# 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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