Longest Prime Subsequence

Given an array of size N ( N) ( all elements are less than or equal to 300 and greater than 1) you need to find the length of the longest subsequence which follows the following property : Let x[1]... x[n] be a subsequence , let p[1],p[2]..p[m] be prime numbers which divide atleast one of the numbers in x[1],..x[n] . Now for each p from 1 to m lets do the following let productX ( a variable ) =1