164084347 · 16229# + 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:	164084347 · 16229# + 1
Verification status (*):	Proven
Official Comment (*):	Arithmetic progression (5,d=20333209*16229#)
Proof-code(s): (*):	p155 : DavisK, NewPGen, OpenPFGW
Decimal Digits:	7009 (log₁₀ is 7008.7344865925)
Rank (*):	87661 (digit rank is 1)
Entrance Rank (*):	44358
Currently on list? (*):	no
Submitted:	3/4/2009 09:09:57 UTC
Last modified:	3/11/2023 15:54:10 UTC
Database id:	86978
Status Flags:	none
Score (*):	31.3378 (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.

Arithmetic Progressions of Primes (archivable class *)
Prime on list: no, rank 142, weight 46.199261840282
Subcategory: "Arithmetic progression (5,d=*)"
(archival tag id 208923, 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 86978

person_id 9

machine RedHat P4 P4

what trial_divided

notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 164084347 16229 # 1 2>&1 [Elapsed time: 759.230 seconds]

modified 2020-07-07 22:30:38

created 2009-03-04 09:18:01

id 103317

field	value
prime_id	86978
person_id	9
machine	RedHat P4 P4
what	trial_divided
notes	Command: /home/caldwell/client/TrialDiv/TrialDiv -q 164084347 16229 # 1 2>&1 [Elapsed time: 759.230 seconds]
modified	2020-07-07 22:30:38
created	2009-03-04 09:18:01
id	103317

field value

prime_id 86978

person_id 9

machine RedHat P4 P4

what prime

notes Command: /home/caldwell/client/pfgw -t -q"164084347*16229#+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 164084347*16229#+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(3072,21) to FFT(3072,20) Reduced from FFT(3072,20) to FFT(3072,19) Reduced from FFT(3072,19) to FFT(3072,18) Reduced from FFT(3072,18) to FFT(3072,17) Reduced from FFT(3072,17) to FFT(3072,16) 46574 bit request FFT size=(3072,16) Calling Brillhart-Lehmer-Selfridge with factored part 33.36% 164084347*16229#+1 is prime! (34.2100s+0.0000s) [Elapsed time: 35.00 seconds]

modified 2020-07-07 22:30:38

created 2009-03-04 09:23:01

id 103318

field	value
prime_id	86978
person_id	9
machine	RedHat P4 P4
what	prime
notes	Command: /home/caldwell/client/pfgw -t -q"16408434716229#+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 16408434716229#+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(3072,21) to FFT(3072,20) Reduced from FFT(3072,20) to FFT(3072,19) Reduced from FFT(3072,19) to FFT(3072,18) Reduced from FFT(3072,18) to FFT(3072,17) Reduced from FFT(3072,17) to FFT(3072,16) 46574 bit request FFT size=(3072,16) Calling Brillhart-Lehmer-Selfridge with factored part 33.36% 164084347*16229#+1 is prime! (34.2100s+0.0000s) [Elapsed time: 35.00 seconds]
modified	2020-07-07 22:30:38
created	2009-03-04 09:23:01
id	103318

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