99993 · 1061858 - 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:99993 · 1061858 - 1
Verification status (*):Proven
Official Comment (*):Near-repdigit
Proof-code(s): (*):p199 : Broadhurst, NewPGen, OpenPFGW
Decimal Digits:61863   (log10 is 61862.999969598)
Rank (*):56790 (digit rank is 1)
Entrance Rank (*):7032
Currently on list? (*):no
Submitted:9/11/2006 00:41:54 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:78458
Status Flags:none
Score (*):38.0738 (normalized score 0.0009)

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.
Near-repdigit (archivable *)
Prime on list: no, rank 128
Subcategory: "Near-repdigit"
(archival tag id 211077, tag last modified 2024-02-07 04:37:20)

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_id78458
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 99993 10 61858 -1 2>&1 [Elapsed time: 8.292 seconds]
modified2020-07-07 22:30:42
created2006-09-11 00:52:02
id86015

fieldvalue
prime_id78458
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -tp -q"99993*10^61858-1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 99993*10^61858-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 19, base 1+sqrt(19) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(28672,20) to FFT(28672,19) Reduced from FFT(28672,19) to FFT(28672,18) Reduced from FFT(28672,18) to FFT(28672,17) Reduced from FFT(28672,17) to FFT(28672,16) 411026 bit request FFT size=(28672,16) Calling Brillhart-Lehmer-Selfridge with factored part 69.89% 99993*10^61858-1 is prime! (1419.7900s+0.0100s) [Elapsed time: 1441 seconds]
modified2020-07-07 22:30:42
created2006-09-11 00:53:01
id86016

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.