Is this problem still open? I know that Henri Brocard conjectured that there are at least four primes in the interval between each pair of consecutive squares of primes from nine onward. http://mathworld.wolfram.com/BrocardsConjecture.html
I know that Brocard's conjecture remains open. I am asking if there is yet a proof for only one prime between each pair of consecutive squares of primes. Is this a problem with or without a name? Where can I find a reference about it or any information on progress made on it?