24099215682 · 2411# · ((4016535947 · 2411#)2 + 44181895417 · 2411#/6 + 1)/27067608 + 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:24099215682 · 2411# · ((4016535947 · 2411#)2 + 44181895417 · 2411#/6 + 1)/27067608 + 1
Verification status (*):Proven
Official Comment (*):4-Carmichael factor (4)
Proof-code(s): (*):p102 : Frind, Underwood, OpenPFGW
Decimal Digits:3102   (log10 is 3101.3557012068)
Rank (*):99241 (digit rank is 1)
Entrance Rank (*):30382
Currently on list? (*):no
Submitted:1/14/2003 05:50:22 UTC
Last modified:2/4/2026 10:47:28 UTC
Database id:63440
Status Flags:none
Score (*):28.8039 (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.
n-Carmichael factor (tolerated *)
Prime on list: no, rank 7
Subcategory: "4-Carmichael factor (4)"
(archival tag id 175356, 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.
fieldvalue
prime_id63440
person_id9
machineUsing: Digital Ocean Droplet
whatprime
notesPFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 24099215682*2411#*((4016535947*2411#)^2+44181895417*2411#/6+1)/27067608+1 [N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000852517680.txt
Prime_Testing_Warning,


Running N-1 test using base 2423
Generic modular reduction using generic reduction FMA3 FFT length 1K on A 10303-bit number
Running N-1 test using base 2437
Generic modular reduction using generic reduction FMA3 FFT length 1K on A 10303-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 33.38%


24099215682*2411#*((4016535947*2411#)^2+44181895417*2411#/6+1)/27067608+1 is prime! (0.8598s+0.0004s)
[Elapsed time: 5.00 seconds]


Helper File:
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14169343
4016535947
2591
modified2026-02-04 10:47:28
created2026-02-04 10:47:23
id187720

fieldvalue
prime_id63440
person_id9
machineLinux PII 200
whatprp
notesPFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 2423 Primality testing 24099215682*2411#*((4016535947*2411#)^2+44181895417*2411#/6+1)/27067608+1 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2437 Running N+1 test using discriminant 2447, base 88+sqrt(2447) Calling N-1 BLS with factored part 33.17% and helper 0.12% (99.62% proof) 2268303729...3068730241 is Fermat and Lucas PRP! (300.250000 seconds)
modified2003-03-25 17:21:51
created2003-01-20 19:25:34
id66850

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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