Phi(11867, - 100)

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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(11867, - 100)
Verification status (*):	PRP
Official Comment (*):	Unique, ECPP
Unofficial Comments:	This prime has 1 user comment below.
Proof-code(s): (*):	c47 : Chandler, Primo
Decimal Digits:	23732 (log₁₀ is 23731.995678626)
Rank (*):	73001 (digit rank is 1)
Entrance Rank (*):	67553
Currently on list? (*):	yes
Submitted:	12/29/2021 22:31:51 UTC
Last modified:	5/20/2023 20:59:19 UTC
Database id:	133095
Status Flags:	Verify
Score (*):	35.1153 (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: yes, rank 5
Subcategory: "Unique"
(archival tag id 226976, tag last modified 2023-05-15 15:37:15)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 74
Subcategory: "ECPP"
(archival tag id 226975, tag last modified 2024-10-27 10:37:10)

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.

Ray Chandler writes (29 Dec 2021): (report abuse)

Phi(47468,10) = Phi(11867,-100) = (100^11867 + 1)/101 ; http://factordb.com/index.php?id=1100000000022736528 ; PRP: Richard Fischer, Sep2008 ; Proven: Primo v4.3.3 - LX64, Ray Chandler, 29Dec2021 ; Intel Xeon(R) Gold 5218R CPU @ 2.10GHz x 40

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 133095

person_id 9

machine Using: Xeon (pool) 4c+4c 3.5GHz

what prp

notes Command: /home/caldwell/clientpool/1/pfgw64 -t -q"Phi(11867,-100)" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing Phi(11867,-100) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Calling Brillhart-Lehmer-Selfridge with factored part 0.21% Phi(11867,-100) is PRP! (10.2026s+0.0201s) [Elapsed time: 11.00 seconds]

modified 2022-07-11 18:21:45

created 2021-12-29 22:36:01

id 178808

field	value
prime_id	133095
person_id	9
machine	Using: Xeon (pool) 4c+4c 3.5GHz
what	prp
notes	Command: /home/caldwell/clientpool/1/pfgw64 -t -q"Phi(11867,-100)" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing Phi(11867,-100) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Calling Brillhart-Lehmer-Selfridge with factored part 0.21% Phi(11867,-100) is PRP! (10.2026s+0.0201s) [Elapsed time: 11.00 seconds]
modified	2022-07-11 18:21:45
created	2021-12-29 22:36:01
id	178808

Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.