Linear Functions

Hi, 

From the way f(x) is defined, we can conclude that if we have some number like a, and another number like b, such that b is greater than a, then f(b) contains f(a) in it, plus other prime numbers that come between a and b. For example, as the question suggests, f(8) contains all the prime numbers that come before f(4), and one other prime number, that comes between 4 and 8, which is, of course, 5. In other words, f(8) = f(4) + 5. With this hint, I think you can now answer the problem. You can then read the lines below to check your answer :)

 f(86) contains the sum of all the prime numbers that are included in f(82), plus the number 83 that comes after 82, so:

f(86) - f(82) = 83.