353270032768 + 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:||353270032768 + 1|
|Verification status (*):||Proven|
|Official Comment (*):||Generalized Fermat|
|Proof-code(s): (*):||p316 : Yama, GeneFer, AthGFNSieve, PrimeGrid, OpenPFGW|
|Decimal Digits:||214569 (log10 is 214568.36225697)|
|Rank (*):||26257 (digit rank is 1)|
|Entrance Rank (*):||2021|
|Currently on list? (*):||no|
|Submitted:||1/24/2011 09:03:05 CDT|
|Last modified:||2/13/2011 12:14:42 CDT|
|Removed (*):||2/27/2012 08:18:16 CDT|
|Score (*):||41.9046 (normalized score 0.0653)|
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.
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 97679 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/TrialDiv/TrialDiv -q 1 3532700 32768 1 2>&1 [Elapsed time: 7.477 seconds] modified 2020-07-07 17:30:32 created 2011-01-24 09:05:02 id 124747
field value prime_id 97679 person_id 9 machine Ditto P4 P4 what prime notes Command: /home/ditto/client/pfgw -t -q"3532700^32768+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 3532700^32768+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 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) 1425570 bit request FFT size=(98304,16) Calling Brillhart-Lehmer-Selfridge with factored part 69.46% 3532700^32768+1 is prime! (-1518.0446s+0.0400s) [Elapsed time: 2.01 hours] modified 2020-07-07 17:30:32 created 2011-01-24 09:08:02 id 124748