(217029 - 1)/418879343
(Another of the Prime Pages' resources)
The Largest Known Primes Icon
  View this page in:   language help
 

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:(217029 - 1)/418879343
Verification status (*):PRP
Official Comment:Mersenne cofactor, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c8 : Water, Broadhurst, Primo
Decimal Digits:5118   (log10 is 5117.6177072182)
Rank (*):80330 (digit rank is 2)
Entrance Rank (*):39398
Currently on list? (*):short
Submitted:9/3/2006 04:16:43 CDT
Last modified:9/3/2006 04:24:02 CDT
Database id:78418
Status Flags:Verify
Score (*):30.3614 (normalized score 0)

Archival tags:

There are certain forms classed as archivable: these prime may (at times) remain on this list even if they do not make the Top 5000 proper.  Such primes are tracked with archival tags.
Mersenne cofactor (archivable *)
Prime on list: yes, rank 20
Subcategory: "Mersenne cofactor"
(archival tag id 195157, tag last modified 2017-10-19 05:50:26)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 379
Subcategory: "ECPP"
(archival tag id 195156, tag last modified 2017-10-19 05:50:25)

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): 
certificate

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_id78418
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/pfgw -o -f -q"(2^17029-1)/418879343" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
trial factoring to 1390751
(2^17029-1)/418879343 has no small factor.
[Elapsed time: 1.058 seconds]
modified2007-03-03 21:00:43
created2006-09-03 04:22:01
id85935

fieldvalue
prime_id78418
person_id9
machineRedHat P4 P4
whatprp
notesCommand: /home/caldwell/client/pfgw -tc -q"(2^17029-1)/418879343" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing (2^17029-1)/418879343 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(2048,21) to FFT(2048,20)
Reduced from FFT(2048,20) to FFT(2048,19)
Reduced from FFT(2048,19) to FFT(2048,18)
Reduced from FFT(2048,18) to FFT(2048,17)
34010 bit request FFT size=(2048,17)
Running N+1 test using discriminant 43, base 1+sqrt(43)
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(2048,21) to FFT(2048,20)
Reduced from FFT(2048,20) to FFT(2048,19)
Reduced from FFT(2048,19) to FFT(2048,18)
Reduced from FFT(2048,18) to FFT(2048,17)
34018 bit request FFT size=(2048,17)
Running N+1 test using discriminant 43, base 2+sqrt(43)
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(2048,21) to FFT(2048,20)
Reduced from FFT(2048,20) to FFT(2048,19)
Reduced from FFT(2048,19) to FFT(2048,18)
Reduced from FFT(2048,18) to FFT(2048,17)
34018 bit request FFT size=(2048,17)
Running N+1 test using discriminant 43, base 4+sqrt(43)
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(2048,21) to FFT(2048,20)
Reduced from FFT(2048,20) to FFT(2048,19)
Reduced from FFT(2048,19) to FFT(2048,18)
Reduced from FFT(2048,18) to FFT(2048,17)
34018 bit request FFT size=(2048,17)
Running N+1 test using discriminant 43, base 7+sqrt(43)
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(2048,21) to FFT(2048,20)
Reduced from FFT(2048,20) to FFT(2048,19)
Reduced from FFT(2048,19) to FFT(2048,18)
Reduced from FFT(2048,18) to FFT(2048,17)
34018 bit request FFT size=(2048,17)
Calling N-1 BLS with factored part 0.25% and helper 0.09% (0.86% proof)
(2^17029-1)/418879343 is Fermat and Lucas PRP! (60.9765s+0.0285s)
[Elapsed time: 61 seconds]
modified2007-03-03 21:00:43
created2006-09-03 04:23:01
id85936

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