Problem 45994. Investigate the frequency of last digits of prime numbers

The last digit of a prime number greater than 5 can be 1, 3, 7, or 9. If the primes are distributed randomly, then these digits should be equally likely. However, mathematicians discovered relatively recently that--as Robert Lemke Oliver put it--these digits "really hate to repeat themselves". In other words, last digits repeat less often than expected.

For example, five primes less than 100 end in a 1 (11, 31, 61, 71, and 91), and none of them are followed by a prime ending in a 1. In fact, none of the primes less than 100 and ending in 3, 7, or 9 are followed by a prime ending in 3, 7, or 9, respectively.

Write a function to compute the frequency of the last digits of primes between 7 and the input number. Return a matrix whose rows correspond to the digits of the first prime and columns correspond to the digits of the next prime. Please remember to (a) omit 2, 3, and 5 and (b) account for the prime following the last prime in your list. For the example given above, the function should return

         0    0.6000    0.4000         0
         0         0    0.3333    0.6667
    0.6667    0.1667         0    0.1667
    0.4000    0.4000    0.2000         0

For example, six primes less than 100 end in 7. They are followed by four primes ending in 1 (including 101), one prime ending in 3, zero primes ending in 7, and one prime ending 9. The frequencies, reported in the third row, are thus 2/3, 1/6, and 1/6.