Question

One for Joe and number theory types.

n, n+2,n+6,n+8 are prime (n>5)

What is the remainder when n is divided by 15

(Going to cut some trees now)

Answer 1

The key here is that n + 4 is not prime. This to me suggests that the last digit of the number is a 1, since for n = {any number ending in a 1, greater than 5}, n + 4 will never be prime because it will be divisible by 5.

Looking for numbers ending in a "1", I think 101 is a good candidate. Plug in 101, 103, 107, and 109 and you will find that they are indeed all prime.

As for the remainder, 101 = 6 * 15 + 11 so R = 11.

Answer 2

Yes, u r on the right track here, a bit short of a complete demonstration.

Of n, n+2,n+4,n+6, n+8, one of them is divisible by 5 and of any three in succession, one is divisible by 3.