The Riemann Hypothesis appeared in 1859. It is based on the Zeta function, which was actually first used by Leonard Euler (1707-1783) in 1777. The Zeta function is defined for all real numbers greater than 1. (I would write the function here but I do not have an equation editor). Its signifigance as Euler showed is that this Zeta function can be expressed diffrently involving ONLY PRIME NUMBERS. This result is called the "Euler-Product Formula" (you can look it up on www.wikipedia.com). Thus there is a relationship between the Zeta function (all the numbers) and prime numbers in a single equation!
Later on Riemann extended the definition for the Zeta function (meaning it was defined for complex numbers besides for the reals), thus this generalization of the Zeta function came to be know as Riemann's Zeta Function. Riemann was interested in finding it zeros (the values for which the function is zero, i.e. solving the zeta equation). There are trivial solution (the obvious non-interesing ones) and the non-trivial. Riemann realized that all the non-trivial solutions had the form 1/2+ai.
Thus, "The non-trivial zeros of the Zeta function have real part equal to 1/2."
Hence to prove, the statement before this one is to prove the Riemann Hypothesis. The Hypothesis is based on zeros, the zeros are based on the zeta function, the zeta function is based on the primes. Thus, this problem concerns prime numbers.