primV(9008, 1, 16200)

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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:	primV(9008, 1, 16200)
Verification status (*):	PRP
Official Comment (*):	Generalized Lucas primitive part
Unofficial Comments:	This prime has 1 user comment below.
Proof-code(s): (*):	x23 : Broadhurst, Water, Renze, OpenPFGW, Primo
Decimal Digits:	34168 (log₁₀ is 34167.98913542)
Rank (*):	66951 (digit rank is 1)
Entrance Rank (*):	14252
Currently on list? (*):	yes
Submitted:	11/8/2005 22:13:58 UTC
Last modified:	3/11/2023 15:54:10 UTC
Database id:	76127
Status Flags:	Verify
Score (*):	36.2416 (normalized score 0.0001)

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.

Generalized Lucas primitive part (archivable *)
Prime on list: yes, rank 7
Subcategory: "Generalized Lucas primitive part"
(archival tag id 190807, tag last modified 2023-03-11 15:53:59)

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.

Chris Caldwell writes (12 May 2021): (report abuse)

CHG proof with ECPP helpers. For a certificate of proof.

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.

field value

prime_id 76127

person_id 9

machine Linux P4 2.8GHz

what prp

notes Command: /home/caldwell/client/pfgw -f -tc -q"primV(9008,1,16200)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing primV(9008,1,16200) [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 10793975 Running N-1 test using base 29 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(14336,20) to FFT(14336,19) Reduced from FFT(14336,19) to FFT(14336,18) Reduced from FFT(14336,18) to FFT(14336,17) Reduced from FFT(14336,17) to FFT(14336,16) 227016 bit request FFT size=(14336,16) Running N-1 test using base 41 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(14336,20) to FFT(14336,19) Reduced from FFT(14336,19) to FFT(14336,18) Reduced from FFT(14336,18) to FFT(14336,17) Reduced from FFT(14336,17) to FFT(14336,16) 227016 bit request FFT size=(14336,16) Running N-1 test using base 43 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(14336,20) to FFT(14336,19) Reduced from FFT(14336,19) to FFT(14336,18) Reduced from FFT(14336,18) to FFT(14336,17) Reduced from FFT(14336,17) to FFT(14336,16) 227016 bit request FFT size=(14336,16) Running N-1 test using base 47 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(14336,20) to FFT(14336,19) Reduced from FFT(14336,19) to FFT(14336,18) Reduced from FFT(14336,18) to FFT(14336,17) Reduced from FFT(14336,17) to FFT(14336,16) 227016 bit request FFT size=(14336,16) Running N-1 test using base 59 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(14336,20) to FFT(14336,19) Reduced from FFT(14336,19) to FFT(14336,18) Reduced from FFT(14336,18) to FFT(14336,17) Reduced from FFT(14336,17) to FFT(14336,16) 227016 bit request FFT size=(14336,16) Running N+1 test using discriminant 67, base 3+sqrt(67) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(14336,20) to FFT(14336,19) Reduced from FFT(14336,19) to FFT(14336,18) Reduced from FFT(14336,18) to FFT(14336,17) Reduced from FFT(14336,17) to FFT(14336,16) 227024 bit request FFT size=(14336,16) Calling N-1 BLS with factored part 1.46% and helper 0.02% (4.41% proof) primV(9008,1,16200) is Fermat and Lucas PRP! (2607.6862s+0.7234s) [Elapsed time: 2608 seconds]

modified 2020-07-07 22:30:43

created 2005-11-08 22:23:01

id 81331

field	value
prime_id	76127
person_id	9
machine	Linux P4 2.8GHz
what	prp
notes	Command: /home/caldwell/client/pfgw -f -tc -q"primV(9008,1,16200)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing primV(9008,1,16200) [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 10793975 Running N-1 test using base 29 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(14336,20) to FFT(14336,19) Reduced from FFT(14336,19) to FFT(14336,18) Reduced from FFT(14336,18) to FFT(14336,17) Reduced from FFT(14336,17) to FFT(14336,16) 227016 bit request FFT size=(14336,16) Running N-1 test using base 41 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(14336,20) to FFT(14336,19) Reduced from FFT(14336,19) to FFT(14336,18) Reduced from FFT(14336,18) to FFT(14336,17) Reduced from FFT(14336,17) to FFT(14336,16) 227016 bit request FFT size=(14336,16) Running N-1 test using base 43 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(14336,20) to FFT(14336,19) Reduced from FFT(14336,19) to FFT(14336,18) Reduced from FFT(14336,18) to FFT(14336,17) Reduced from FFT(14336,17) to FFT(14336,16) 227016 bit request FFT size=(14336,16) Running N-1 test using base 47 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(14336,20) to FFT(14336,19) Reduced from FFT(14336,19) to FFT(14336,18) Reduced from FFT(14336,18) to FFT(14336,17) Reduced from FFT(14336,17) to FFT(14336,16) 227016 bit request FFT size=(14336,16) Running N-1 test using base 59 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(14336,20) to FFT(14336,19) Reduced from FFT(14336,19) to FFT(14336,18) Reduced from FFT(14336,18) to FFT(14336,17) Reduced from FFT(14336,17) to FFT(14336,16) 227016 bit request FFT size=(14336,16) Running N+1 test using discriminant 67, base 3+sqrt(67) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(14336,20) to FFT(14336,19) Reduced from FFT(14336,19) to FFT(14336,18) Reduced from FFT(14336,18) to FFT(14336,17) Reduced from FFT(14336,17) to FFT(14336,16) 227024 bit request FFT size=(14336,16) Calling N-1 BLS with factored part 1.46% and helper 0.02% (4.41% proof) primV(9008,1,16200) is Fermat and Lucas PRP! (2607.6862s+0.7234s) [Elapsed time: 2608 seconds]
modified	2020-07-07 22:30:43
created	2005-11-08 22:23:01
id	81331

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