Problem A - Prime Distance
The branch of mathematics called number theory is about properties of
numbers. One of the areas that has captured the interest of number
theoreticians for thousands of years is the question of primality. A
prime number is a number that is has no proper factors (it is only
evenly divisible by 1 and itself). The first prime numbers are
2,3,5,7 but they quickly become less frequent. One of the interesting
questions is how dense they are in various ranges. Adjacent primes
are two numbers that are both primes, but there are no other prime
numbers between the adjacent primes. For example, 2,3 are the only
adjacent primes that are also adjacent numbers.
Your program is given 2 numbers: L and U
(1<=L<U<=2,147,483,647), and you are to find the two
adjacent primes C1 and C2 (L<=C1<C2<=U) that are closest
(i.e. C2-C1 is the minimum). If there are other pairs
that are the same distance apart, use the first pair. You are
also to find the two adjacent primes D1 and D2 (L<=D1<D2<=U)
where D1 and D2 are as distant from each other as possible (again
choosing the first pair if there is a tie).
Input
Each line of input will contain two positive integers, L and
U, with L < U. The difference between L and U will
not exceed 1,000,000.
Output
For each L and U,
the output will either be the statement that there are no adjacent
primes (because there are less than two primes between the two given
numbers) or a line giving the two pairs of adjacent primes.
Sample Input
2 17
14 17
Output for Sample Input
2,3 are closest, 7,11 are most distant.
There are no adjacent primes.