208003! - 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:	208003! - 1
Verification status (*):	Proven
Official Comment (*):	Factorial
Proof-code(s): (*):	p394 : Fukui, MultiSieve, OpenPFGW
Decimal Digits:	1015843 (log₁₀ is 1015842.9337607)
Rank (*):	2508 (digit rank is 1)
Entrance Rank (*):	167
Currently on list? (*):	yes
Submitted:	7/25/2016 22:23:03 UTC
Last modified:	5/20/2023 20:59:19 UTC
Database id:	121944
Status Flags:	none
Score (*):	46.6812 (normalized score 4.7302)

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 4
Subcategory: "Factorial"
(archival tag id 218371, tag last modified 2023-03-11 15:53:59)

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 121944

person_id 9

machine Using: Xeon 4c+4c 3.5GHz

what prime

notes Command: /home/caldwell/client/pfgw/pfgw64 -tp -q"208003!-1" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 208003!-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 208009, base 1+sqrt(208009) Calling Brillhart-Lehmer-Selfridge with factored part 33.66% 208003!-1 is prime! (114492.3238s+1.5017s) [Elapsed time: 31.80 hours]

modified 2020-07-07 22:30:16

created 2016-07-25 22:31:01

id 167583

field	value
prime_id	121944
person_id	9
machine	Using: Xeon 4c+4c 3.5GHz
what	prime
notes	Command: /home/caldwell/client/pfgw/pfgw64 -tp -q"208003!-1" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 208003!-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 208009, base 1+sqrt(208009) Calling Brillhart-Lehmer-Selfridge with factored part 33.66% 208003!-1 is prime! (114492.3238s+1.5017s) [Elapsed time: 31.80 hours]
modified	2020-07-07 22:30:16
created	2016-07-25 22:31:01
id	167583

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.