Number Theory
# Prime Numbers

$2^{2014}+ 1007^4$ Is this sum equal to a prime number?

Mr. White is an approximately forty years old father with 4 sons of distinct ages. Writing his age 3 times in succession, we get a 6-digit number that is equal to the product of his age, his wife's age and his 4 sons' ages.

Give the sum of his wife's age and all 4 sons' ages.

How many integers from $1$ to $100$ inclusive can be written as the product of two (not necessarily distinct) primes?

If you can find a computer science or combinatorics approach, post your solution!