number theory, prime

Find the smallest prime in the arithmetic progression an + b , where
a) a = 5, b = 1
b) a = 7, b = 2
c) a = 23, b =13

Thanks very much guys!!!:)

Quote:

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Originally Posted by suedenation

Find the smallest prime in the arithmetic progression an + b , where
a) a = 5, b = 1
b) a = 7, b = 2
c) a = 23, b =13

Thanks very much guys!!!:)

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Just list your number out until you reach a prime (by Dirichelts theorem there will be primes in fact infinitely many).
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a)5n+1:
6,11,--->We got a prime.

b)7n+2:
9,16,23,--->We got a prime.

c)23n+13:
36,59,--->We got a prime.