Show that there are infinitely many primes that start with 2013.
I may be taking the wrong route on this but my idea was to take numbers of the form 2013n +1 which has infinite primes since gcd(2013, 1)= 1 and then take only n = 10^k. where k is a natural number and k 1 but I'm not sure if I can still say that there would be infinitely primes when I limit the set of numbers like that.

Question

Show that there are infinitely many primes that start with 2013.
I may be taking the wrong route on this but my idea was to take numbers of the form 2013n +1 which has infinite primes since gcd(2013, 1)= 1 and then take only n = 10^k. where k is a natural number and k > 1 but I'm not sure if I can still say that there would be infinitely primes when I limit the set of numbers like that.

anonymous · Answer

If this is the wrong method to use then please tell me, but I cannot see another route.