150209! + 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:	150209! + 1
Verification status (*):	Proven
Official Comment (*):	Factorial
Proof-code(s): (*):	p3 : Dohmen, OpenPFGW
Decimal Digits:	712355 (log₁₀ is 712354.37028954)
Rank (*):	4269 (digit rank is 1)
Entrance Rank (*):	73
Currently on list? (*):	yes
Submitted:	10/31/2011 13:21:31 UTC
Last modified:	3/11/2023 15:54:10 UTC
Database id:	102627
Status Flags:	none
Score (*):	45.592 (normalized score 1.5916)

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 5
Subcategory: "Factorial"
(archival tag id 213604, 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 102627

person_id 9

machine RedHat P4 P4

what prime

notes Command: /home/caldwell/client/pfgw -t -q"150209!+1" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 150209!+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 150211 Running N-1 test using base 150217 Calling Brillhart-Lehmer-Selfridge with factored part 33.45% 150209!+1 is prime! (240480.6224s+2.6547s) [Elapsed time: 2.78 days]

modified 2020-07-07 22:30:30

created 2011-10-31 13:23:01

id 134845

field	value
prime_id	102627
person_id	9
machine	RedHat P4 P4
what	prime
notes	Command: /home/caldwell/client/pfgw -t -q"150209!+1" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 150209!+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 150211 Running N-1 test using base 150217 Calling Brillhart-Lehmer-Selfridge with factored part 33.45% 150209!+1 is prime! (240480.6224s+2.6547s) [Elapsed time: 2.78 days]
modified	2020-07-07 22:30:30
created	2011-10-31 13:23:01
id	134845

field value

prime_id 102627

person_id 9

machine Ditto P4 P4

what trial_divided

notes Command: /home/ditto/client/TrialDiv/TrialDiv -q 1 150209 ! 1 2>&1 [Elapsed time: 59234.044 seconds]

modified 2020-07-07 22:30:30

created 2011-10-31 13:35:02

id 134846

field	value
prime_id	102627
person_id	9
machine	Ditto P4 P4
what	trial_divided
notes	Command: /home/ditto/client/TrialDiv/TrialDiv -q 1 150209 ! 1 2>&1 [Elapsed time: 59234.044 seconds]
modified	2020-07-07 22:30:30
created	2011-10-31 13:35:02
id	134846

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