Let and be two classes of Positive integers. Let be the number of integers in which are less than or
equal to , and let be the number of integers in which are less than or equal to . Then if
The four classes of Primes , , , are equinumerous. Similarly, since and are both of the form , and and are both of the form , and are also equinumerous.
See also Bertrand's Postulate, Choquet Theory, Prime Counting Function
Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, pp. 21-22 and 31-32, 1993.