Tell me more ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
up vote -5 down vote favorite
1

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

share|improve this question
2  
What about 2012 ones? This N is not a prime as 11 divides it. – hardmath Dec 1 '12 at 17:21
2  
What about 22222...2222 (1006 of 2's)? – Tengu Dec 1 '12 at 17:22
2  
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

1 Answer

up vote 4 down vote accepted

Since 10N has the same sum of digits as N, knowing the sum of digits does not imply primality for any such sum base ten (or for that matter, any radix > 1).

In base ten the sum of digits does determine the residue mod 9, a well-known consequence often called "casting out nines".

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.