Phi(4613, - 100000000)

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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(4613, - 100000000)
Verification status (*):	PRP
Official Comment (*):	Unique, ECPP
Unofficial Comments:	This prime has 1 user comment below.
Proof-code(s): (*):	E1 : Batalov, CM
Decimal Digits:	31585 (log₁₀ is 31584.000000004)
Rank (*):	70640 (digit rank is 3)
Entrance Rank (*):	70628
Currently on list? (*):	yes
Submitted:	8/6/2025 08:47:58 UTC
Last modified:	8/9/2025 14:37:21 UTC
Database id:	140980
Status Flags:	Verify
Score (*):	35.9987 (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 38
Subcategory: "ECPP"
(archival tag id 239453, tag last modified 2025-08-09 14:37:23)
Unique (archivable *)
Prime on list: yes, rank 4
Subcategory: "Unique"
(archival tag id 239454, tag last modified 2025-08-09 14:37:23)

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.

Serge Batalov writes (6 Aug 2025): (report abuse)

Certificate at FactorDB.

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 140980

person_id 9

machine Using: Digital Ocean Droplet

what prp

notes Command: /var/www/clientpool/1/pfgw64 -V -f -t -q"Phi(4613,-100000000)" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing Phi(4613,-100000000) [N-1, Brillhart-Lehmer-Selfridge]
trial

Running N-1 test using base 19
Generic modular reduction using generic reduction FMA3 FFT length 10K, Pass1=128, Pass2=80, clm=2 on A 104920-bit number
Running N-1 test using base 43
Generic modular reduction using generic reduction FMA3 FFT length 10K, Pass1=128, Pass2=80, clm=2 on A 104920-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.37%

Phi(4613,-100000000) is PRP! (54.0564s+0.9808s)
[Elapsed time: 60.00 seconds]

modified 2025-08-09 13:44:03

created 2025-08-09 13:43:03

id 187069

field	value
prime_id	140980
person_id	9
machine	Using: Digital Ocean Droplet
what	prp
notes	Command: /var/www/clientpool/1/pfgw64 -V -f -t -q"Phi(4613,-100000000)" >command_output 2>&1 PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11] Primality testing Phi(4613,-100000000) [N-1, Brillhart-Lehmer-Selfridge] trial Running N-1 test using base 19 Generic modular reduction using generic reduction FMA3 FFT length 10K, Pass1=128, Pass2=80, clm=2 on A 104920-bit number Running N-1 test using base 43 Generic modular reduction using generic reduction FMA3 FFT length 10K, Pass1=128, Pass2=80, clm=2 on A 104920-bit number Calling Brillhart-Lehmer-Selfridge with factored part 0.37% Phi(4613,-100000000) is PRP! (54.0564s+0.9808s) [Elapsed time: 60.00 seconds]
modified	2025-08-09 13:44:03
created	2025-08-09 13:43:03
id	187069

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