We define a merge prime as a prime number that can be split into two prime numbers.
Some examples of merge primes are:
- 73 because 7 and 3 are both prime numbers.
- 373 because 37 and 3 are both prime numbers.
What are the last three digits of the sum of all 7-digit merge primes?
- \(9998903\) is a merge prime because \(99989\) and \(3\) are primes.