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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 ...
First, the digits of the number being tested are grouped in blocks of three. The odd numbered groups are summed. The sum of the even numbered groups is then subtracted from the sum of the odd numbered groups. The test number is divisible by 7, 11 or 13 iff the result of the summation is divisible by 7, 11 or 13 respectively. [2] [3] Example:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ... The prime numbers p n , with n ≥ 1 . A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers.
Such method is 6.7% more efficient than MIME-64 which encodes a 24 bit number into 4 printable characters. 89: Largest base for which all left-truncatable primes are known. 90: Nonagesimal: Related to Goormaghtigh conjecture for the generalized repunit numbers (111 in base 90 = 1111111111111 in base 2). 95: Number of printable ASCII characters ...
627: 62 + 70 = 132: 13 + 20 = 33 = 3 × 11. If the number of digits is even, add the first and subtract the last digit from the rest. The result must be divisible by 11. 918,082: the number of digits is even (6) → 1808 + 9 − 2 = 1815: 81 + 1 − 5 = 77 = 7 × 11 If the number of digits is odd, subtract the first and last digit from the rest.
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Fuller called these numbers Scheherazade numbers because they must have a factor of 1001. Scheherazade is the storyteller of One Thousand and One Nights, telling a new story each night to delay her execution. Since n must be at least 13, the primorial must be at least 1·2·3·5·7·11·13, and 7×11×13 = 1001. Fuller also refers to powers of ...
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