632760! - 1

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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:	632760! - 1
Verification status (*):	Proven
Official Comment (*):	Factorial
Unofficial Comments:	This prime has 1 user comment below.
Proof-code(s): (*):	A43 : Propper, MultiSieve, PRST
Decimal Digits:	3395992 (log₁₀ is 3395991.1239772)
Rank (*):	128 (digit rank is 1)
Entrance Rank (*):	124
Currently on list? (*):	yes
Submitted:	10/20/2024 15:35:40 UTC
Last modified:	12/12/2024 07:37:15 UTC
Database id:	138667
Status Flags:	none
Score (*):	50.3809 (normalized score 185.7176)

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.

Factorial primes (archivable *)
Prime on list: yes, rank 1
Subcategory: "Factorial"
(archival tag id 229785, tag last modified 2024-12-12 07:37:17)

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.

Ryan Propper writes (21 Oct 2024): (report abuse)

PFGW Version 4.1.3.64BIT.20240114.x86_Dev [GWNUM 30.19]

CPU Information (From Woltman v26 library code)
Intel(R) Xeon(R) Gold 6154 CPU @ 3.00GHz
CPU speed: 2992.96 MHz, 36 hyperthreaded cores
CPU features: RDTSC, CMOV, Prefetch, MMX, SSE, SSE2, SSE4.1, SSE4.2
L1 cache size: 32 KB
L2 cache size: 1 MB, L3 cache size: 25344 KB
L1 cache line size: 64 bytes
L2 cache line size: 64 bytes
TLBS: 64

Primality testing 632760!-1 [N+1, Brillhart-Lehmer-Selfridge]                    
Running N+1 test using discriminant 632813, base 1+sqrt(632813)                  
Generic modular reduction using Montgomery reduction AVX-512 FFT length 2x672K, Pass1=1536, Pass2=448, clm=2, 16 threads on A 11281239-bit number                
Calling Brillhart-Lehmer-Selfridge with factored part 33.67%
632760!-1 is prime! (187466.5830s+6.8604s)

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 138667

person_id 9

machine Using: Digital Ocean Droplet

what prime

notes Command: /var/www/clientpool/1/pfgw64 -V -f -tp -q"632760!-1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 632760!-1 [N+1, Brillhart-Lehmer-Selfridge]
trial
Running N+1 test using discriminant 632813, base 1+sqrt(632813)
Generic modular reduction using generic reduction FMA3 FFT length 1152K, Pass1=384, Pass2=3K, clm=2 on A 11281239-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 38/11281871 ERROR: ROUND OFF 0.5>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 632813, base 1+sqrt(632813)
Generic modular reduction using generic reduction FMA3 FFT length 1200K, Pass1=320, Pass2=3840, clm=2 on A 11281239-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 11281123/11281871 ERROR: ROUND OFF 0.5>0.45
(Test aborted, try again using the -a2 (or possibly -a0) switch)
Running N+1 test using discriminant 632813, base 1+sqrt(632813)
Generic modular reduction using generic reduction FMA3 FFT length 1280K, Pass1=320, Pass2=4K, clm=2 on A 11281239-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 11281127/11281871 ERROR: ROUND OFF 0.5>0.45
(Test aborted
Running N+1 test using discriminant 632813, base 1+sqrt(632813)
Generic modular reduction using generic reduction FMA3 FFT length 1344K, Pass1=448, Pass2=3K, clm=2 on A 11281239-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 33.67%

632760!-1 is prime! (4428373.6141s+8.4818s)
[Elapsed time: 51.25 days]

modified 2024-12-12 07:14:48

created 2024-10-22 01:08:22

id 184511

field	value
prime_id	138667
person_id	9
machine	Using: Digital Ocean Droplet
what	prime
notes	Command: /var/www/clientpool/1/pfgw64 -V -f -tp -q"632760!-1" >command_output 2>&1 PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11] Primality testing 632760!-1 [N+1, Brillhart-Lehmer-Selfridge] trial Running N+1 test using discriminant 632813, base 1+sqrt(632813) Generic modular reduction using generic reduction FMA3 FFT length 1152K, Pass1=384, Pass2=3K, clm=2 on A 11281239-bit number Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate Iteration: 38/11281871 ERROR: ROUND OFF 0.5>0.45 (Test aborted, try again using the -a1 switch) Running N+1 test using discriminant 632813, base 1+sqrt(632813) Generic modular reduction using generic reduction FMA3 FFT length 1200K, Pass1=320, Pass2=3840, clm=2 on A 11281239-bit number Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate Iteration: 11281123/11281871 ERROR: ROUND OFF 0.5>0.45 (Test aborted, try again using the -a2 (or possibly -a0) switch) Running N+1 test using discriminant 632813, base 1+sqrt(632813) Generic modular reduction using generic reduction FMA3 FFT length 1280K, Pass1=320, Pass2=4K, clm=2 on A 11281239-bit number Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate Iteration: 11281127/11281871 ERROR: ROUND OFF 0.5>0.45 (Test aborted Running N+1 test using discriminant 632813, base 1+sqrt(632813) Generic modular reduction using generic reduction FMA3 FFT length 1344K, Pass1=448, Pass2=3K, clm=2 on A 11281239-bit number Calling Brillhart-Lehmer-Selfridge with factored part 33.67% 632760!-1 is prime! (4428373.6141s+8.4818s) [Elapsed time: 51.25 days]
modified	2024-12-12 07:14:48
created	2024-10-22 01:08:22
id	184511

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