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A proof which can be accomplished using only real numbers (i.e., real analysis instead of complex analysis; Hoffman 1998, pp. 92-93).

The extended complex plane is the name given to the complex plane with a point at infinity attached: C union {infty^~}, where infty^~ denotes complex infinity. It is also ...

The field of rationals is the set of rational numbers, which form a field. This field is commonly denoted Q (doublestruck Q).

If x_1<x_2<...<x_n denote the zeros of p_n(x), there exist real numbers lambda_1,lambda_2,...,lambda_n such that ...

Grimm conjectured that if n+1, n+2, ..., n+k are all composite numbers, then there are distinct primes p_(i_j) such that p_(i_j)|(n+j) for 1<=j<=k.

The axis in the complex plane corresponding to zero real part, R[z]=0.

A pair of values x and y one or both of which is complex.

A line in the complex plane with slope +/-i. An isotropic line passes through either of the circular points at infinity. Isotropic lines are perpendicular to themselves.

The portion of the complex plane z=x+iy with real part R[z]<0.

Lehmer's formula is a formula for the prime counting function, pi(x) = (1) where |_x_| is the floor function, a = pi(x^(1/4)) (2) b = pi(x^(1/2)) (3) b_i = pi(sqrt(x/p_i)) ...