# How to prove a number $N$ is prime

Let $N$ be a natural number. If the sum of the digits(ciphers) of $N$ is $2012$ show that $N$ is prime.

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What about 2012 ones? This N is not a prime as 11 divides it. –  hardmath Dec 1 '12 at 17:21
What about 22222...2222 (1006 of 2's)? –  Tengu Dec 1 '12 at 17:22
Or in fact take any number $m$ with digit sum $2010$ and consider $n=10m+2=2\cdot(5m+1)$. Or any number $m'$ with digit sum $2007$ and consider $n=10m'+5=5\cdot(2m'+1)$. –  Hagen von Eitzen Dec 1 '12 at 17:24