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The senary numeral system (also known as base-6 or heximal) has six as its base. It has been adopted independently by a small number of cultures. Like decimal, it is a semiprime, though being the product of the only two consecutive numbers that are both prime (2 and 3) it has a high degree of mathematical properties for its size. As six is a superior highly composite number, many of the arguments made in favor of the duodecimal system also apply to this base. == Mathematical properties == Senary may be considered useful in the study of prime numbers, since all primes other than 2 and 3, when expressed in senary, have 1 or 5 as the final digit. In senary the prime numbers are written :2, 3, 5, 11, 15, 21, 25, 31, 35, 45, 51, 101, 105, 111, 115, 125, 135, 141, 151, 155, 201, 211, ... That is, for every prime number ''p'' greater than 3, one has the modular arithmetic relations that either ''p'' ≡ 1 or 5 (mod 6) (that is, 6 divides either ''p'' − 1 or ''p'' − 5); the final digits is a 1 or a 5. This is proved by contradiction. For any integer ''n'': * If ''n'' ≡ 0 (mod 6), 6 | ''n'' * If ''n'' ≡ 2 (mod 6), 2 | ''n'' * If ''n'' ≡ 3 (mod 6), 3 | ''n'' * If ''n'' ≡ 4 (mod 6), 2 | ''n'' Additionally, since the smallest four primes (2, 3, 5, 7) are either divisors or neighbors of 6, senary has simple divisibility tests for many numbers. Furthermore, all even perfect numbers besides 6 have 44 as the final two digits when expressed in senary, which is proven by the fact that every even perfect number is of the form 2''p''−1(2''p''−1), where 2''p''−1 is prime. Senary is also the largest number base ''r'' that has no totatives other than 1 and ''r'' − 1, making its multiplication table highly regular for its size, minimizing the amount of effort required to memorize its table. This property maximizes the probability that the result of an integer multiplication will end in zero, given that neither of its factors do. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「senary」の詳細全文を読む スポンサード リンク
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