- E(7894)/19

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: - E(7894)/19
Verification status (*):External
Official Comment (*):Euler irregular, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):E10 : Doornink, CM
Decimal Digits:25790   (log10 is 25789.946431715)
Rank (*):71389 (digit rank is 1)
Entrance Rank (*):69179
Currently on list? (*):short
Submitted:5/12/2023 15:57:57 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:136041
Status Flags:Verify
Score (*):35.3724 (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.
Euler Irregular primes (archivable *)
Prime on list: yes, rank 4
Subcategory: "Euler Irregular primes"
(archival tag id 228558, tag last modified 2023-10-06 17:37:13)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 50
Subcategory: "ECPP"
(archival tag id 228559, tag last modified 2023-12-16 03:37:30)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

Frank Doornink writes (13 May 2023):  (report abuse)
Originally found to be PRP by David Broadhurst in 2006. For certificate see factordb

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_id136041
person_id9
machineUsing: Digital Ocean Droplet
whatprp
notesPFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 8839581715...9858148799 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Generic modular reduction using generic reduction AVX-512 FFT length 8K, Pass1=128, Pass2=64, clm=1 on A 85673-bit number
Running N-1 test using base 11
Generic modular reduction using generic reduction AVX-512 FFT length 8K, Pass1=128, Pass2=64, clm=1 on A 85673-bit number
Running N+1 test using discriminant 17, base 1+sqrt(17)
Generic modular reduction using generic reduction AVX-512 FFT length 8K, Pass1=128, Pass2=64, clm=1 on A 85673-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 3598/85810 ERROR: ROUND OFF 0.5>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 17, base 1+sqrt(17)
Generic modular reduction using generic reduction AVX-512 FFT length 9K on A 85673-bit number
Calling N+1 BLS with factored part 0.07% and helper 0.05% (0.26% proof)


8839581715...9858148799 is Fermat and Lucas PRP! (38.1503s+0.0096s)
[Elapsed time: 38.00 seconds]
modified2023-05-12 22:06:39
created2023-05-12 22:06:01
id181871

fieldvalue
prime_id136041
person_id9
machineUsing: Digital Ocean Droplet
whatrequested
notespfgw
modified2023-05-12 22:04:34
created2023-05-12 22:04:34
id181870

fieldvalue
prime_id136041
person_id9
machineUsing: Digital Ocean Droplet
whatrequested
notespfgw
modified2023-05-12 22:03:02
created2023-05-12 22:03:02
id181869

fieldvalue
prime_id136041
person_id9
machineUsing: Digital Ocean Droplet
whatrequested
notespfgw
modified2023-05-12 22:03:01
created2023-05-12 22:03:01
id181868

fieldvalue
prime_id136041
person_id9
machineUsing: Digital Ocean Droplet
whatrequested
notespfgw
modified2023-05-12 15:58:01
created2023-05-12 15:58:01
id181864

fieldvalue
prime_id136041
person_id9
machineUsing: Digital Ocean Droplet
whatrequested
notespfgw
modified2023-05-12 15:58:01
created2023-05-12 15:58:01
id181863

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