Inspired by Project Euler n°28 and 58.

A n x n spiral matrix is obtained by starting with the number 1 and moving to the right in a clockwise direction.

For example with n=5, the spiral matrix is :

                       21 22 23 24 25
                       20  7  8  9 10
                       19  6  1  2 11
                       18  5  4  3 12
                       17 16 15 14 13

The sum of the numbers on the diagonals is 101 (See problem 2340) and you have 5 primes (3, 5, 7, 13, 17) out of the 9 numbers lying along both diagonals. So the prime ratio is 5/9 ≈ 55%.

With a 7x7 spiral matrix, the ratio is 62% (8 primes out of the 13 diagonal numbers).

What is the side length (always odd) of the square spiral for which the ratio of primes along both diagonals FIRST falls below p% ? (0<p<1)