4 · 10103958 + 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:4 · 10103958 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Proof-code(s): (*):g375 : Benson, NewPGen, OpenPFGW, Proth.exe
Decimal Digits:103959   (log10 is 103958.60206)
Rank (*):47692 (digit rank is 1)
Entrance Rank (*):654
Currently on list? (*):no
Submitted:12/31/2004 09:46:19 UTC
Last modified:3/11/2023 15:54:10 UTC
Removed (*):11/29/2008 02:50:20 UTC
Database id:72946
Status Flags:none
Score (*):39.6738 (normalized score 0.0048)

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.
Generalized Fermat (archivable *)
Prime on list: no, rank 4797
Subcategory: "Generalized Fermat"
(archival tag id 204986, tag last modified 2024-05-19 19:37:17)

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_id72946
person_id9
machineLinux P4 2.8GHz
whatprime
notesCommand: /home/caldwell/client/pfgw -f -t -q"4*10^103958+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 4*10^103958+1 [N-1, Brillhart-Lehmer-Selfridge] trial factoring to 35531467 Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(49152,20) to FFT(49152,19) Reduced from FFT(49152,19) to FFT(49152,18) Reduced from FFT(49152,18) to FFT(49152,17) Reduced from FFT(49152,17) to FFT(49152,16) 690696 bit request FFT size=(49152,16) Calling Brillhart-Lehmer-Selfridge with factored part 69.90% 4*10^103958+1 is prime! (2124.3900s+0.0100s)
modified2020-07-07 22:30:45
created2004-12-31 10:11:09
id77951

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