320607 · 21800434 - 1
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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:320607 · 21800434 - 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):g337 : Hsieh, NewPGen, PRP, Proth.exe
Decimal Digits:541991   (log10 is 541990.145186284)
Rank (*):2237 (digit rank is 1)
Entrance Rank (*):1878
Currently on list? (*):yes
Submitted:1/11/2019 02:38:21 CDT
Last modified:1/11/2019 03:20:15 CDT
Database id:125912
Status Flags:TrialDiv
Score (*):44.7528 (normalized score 1.9781)

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_id125912
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/client/llr.pl 320607*2^1800434-1 2>&1
Starting Lucas Lehmer Riesel prime test of 320607*2^1800434-1
Using AVX FFT length 168K, Pass1=896, Pass2=192
V1 = 3 ; Computing U0...
V1 = 3 ; Computing U0...done.Starting Lucas-Lehmer loop...


320607*2^1800434-1 is prime! (541991 decimal digits) Time : 1506.081 sec.
[Elapsed time: 25.10 minutes]
modified2019-01-11 03:06:07
created2019-01-11 02:41:01
id171589

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