Write a function in Python to test whether an integer is prime,

then write a Python script to check Goldbach's conjecture -- that every even integer greater than two is the sum of two primes -- for even integers up to 5,000. For each even integer n in this range, the script should output a pair of primes (p1,p2) with the property that p1+p2=n, and p1 is the smallest prime for which p2=np1is also prime. Finally, identify the integer n in this range such that p1as described above is largest.