Phi(9455, - 10)

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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(9455, - 10)
Verification status (*):	PRP
Official Comment (*):	Unique, ECPP
Unofficial Comments:	This prime has 1 user comment below.
Proof-code(s): (*):	c33 : Chaglassian, Primo
Decimal Digits:	7200 (log₁₀ is 7199.9586116578)
Rank (*):	87219 (digit rank is 1)
Entrance Rank (*):	32342
Currently on list? (*):	no
Submitted:	7/7/2005 19:47:34 UTC
Last modified:	3/11/2023 15:54:10 UTC
Database id:	75005
Status Flags:	Verify
Score (*):	31.4213 (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.

Unique (archivable *)
Prime on list: no, rank 21
Subcategory: "Unique"
(archival tag id 210368, tag last modified 2023-05-15 15:37:15)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 457
Subcategory: "ECPP"
(archival tag id 210367, tag last modified 2024-12-16 19:37:11)

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.

Raffi Chaglassian writes (12 May 2021): (report abuse)

certificate: primes.siliconsoul.com/cert/p7200.zip

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 75005

person_id 9

machine Linux P4 2.8GHz

what prp

notes Command: /home/caldwell/client/pfgw -f -t -q"Phi(9455,-10)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing Phi(9455,-10) [N-1, Brillhart-Lehmer-Selfridge] trial factoring to 2013771 Running N-1 test using base 2 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) Reduced from FFT(3072,17) to FFT(3072,16) 47844 bit request FFT size=(3072,16) Running N-1 test using base 3 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) Reduced from FFT(3072,17) to FFT(3072,16) 47844 bit request FFT size=(3072,16) 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) Reduced from FFT(3072,17) to FFT(3072,16) 47844 bit request FFT size=(3072,16) Running N-1 test using base 11 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) Reduced from FFT(3072,17) to FFT(3072,16) 47844 bit request FFT size=(3072,16) Running N-1 test using base 31 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) Reduced from FFT(3072,17) to FFT(3072,16) 47844 bit request FFT size=(3072,16) Running N-1 test using base 67 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) Reduced from FFT(3072,17) to FFT(3072,16) 47844 bit request FFT size=(3072,16) Calling Brillhart-Lehmer-Selfridge with factored part 0.70% Phi(9455,-10) is PRP! (64.5425s+0.0119s)

modified 2020-07-07 22:30:43

created 2005-07-07 21:06:36

id 80100

field	value
prime_id	75005
person_id	9
machine	Linux P4 2.8GHz
what	prp
notes	Command: /home/caldwell/client/pfgw -f -t -q"Phi(9455,-10)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing Phi(9455,-10) [N-1, Brillhart-Lehmer-Selfridge] trial factoring to 2013771 Running N-1 test using base 2 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) Reduced from FFT(3072,17) to FFT(3072,16) 47844 bit request FFT size=(3072,16) Running N-1 test using base 3 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) Reduced from FFT(3072,17) to FFT(3072,16) 47844 bit request FFT size=(3072,16) 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) Reduced from FFT(3072,17) to FFT(3072,16) 47844 bit request FFT size=(3072,16) Running N-1 test using base 11 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) Reduced from FFT(3072,17) to FFT(3072,16) 47844 bit request FFT size=(3072,16) Running N-1 test using base 31 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) Reduced from FFT(3072,17) to FFT(3072,16) 47844 bit request FFT size=(3072,16) Running N-1 test using base 67 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) Reduced from FFT(3072,17) to FFT(3072,16) 47844 bit request FFT size=(3072,16) Calling Brillhart-Lehmer-Selfridge with factored part 0.70% Phi(9455,-10) is PRP! (64.5425s+0.0119s)
modified	2020-07-07 22:30:43
created	2005-07-07 21:06:36
id	80100

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