7351117# + 1

Previous Next Random

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:	7351117# + 1
Verification status (*):	Proven
Official Comment (*):	Primorial
Proof-code(s): (*):	p448 : Little, MultiSieve, PrimeGrid, PRST, OpenPFGW
Decimal Digits:	3191401 (log₁₀ is 3191400.1163184)
Rank (*):	147 (digit rank is 1)
Entrance Rank (*):	136
Currently on list? (*):	yes
Submitted:	9/20/2024 01:35:38 UTC
Last modified:	11/8/2024 16:37:10 UTC
Database id:	138558
Status Flags:	none
Score (*):	50.1906 (normalized score 158.123)

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.

Primorial (archivable *)
Prime on list: yes, rank 1
Subcategory: "Primorial"
(archival tag id 229737, tag last modified 2024-11-08 16:37:12)

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 138558

person_id 9

machine Using: Digital Ocean Droplet

what prime

notes Command: /var/www/clientpool/1/pfgw64 -V -f -t -q"7351117#+1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 7351117#+1 [N-1, Brillhart-Lehmer-Selfridge]
trial

Running N-1 test using base 2
Generic modular reduction using generic reduction FMA3 FFT length 1120K, Pass1=448, Pass2=2560, clm=2 on A 10601602-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 33.33%

7351117#+1 is prime! (4154493.9822s+25.3299s)
[Elapsed time: 48.08 days]

modified 2024-11-08 16:29:35

created 2024-09-21 14:27:30

id 184402

field	value
prime_id	138558
person_id	9
machine	Using: Digital Ocean Droplet
what	prime
notes	Command: /var/www/clientpool/1/pfgw64 -V -f -t -q"7351117#+1" >command_output 2>&1 PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11] Primality testing 7351117#+1 [N-1, Brillhart-Lehmer-Selfridge] trial Running N-1 test using base 2 Generic modular reduction using generic reduction FMA3 FFT length 1120K, Pass1=448, Pass2=2560, clm=2 on A 10601602-bit number Calling Brillhart-Lehmer-Selfridge with factored part 33.33% 7351117#+1 is prime! (4154493.9822s+25.3299s) [Elapsed time: 48.08 days]
modified	2024-11-08 16:29:35
created	2024-09-21 14:27:30
id	184402

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