 · 23327650 + 1
(Another of the Prime Pages' resources)
The Largest Known Primes Icon
  View this page in:   language help
 
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:8319 · 23327650 + 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):L1204 : Brown1, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:1001727   (log10 is 1001726.38514237)
Rank (*):590 (digit rank is 1)
Entrance Rank (*):553
Currently on list? (*):short
Submitted:2/1/2020 04:19:08 CDT
Last modified:2/1/2020 05:50:25 CDT
Database id:130317
Status Flags:TrialDiv
Score (*):46.6383 (normalized score 12.2032)

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_id130317
person_id9
machineUsing: Xeon (pool) 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/clientpool/4/pfgw64 -t -q"8319*2^3327650+1" 2>&1
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing 8319*2^3327650+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%


8319*2^3327650+1 is prime! (4740.0326s+0.0016s)
[Elapsed time: 79.00 minutes]
modified2020-02-01 05:42:02
created2020-02-01 04:23:02
id176003

Query times: 0.0006 seconds to select prime, 0.0004 seconds to seek comments.