Senary
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In mathematics, a senary numeral system is a base-6 numeral system. The name heximal is also valid for such a numeral system, but is deprecated to avoid confusion with the more often used hexadecimal number base, colloquially known as 'hex'.
Senary may be considered useful in the study of prime numbers since all primes, when expressed in base-six, other than 2 and 3 have 1 or 5 as the final digit. Writing out the prime numbers in base-six (and using the subscript 6 to denote that these are senary numbers), the first few primes are
- [2_6,3_6,5_6,11_6,15_6,21_6,25_6,31_6,35_6,45_6,51_6,]
- [101_6,105_6,111_6,115_6,125_6,\ldots]
Base six can be counted on hands by using each hand to represent a digit, 0 to 5. The digit zero is represented by a fist (no fingers extended). Using this method, it is possible for one person to represent values from zero to 55senary (= 35decimal), rather than the usual ten obtained in standard finger-counting.
Fractions
Due to the fact that six is the product of the first two prime numbers and is adjacent to the next two prime numbers, many senary fractions have simple representations:
Decimal Senary 1/2 1/2 = 0.3 1/3 1/3 = 0.2 1/4 1/4 = 0.13 1/5 1/5 = 0.1111 recurring 1/6 1/10 = 0.1 1/7 1/11 = 0.05050505 recurring 1/8 1/12 = 0.043 1/9 1/13 = 0.04 1/10 1/14 = 0.03333 recurring 1/12 1/20 = 0.03 1/14 1/22 = 0.023232323 recurring 1/15 1/23 = 0.022222222 recurring 1/16 1/24 = 0.0213 1/18 1/30 = 0.02 1/20 1/32 = 0.014444444 recurring
Closely Related Number Systems
- Hexatridecimal base 36
- Duodecimal base 12
See also
External links
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