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Revision as of 20:29, 7 May 2015

Problem

The difference between two prime numbers is $11$. Find their sum.

Solution

We know that any prime number, excluding $2$, is congruent to $1 \pmod 2$. Thus, if both of the primes are not $2$, their difference would be congruent to $0 \pmod 2$. Because $11 \equiv 1 \pmod 2$, one of the primes must be $2$. It follows that the other prime must then be $13$. Therefore, the sum of the two is $13+2=\boxed{15}$.

See also

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