2011 AMC 8 Problems/Problem 24
In how many ways can be written as the sum of two primes?
Solution
For the sum of two numbers to be odd, one must be odd and the other must be even, because All odd numbers are of the form where n is an integer, and all even numbers are of the form
where m is an integer.
and
is an integer because
and
are both integers.
The only even prime number is
so our only combination could be
and
However,
is clearly divisible by
so the number of ways
can be written as the sum of two primes is
Solution #2: The estoy regular theorem states that any number in the form cannot be expressed as the sum of
primes.
satisfies this condition; thus,
can not be expressed as the sum of
primes. The answer is
.
See Also
2011 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 23 |
Followed by Problem 25 | |
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