338707 · 21354830 + 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.

Description:338707 · 21354830 + 1
Verification status (*):Proven
Official Comment (*):Cullen
Proof-code(s): (*):L124 : Rodenkirch, MultiSieve, LLR
Decimal Digits:407850   (log10 is 407849.9988496)
Rank (*):9912 (digit rank is 1)
Entrance Rank (*):35
Currently on list? (*):short
Submitted:8/25/2005 12:41:53 CDT
Last modified:8/25/2005 21:12:18 CDT
Database id:75433
Status Flags:none
Score (*):43.8792 (normalized score 0.4893)

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.
Cullen primes (archivable *)
Prime on list: yes, rank 3
Subcategory: "Cullen primes"
(archival tag id 187064, tag last modified 2009-08-04 21:58:38)

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.
machineLinux P4 2.8GHz
notesCommand: /home/caldwell/client/pfgw -f -t -q"338707*2^1354830+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 338707*2^1354830+1 [N-1, Brillhart-Lehmer-Selfridge] trial factoring to 152360491 Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(196608,19) to FFT(196608,18) Reduced from FFT(196608,18) to FFT(196608,17) Reduced from FFT(196608,17) to FFT(196608,16) 2709706 bit request FFT size=(196608,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 338707*2^1354830+1 is prime! (29810.3456s+0.0011s) [Elapsed time: 29810 seconds]
modified2020-07-07 17:30:43
created2005-08-25 12:55:28

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