(2110615 + 1)2 - 2
(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:(2110615 + 1)2 - 2
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):p126 : Minovic, MultiSieve, OpenPFGW
Decimal Digits:66597   (log10 is 66596.8659407426)
Rank (*):48099 (digit rank is 1)
Entrance Rank (*):1019
Currently on list? (*):no
Submitted:2/19/2004 07:15:10 CDT
Last modified:2/19/2004 07:15:10 CDT
Removed (*):3/7/2006 13:43:44 CDT
Database id:68900
Status Flags:none
Score (*):38.3012 (normalized score 0.0032)

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_id68900
person_id9
machineLinux P4 2.8GHz
whatprime
notesPFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 7344136540...6482191359 [N-1/N+1, Brillhart-Lehmer-Selfridge]
trial factoring to 22072149
Running N-1 test using base 3
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(28672,20) to FFT(28672,19)
Reduced from FFT(28672,19) to FFT(28672,18)
Reduced from FFT(28672,18) to FFT(28672,17)
Reduced from FFT(28672,17) to FFT(28672,16)
442470 bit request FFT size=(28672,16)
Running N+1 test using discriminant 7, base 20+sqrt(7)
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(28672,20) to FFT(28672,19)
Reduced from FFT(28672,19) to FFT(28672,18)
Reduced from FFT(28672,18) to FFT(28672,17)
Reduced from FFT(28672,17) to FFT(28672,16)
442478 bit request FFT size=(28672,16)
Running N+1 test using discriminant 7, base 25+sqrt(7)
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(28672,20) to FFT(28672,19)
Reduced from FFT(28672,19) to FFT(28672,18)
Reduced from FFT(28672,18) to FFT(28672,17)
Reduced from FFT(28672,17) to FFT(28672,16)
442478 bit request FFT size=(28672,16)
Calling N+1 BLS with factored part 50.01% and helper 0.02% (150.04% proof)
7344136540...6482191359 is prime! (-212.5773s+0.1400s)
modified2004-02-19 14:50:58
created2004-02-19 12:14:23
id73855

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