1268118079424 · 8501# - 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:	1268118079424 · 8501# - 1
Verification status (*):	Proven
Official Comment (*):	Cunningham chain (8p+7)
Proof-code(s): (*):	p434 : Doornink, MultiSieve, OpenPFGW
Decimal Digits:	3640 (log₁₀ is 3639.7856405292)
Rank (*):	94919 (digit rank is 2)
Entrance Rank (*):	92712
Currently on list? (*):	yes
Submitted:	10/22/2023 17:01:57 UTC
Last modified:	10/23/2023 10:37:18 UTC
Database id:	136560
Status Flags:	none
Score (*):	29.3021 (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.

Cunningham Chains (1st kind) (archivable class *)
Prime on list: yes, rank 1, weight 45.658450679111
Subcategory: "Cunningham chain (8p+7)"
(archival tag id 228891, tag last modified 2023-10-23 10:37:23)

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 136560

person_id 9

machine Using: Digital Ocean Droplet

what prime

notes Command: /var/www/clientpool/1/pfgw64 -V -f -tp -q"1268118079424*8501#-1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 1268118079424*8501#-1 [N+1, Brillhart-Lehmer-Selfridge]
trial
Running N+1 test using discriminant 8521, base 1+sqrt(8521)
Generic modular reduction using generic reduction AVX-512 FFT length 1536 on A 12092-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 33.43%

1268118079424*8501#-1 is prime! (3.7933s+0.0005s)
[Elapsed time: 5.00 seconds]

modified 2023-10-23 10:15:46

created 2023-10-23 10:15:41

id 182395

field	value
prime_id	136560
person_id	9
machine	Using: Digital Ocean Droplet
what	prime
notes	Command: /var/www/clientpool/1/pfgw64 -V -f -tp -q"12681180794248501#-1" >command_output 2>&1 PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11] Primality testing 12681180794248501#-1 [N+1, Brillhart-Lehmer-Selfridge] trial Running N+1 test using discriminant 8521, base 1+sqrt(8521) Generic modular reduction using generic reduction AVX-512 FFT length 1536 on A 12092-bit number Calling Brillhart-Lehmer-Selfridge with factored part 33.43% 1268118079424*8501#-1 is prime! (3.7933s+0.0005s) [Elapsed time: 5.00 seconds]
modified	2023-10-23 10:15:46
created	2023-10-23 10:15:41
id	182395

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