4977 · 21338908 + 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:4977 · 21338908 + 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):L1733 : Murphy, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:403056   (log10 is 403055.16640211)
Rank (*):6400 (digit rank is 1)
Entrance Rank (*):2209
Currently on list? (*):no
Submitted:4/22/2015 16:04:41 CDT
Last modified:4/22/2015 16:50:25 CDT
Removed (*):5/5/2018 07:19:12 CDT
Database id:119792
Status Flags:TrialDiv
Score (*):43.8429 (normalized score 0.8104)

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"4977*2^1338908+1" 2>&1
PFGW Version [GWNUM 27.11]
Primality testing 4977*2^1338908+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%

4977*2^1338908+1 is prime! (669.6794s+0.0003s)
[Elapsed time: 11.17 minutes]
modified2015-05-07 06:34:53
created2015-04-22 16:22:11

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.