U(37511)

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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(37511)
Verification status (*):	PRP
Official Comment (*):	Fibonacci number
Proof-code(s): (*):	x13 : Renze
Decimal Digits:	7839 (log₁₀ is 7838.98588841)
Rank (*):	85795 (digit rank is 1)
Entrance Rank (*):	31068
Currently on list? (*):	yes
Submitted:	6/27/2005 16:41:45 UTC
Last modified:	3/11/2023 15:54:10 UTC
Database id:	74907
Status Flags:	Verify
Score (*):	31.6851 (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.

Fibonacci Number (archivable *)
Prime on list: yes, rank 7
Subcategory: "Fibonacci Number"
(archival tag id 194522, tag last modified 2023-09-15 17:37:10)

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 74907

person_id 9

machine Linux P4 2.8GHz

what prp

notes Command: /home/caldwell/client/pfgw -f -tc -q"U(37511)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing U(37511) [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 2208025 Running N-1 test using base 7 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(3072,21) to FFT(3072,20) Reduced from FFT(3072,20) to FFT(3072,19) Reduced from FFT(3072,19) to FFT(3072,18) Reduced from FFT(3072,18) to FFT(3072,17) 52090 bit request FFT size=(3072,17) Running N+1 test using discriminant 13, base 6+sqrt(13) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(3072,21) to FFT(3072,20) Reduced from FFT(3072,20) to FFT(3072,19) Reduced from FFT(3072,19) to FFT(3072,18) Reduced from FFT(3072,18) to FFT(3072,17) 52098 bit request FFT size=(3072,17) Calling N-1 BLS with factored part 1.07% and helper 0.63% (3.84% proof) U(37511) is Fermat and Lucas PRP! (52.7200s+0.0017s)

modified 2020-07-07 22:30:43

created 2005-06-27 16:53:00

id 79979

field	value
prime_id	74907
person_id	9
machine	Linux P4 2.8GHz
what	prp
notes	Command: /home/caldwell/client/pfgw -f -tc -q"U(37511)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing U(37511) [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 2208025 Running N-1 test using base 7 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(3072,21) to FFT(3072,20) Reduced from FFT(3072,20) to FFT(3072,19) Reduced from FFT(3072,19) to FFT(3072,18) Reduced from FFT(3072,18) to FFT(3072,17) 52090 bit request FFT size=(3072,17) Running N+1 test using discriminant 13, base 6+sqrt(13) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(3072,21) to FFT(3072,20) Reduced from FFT(3072,20) to FFT(3072,19) Reduced from FFT(3072,19) to FFT(3072,18) Reduced from FFT(3072,18) to FFT(3072,17) 52098 bit request FFT size=(3072,17) Calling N-1 BLS with factored part 1.07% and helper 0.63% (3.84% proof) U(37511) is Fermat and Lucas PRP! (52.7200s+0.0017s)
modified	2020-07-07 22:30:43
created	2005-06-27 16:53:00
id	79979

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.