Phi(10455, 10)/239603947111

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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(10455, 10)/239603947111
Verification status (*):	PRP
Official Comment (*):	ECPP
Unofficial Comments:	This prime has 1 user comment below.
Proof-code(s): (*):	c4 : Broadhurst, Primo
Decimal Digits:	5109 (log₁₀ is 5108.575187396)
Rank (*):	94975 (digit rank is 1)
Entrance Rank (*):	28728
Currently on list? (*):	no
Submitted:	10/24/2003 19:07:22 UTC
Last modified:	9/2/2026 15:32:29 UTC
Database id:	66796
Status Flags:	Verify
Score (*):	30.3559 (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 612
Subcategory: "ECPP"
(archival tag id 210377, tag last modified 2026-08-09 05:37:21)

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.

David Broadhurst writes (11 Sep 2014): (report abuse)

certificate

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 66796

person_id 9

machine Linux P4 2.8GHz

what prp

notes Command: /home/caldwell/client/pfgw -f -tc -q"Phi(10455,10)/239603947111" 2>&1 PFGW Version 20030811.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 1388087 Running N-1 test using base 23 Primality testing Phi(10455,10)/239603947111 [N-1/N+1, Brillhart-Lehmer-Selfridge] Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(2048,21) to FFT(2048,20) Reduced from FFT(2048,20) to FFT(2048,19) Reduced from FFT(2048,19) to FFT(2048,18) Reduced from FFT(2048,18) to FFT(2048,17) 33950 bit request FFT size=(2048,17) Running N-1 test using base 31 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(2048,21) to FFT(2048,20) Reduced from FFT(2048,20) to FFT(2048,19) Reduced from FFT(2048,19) to FFT(2048,18) Reduced from FFT(2048,18) to FFT(2048,17) 33950 bit request FFT size=(2048,17) Running N+1 test using discriminant 53, base 4+sqrt(53) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(2048,21) to FFT(2048,20) Reduced from FFT(2048,20) to FFT(2048,19) Reduced from FFT(2048,19) to FFT(2048,18) Reduced from FFT(2048,18) to FFT(2048,17) 33958 bit request FFT size=(2048,17) Calling N+1 BLS with factored part 0.21% and helper 0.15% (0.79% proof) Phi(10455,10)/239603947111 is Fermat and Lucas PRP! (17.9100s+0.0000s)

modified 2020-07-07 22:30:47

created 2003-10-24 19:23:01

id 71711

field	value
prime_id	66796
person_id	9
machine	Linux P4 2.8GHz
what	prp
notes	Command: /home/caldwell/client/pfgw -f -tc -q"Phi(10455,10)/239603947111" 2>&1 PFGW Version 20030811.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 1388087 Running N-1 test using base 23 Primality testing Phi(10455,10)/239603947111 [N-1/N+1, Brillhart-Lehmer-Selfridge] Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(2048,21) to FFT(2048,20) Reduced from FFT(2048,20) to FFT(2048,19) Reduced from FFT(2048,19) to FFT(2048,18) Reduced from FFT(2048,18) to FFT(2048,17) 33950 bit request FFT size=(2048,17) Running N-1 test using base 31 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(2048,21) to FFT(2048,20) Reduced from FFT(2048,20) to FFT(2048,19) Reduced from FFT(2048,19) to FFT(2048,18) Reduced from FFT(2048,18) to FFT(2048,17) 33950 bit request FFT size=(2048,17) Running N+1 test using discriminant 53, base 4+sqrt(53) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(2048,21) to FFT(2048,20) Reduced from FFT(2048,20) to FFT(2048,19) Reduced from FFT(2048,19) to FFT(2048,18) Reduced from FFT(2048,18) to FFT(2048,17) 33958 bit request FFT size=(2048,17) Calling N+1 BLS with factored part 0.21% and helper 0.15% (0.79% proof) Phi(10455,10)/239603947111 is Fermat and Lucas PRP! (17.9100s+0.0000s)
modified	2020-07-07 22:30:47
created	2003-10-24 19:23:01
id	71711

Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.