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At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: 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:
field (help) | value |
Description: | 346762232768 + 1 |
Verification status (*): | Proven |
Official Comment: | Generalized Fermat |
Proof-code(s): (*): | p316 : Yama, GeneFer, AthGFNSieve, PrimeGrid, OpenPFGW |
Decimal Digits: | 214304 (log10 is 214303.76037182) |
Rank (*): | 22345 (digit rank is 1) |
Entrance Rank (*): | 2010 |
Currently on list? (*): | no |
Submitted: | 1/20/2011 04:43:33 CDT |
Last modified: | 2/13/2011 12:14:57 CDT |
Removed (*): | 2/26/2012 12:15:11 CDT |
Database id: | 97524 |
Status Flags: | none |
Score (*): | 41.9008 (normalized score 0.1143) |
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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 1111
Subcategory: "Generalized Fermat"
(archival tag id 213093, tag last modified 2019-12-04 09:50:21)
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.
field | value |
prime_id | 97524 |
person_id | 9 |
machine | RedHat P4 P4 |
what | trial_divided |
notes | Command: /home/caldwell/client/TrialDiv/TrialDiv -q 1 3467622 32768 1 2>&1 [Elapsed time: 8.191 seconds]
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modified | 2011-12-27 16:48:35 |
created | 2011-01-20 04:48:09 |
id | 124438 |
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field | value |
prime_id | 97524 |
person_id | 9 |
machine | Ditto P4 P4 |
what | prime |
notes | Command: /home/ditto/client/pfgw -t -q"3467622^32768+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 3467622^32768+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 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) 1423812 bit request FFT size=(98304,16) Calling Brillhart-Lehmer-Selfridge with factored part 88.10% 3467622^32768+1 is prime! (-287.0246s+0.0500s) [Elapsed time: 2.59 hours]
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modified | 2011-03-25 10:27:31 |
created | 2011-01-20 05:08:01 |
id | 124440 |
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Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.
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