A mathematician, a physicist, and an engineer found themselves caught in an ancient anecdote. Lacking a chemist to brew them an anecdote antidote, they fell to arguing over which of them was to be the butt of the joke ... when suddenly the physicist and the engineer disappeared! Between the spots where they'd been standing, a magician stood glaring at the mathematician.
"Long have those of thy profession sought to ridicule my kin," he said menacingly. "Wherefore then, now that thou art in my power, should I release thee? I shall trap thee in unamusing tales with thy fellow scientists for ever."
"As I see you are a magician," the mathematician began, "will a magic square enable me to avert your power?"
The magician scoffed. "What is thy field of expertise within that arid wasteland, Mathematics?"
"Number theory," the unperturbed1 mathematician replied.
"Ha! Those fools who seek to discover pattern among the prime numbers! In that case, I challenge thee to find a $2015\times2015$ magic square all of whose entries are prime. If thou canst achieve this feat, I shall release thee unharmed; otherwise, thou art my slave for ever!"
Can the mathematician succeed? Give a proof either that such a magic square exists or that it cannot exist. Unlike the unfortunate mathematician, you don't actually need to construct it!
1Well, of course he was unperturbed. Perturbation theory is a branch of analysis, not number theory!