Phi(4029, - 1000)

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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:	Phi(4029, - 1000)
Verification status (*):	PRP
Official Comment (*):	Unique, ECPP
Proof-code(s): (*):	c47 : Chandler, Primo
Decimal Digits:	7488 (log₁₀ is 7487.9995659229)
Rank (*):	85765 (digit rank is 1)
Entrance Rank (*):	45763
Currently on list? (*):	short
Submitted:	8/18/2009 12:45:51 UTC
Last modified:	3/11/2023 15:54:10 UTC
Database id:	89682
Status Flags:	Verify
Score (*):	31.543 (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.

Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 425
Subcategory: "ECPP"
(archival tag id 210494, tag last modified 2024-04-19 02:37:11)
Unique (archivable *)
Prime on list: yes, rank 20
Subcategory: "Unique"
(archival tag id 210495, tag last modified 2023-05-15 15:37:15)

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 89682

person_id 9

machine RedHat P4 P4

what trial_divided

notes Command: /home/caldwell/client/pfgw -o -f -q"Phi(4029,-1000)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 2101180 Phi(4029,-1000) has no small factor. [Elapsed time: 1.478 seconds]

modified 2020-07-07 22:30:37

created 2009-08-18 12:48:02

id 108734

field	value
prime_id	89682
person_id	9
machine	RedHat P4 P4
what	trial_divided
notes	Command: /home/caldwell/client/pfgw -o -f -q"Phi(4029,-1000)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 2101180 Phi(4029,-1000) has no small factor. [Elapsed time: 1.478 seconds]
modified	2020-07-07 22:30:37
created	2009-08-18 12:48:02
id	108734

field value

prime_id 89682

person_id 9

machine RedHat P4 P4

what prp

notes Command: /home/caldwell/client/pfgw -t -q"Phi(4029,-1000)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing Phi(4029,-1000) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 47 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) 49758 bit request FFT size=(3072,17) Calling Brillhart-Lehmer-Selfridge with factored part 0.83% Phi(4029,-1000) is PRP! (7.6400s+0.0000s) [Elapsed time: 8.00 seconds]

modified 2020-07-07 22:30:37

created 2009-08-18 12:53:01

id 108735

field	value
prime_id	89682
person_id	9
machine	RedHat P4 P4
what	prp
notes	Command: /home/caldwell/client/pfgw -t -q"Phi(4029,-1000)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing Phi(4029,-1000) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 47 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) 49758 bit request FFT size=(3072,17) Calling Brillhart-Lehmer-Selfridge with factored part 0.83% Phi(4029,-1000) is PRP! (7.6400s+0.0000s) [Elapsed time: 8.00 seconds]
modified	2020-07-07 22:30:37
created	2009-08-18 12:53:01
id	108735

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