(2253987 - 1)2 - 2

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:(2253987 - 1)2 - 2
Verification status (*):Proven
Official Comment (*):[none]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p89 : Emmanuel, OpenPFGW
Decimal Digits:152916   (log10 is 152915.41101742)
Rank (*):41425 (digit rank is 1)
Entrance Rank (*):912
Currently on list? (*):no
Submitted:5/7/2007 20:02:47 UTC
Last modified:3/11/2023 15:54:10 UTC
Removed (*):6/3/2010 18:44:26 UTC
Database id:80384
Status Flags:none
Score (*):40.8622 (normalized score 0.0146)

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.

David Broadhurst writes (11 Sep 2014):  (report abuse)
Near-square prime

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_id80384
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/pfgw -o -f -q"(2^253987-1)^2-2" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 53636202 (2^253987-1)^2-2 has no small factor. [Elapsed time: 611.666 seconds]
modified2020-07-07 22:30:41
created2007-05-07 20:22:13
id89880

fieldvalue
prime_id80384
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -tc -q"(2^253987-1)^2-2" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing (2^253987-1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(65536,20) to FFT(65536,19) Reduced from FFT(65536,19) to FFT(65536,18) Reduced from FFT(65536,18) to FFT(65536,17) Reduced from FFT(65536,17) to FFT(65536,16) 1015956 bit request FFT size=(65536,16) Running N+1 test using discriminant 11, base 2+sqrt(11) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(65536,20) to FFT(65536,19) Reduced from FFT(65536,19) to FFT(65536,18) Reduced from FFT(65536,18) to FFT(65536,17) Reduced from FFT(65536,17) to FFT(65536,16) 1015964 bit request FFT size=(65536,16) Running N+1 test using discriminant 11, base 3+sqrt(11) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(65536,20) to FFT(65536,19) Reduced from FFT(65536,19) to FFT(65536,18) Reduced from FFT(65536,18) to FFT(65536,17) Reduced from FFT(65536,17) to FFT(65536,16) 1015964 bit request FFT size=(65536,16) Running N+1 test using discriminant 11, base 4+sqrt(11) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(65536,20) to FFT(65536,19) Reduced from FFT(65536,19) to FFT(65536,18) Reduced from FFT(65536,18) to FFT(65536,17) Reduced from FFT(65536,17) to FFT(65536,16) 1015964 bit request FFT size=(65536,16) Calling N+1 BLS with factored part 50.00% and helper 0.01% (150.02% proof) (2^253987-1)^2-2 is prime! (-1201.8184s+0.0200s) [Elapsed time: 34402 seconds]
modified2020-07-07 22:30:41
created2007-05-07 20:23:03
id89881

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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