102000007 - 101127194 - 10872812 - 1

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:102000007 - 101127194 - 10872812 - 1
Verification status (*):Proven
Official Comment (*):Palindrome
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p423 : Propper, Batalov, EMsieve, OpenPFGW
Decimal Digits:2000007   (log10 is 2000007)
Rank (*):277 (digit rank is 1)
Entrance Rank (*):254
Currently on list? (*):short
Submitted:1/12/2024 20:49:34 UTC
Last modified:1/17/2024 08:37:10 UTC
Database id:136879
Status Flags:none
Score (*):48.7587 (normalized score 41.4862)

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.
Palindrome (archivable *)
Prime on list: yes, rank 1
Subcategory: "Palindrome"
(archival tag id 229157, tag last modified 2024-01-17 08:37:12)

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.

Serge Batalov writes (12 Jan 2024):  (report abuse)
A near-near-repdigit, palindrome prime (decimal expansion is all 'nines' except two 'eights', equidistant from 'ends').
A sieve is sketched out in this mersenneforum post.

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.
machineUsing: Digital Ocean Droplet
notesCommand: /var/www/clientpool/1/pfgw64 -V -f -tp -q"10^2000007-10^1127194-10^872812-1" >command_output 2>&1
PFGW Version [GWNUM 30.11]
Primality testing 10^2000007-10^1127194-10^872812-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
Generic modular reduction using generic reduction AVX-512 FFT length 672K, Pass1=1344, Pass2=512, clm=1 on A 6643880-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 39/6643887 ERROR: ROUND OFF 0.49613>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 3, base 1+sqrt(3)
Generic modular reduction using generic reduction AVX-512 FFT length 720K, Pass1=1152, Pass2=640, clm=1 on A 6643880-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 43.64%

10^2000007-10^1127194-10^872812-1 is prime! (377248.0194s+0.0302s)
[Elapsed time: 4.37 days]
modified2024-01-17 08:11:38
created2024-01-12 23:24:09

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