13

This number is a prime.

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A four-digit number abcd is divisible by 13 if 13 divides a + 4b + 3c + 12d. d is calculated using the coefficients of a + 4b + 3c which shows if a three-digit number is divisible by 13. b * c / a = 12 and a five-digit number is divisible by 13 if 13 divides a + 4b + 3c + 12d + 9e because the coefficients of c * d / b = 9. multiplying the last two coefficients and dividing by the one before them will always give the next term in this equation and therefore any number of any length can be checked for divisibility by 13. [Homewood]

Submitted: 2019-01-15 13:51:18;   Last Modified: 2019-01-15 15:00:07.
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