primV(180906)

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:primV(180906)
Verification status (*):PRP
Official Comment (*):Lucas primitive part, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):E1 : Batalov, CM
Decimal Digits:22905   (log10 is 22904.987572087)
Rank (*):73098 (digit rank is 1)
Entrance Rank (*):73049
Currently on list? (*):short
Submitted:9/30/2024 22:12:27 UTC
Last modified:9/30/2024 23:37:10 UTC
Database id:138595
Status Flags:Verify
Score (*):35.0057 (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.
Lucas primitive part (archivable *)
Prime on list: yes, rank 7
Subcategory: "Lucas primitive part"
(archival tag id 229665, tag last modified 2024-10-11 22:37:11)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 82
Subcategory: "ECPP"
(archival tag id 229666, tag last modified 2024-10-11 22:37:10)

User comments about this prime (disclaimer):

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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.
fieldvalue
prime_id138595
person_id9
machineUsing: Digital Ocean Droplet
whatprp
notesPFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 9717892427...6288988001 [N-1/N+1, Brillhart-Lehmer-Selfridge]
trial


Running N-1 test using base 17
Generic modular reduction using generic reduction AVX-512 FFT length 7680 on A 76089-bit number
Running N-1 test using base 29
Generic modular reduction using generic reduction AVX-512 FFT length 7680 on A 76089-bit number
Running N+1 test using discriminant 53, base 6+sqrt(53)
Generic modular reduction using generic reduction AVX-512 FFT length 7680 on A 76089-bit number
Calling N-1 BLS with factored part 0.31% and helper 0.01% (0.94% proof)


9717892427...6288988001 is Fermat and Lucas PRP! (25.3595s+0.0047s)
[Elapsed time: 30.00 seconds]
modified2024-09-30 22:41:24
created2024-09-30 22:40:49
id184439

Query times: 0.0043 seconds to select prime, 0.0005 seconds to seek comments.
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