Thread: 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!!!

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!!!

Just list your number out until you reach a prime (by Dirichelts theorem there will be primes in fact infinitely many).
---
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.