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The following is pseudocode which combines Atkin's algorithms 3.1, 3.2, and 3.3 [1] by using a combined set s of all the numbers modulo 60 excluding those which are multiples of the prime numbers 2, 3, and 5, as per the algorithms, for a straightforward version of the algorithm that supports optional bit-packing of the wheel; although not specifically mentioned in the referenced paper, this ...
Add the last digit to twice the rest. The result must be divisible by 8. 56: (5 × 2) + 6 = 16. The last three digits are divisible by 8. [2] [3] 34,152: examine divisibility of just 152: 19 × 8. The sum of the ones digit, double the tens digit, and four times the hundreds digit is divisible by 8. 34,152: 4 × 1 + 5 × 2 + 2 = 16. 9
Accordingly, no number that consists only of a string of repetitions of the same digit in at least one base, can be a prime unless it is a string of 1s in that base. Furthermore, the string must be of prime length, otherwise, if the string is of length mXn, it is divisible by strings of lengths m and n in that base. For example 111111111111111 ...
The tables below list all of the divisors of the numbers 1 to 1000. A divisor of an integer n is an integer m, for which n/m is again an integer (which is necessarily also a divisor of n). For example, 3 is a divisor of 21, since 21/7 = 3 (and therefore 7 is also a divisor of 21). If m is a divisor of n, then so is −m. The tables below only ...
The next number not yet crossed out in the list after 5 is 7; the next step would be to cross out every 7th number in the list after 7, but they are all already crossed out at this point, as these numbers (14, 21, 28) are also multiples of smaller primes because 7 × 7 is greater than 30.
Duff realized that to handle cases where count is not divisible by eight, the assembly programmer's technique of jumping into the loop body could be implemented by interlacing the structures of a switch statement and a loop, putting the switch's case labels at the points of the loop body that correspond to the remainder of count/8: [1]
The number 18 is a harshad number in base 10, because the sum of the digits 1 and 8 is 9, and 18 is divisible by 9.; The Hardy–Ramanujan number (1729) is a harshad number in base 10, since it is divisible by 19, the sum of its digits (1729 = 19 × 91).
Also, 2 is a prime dividing 100, which immediately proves that 100 is not prime. Every positive integer except 1 is divisible by at least one prime number by the Fundamental Theorem of Arithmetic. Therefore the algorithm need only search for prime divisors less than or equal to .