3

Part of 2011 Philippine MO

Problems(1)

Consecutive Numbers Containing 2011 Primes

Source: 2011 Philippine Math Olympiad National Stage Problem 3

2011

th prime number is

17483

and the next prime is

17489

. Does there exist a sequence of

2011^{2011}

consecutive positive integers that contain exactly

2011

number theoryprime numberscombinatorial geometrynumber theory unsolved