Puzzle #152: Prime Births

One fine day, a prime number of babies were born in Whoville. The number of boy babies born was also prime, and so was the number of girl babies born. There were more boys than girls, but it was not at least twice as many. How many of each sex were born that day?

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, May 4, 2016 at noon Pacific Time. I will post the answer shortly after.