U(11200, - 1, 5039)

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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:	U(11200, - 1, 5039)
Verification status (*):	PRP
Official Comment (*):	Generalized Lucas number, cyclotomy
Unofficial Comments:	This prime has 1 user comment below.
Proof-code(s): (*):	x25 : Broadhurst, Water, OpenPFGW, Primo
Decimal Digits:	20400 (log₁₀ is 20399.960415652)
Rank (*):	73822 (digit rank is 1)
Entrance Rank (*):	14936
Currently on list? (*):	short
Submitted:	3/9/2004 15:09:50 UTC
Last modified:	3/11/2023 15:54:10 UTC
Database id:	69430
Status Flags:	Verify
Score (*):	34.6475 (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.

Cyclotomy Proof (tolerated *)
Prime on list: no, rank 10
Subcategory: "Cyclotomy Proof"
(archival tag id 192169, tag last modified 2023-03-11 15:53:59)
Generalized Lucas Number (archivable *)
Prime on list: yes, rank 18
Subcategory: "Generalized Lucas Number"
(archival tag id 192168, tag last modified 2023-10-24 02:37:13)

User comments about this prime (disclaimer):

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David Broadhurst writes (12 May 2021): (report abuse)

WL 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 69430

person_id 9

machine Linux P4 2.8GHz

what prp

notes Command: /home/caldwell/client/pfgw -f -tc -q"lucasU(11200,-1,5039)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing lucasU(11200,-1,5039) [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 6199893 Running N-1 test using base 37 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(8192,21) to FFT(8192,20) Reduced from FFT(8192,20) to FFT(8192,19) Reduced from FFT(8192,19) to FFT(8192,18) Reduced from FFT(8192,18) to FFT(8192,17) 135544 bit request FFT size=(8192,17) Running N-1 test using base 59 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(8192,21) to FFT(8192,20) Reduced from FFT(8192,20) to FFT(8192,19) Reduced from FFT(8192,19) to FFT(8192,18) Reduced from FFT(8192,18) to FFT(8192,17) 135544 bit request FFT size=(8192,17) Running N-1 test using base 61 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(8192,21) to FFT(8192,20) Reduced from FFT(8192,20) to FFT(8192,19) Reduced from FFT(8192,19) to FFT(8192,18) Reduced from FFT(8192,18) to FFT(8192,17) 135544 bit request FFT size=(8192,17) Running N+1 test using discriminant 79, base 16+sqrt(79) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(8192,21) to FFT(8192,20) Reduced from FFT(8192,20) to FFT(8192,19) Reduced from FFT(8192,19) to FFT(8192,18) Reduced from FFT(8192,18) to FFT(8192,17) 135552 bit request FFT size=(8192,17) Calling N-1 BLS with factored part 1.24% and helper 0.26% (3.97% proof) lucasU(11200,-1,5039) is Fermat and Lucas PRP! (559.4009s+0.0258s)

modified 2020-07-07 22:30:45

created 2004-03-09 15:23:00

id 74383

field	value
prime_id	69430
person_id	9
machine	Linux P4 2.8GHz
what	prp
notes	Command: /home/caldwell/client/pfgw -f -tc -q"lucasU(11200,-1,5039)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing lucasU(11200,-1,5039) [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 6199893 Running N-1 test using base 37 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(8192,21) to FFT(8192,20) Reduced from FFT(8192,20) to FFT(8192,19) Reduced from FFT(8192,19) to FFT(8192,18) Reduced from FFT(8192,18) to FFT(8192,17) 135544 bit request FFT size=(8192,17) Running N-1 test using base 59 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(8192,21) to FFT(8192,20) Reduced from FFT(8192,20) to FFT(8192,19) Reduced from FFT(8192,19) to FFT(8192,18) Reduced from FFT(8192,18) to FFT(8192,17) 135544 bit request FFT size=(8192,17) Running N-1 test using base 61 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(8192,21) to FFT(8192,20) Reduced from FFT(8192,20) to FFT(8192,19) Reduced from FFT(8192,19) to FFT(8192,18) Reduced from FFT(8192,18) to FFT(8192,17) 135544 bit request FFT size=(8192,17) Running N+1 test using discriminant 79, base 16+sqrt(79) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(8192,21) to FFT(8192,20) Reduced from FFT(8192,20) to FFT(8192,19) Reduced from FFT(8192,19) to FFT(8192,18) Reduced from FFT(8192,18) to FFT(8192,17) 135552 bit request FFT size=(8192,17) Calling N-1 BLS with factored part 1.24% and helper 0.26% (3.97% proof) lucasU(11200,-1,5039) is Fermat and Lucas PRP! (559.4009s+0.0258s)
modified	2020-07-07 22:30:45
created	2004-03-09 15:23:00
id	74383

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