218252832768 - 218252816384 + 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:218252832768 - 218252816384 + 1
Verification status (*):Proven
Official Comment (*):Generalized unique
Proof-code(s): (*):f7 : Heuer, ForEis, PhiSieve, PIES, OpenPFGW
Decimal Digits:207716   (log10 is 207715.03551436)
Rank (*):30799 (digit rank is 2)
Entrance Rank (*):344
Currently on list? (*):no
Submitted:2/21/2007 13:01:02 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:79476
Status Flags:none
Score (*):41.8047 (normalized score 0.0397)

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 Unique (archivable *)
Prime on list: no, rank 165
Subcategory: "Generalized Unique"
(archival tag id 224229, tag last modified 2023-12-18 15:37:22)

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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -t -q"Phi(3,-2182528^16384)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing Phi(3,-2182528^16384) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(98304,20) to FFT(98304,19) Reduced from FFT(98304,19) to FFT(98304,18) Reduced from FFT(98304,18) to FFT(98304,17) Reduced from FFT(98304,17) to FFT(98304,16) 1380038 bit request FFT size=(98304,16) Calling Brillhart-Lehmer-Selfridge with factored part 36.03% Phi(3,-2182528^16384) is prime! (-719.4546s+0.7600s) [Elapsed time: 7980 seconds]
modified2020-07-07 22:30:41
created2007-02-21 13:02:33

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -o -f1{98304} -q"Phi(3,-2182528^16384)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Factoring numbers to 1% of normal. Using modular factorization: {98304} trial factoring to 13968951486 Phi(3,-2182528^16384) has no small factor. [Elapsed time: 18.429 seconds]
modified2020-07-07 22:30:41
created2007-02-21 13:22:01

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