maksyuki 发表于 oj 分类,标签:

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).


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.


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

Sample Output

2,3 are closest, 7,11 are most distant.

There are no adjacent primes.


Waterloo local 1998.10.17



算法分析:由于问题的规模比较大,不可能将所有的范围内的素数都打表出来,只能将1~sqrt (2 ^ 31 - 1)内的素数先打表出来,然后再对于每个给定的区间(区间长度小于1000000)筛出素数,然后对于打出的素数表,遍历一次并维护相邻两个素数的最大值(和两个下标)和最小值(和两个下标)即可