The 100000th prime number is exactly 1299709.
641 divides 2^{32} + 1 exactly.
There are no positive integer solutions to the equation x^4 + y^4 = z^4.
A real number is rational if and only if its decimal expansion is eventually periodic.
The integer 1 is a prime number.
The infinite sum from n=1 to infinity of 1/n^2 equals exactly π²/6.
For any triangle with sides a, b, c where a² + b² = c² then the angle opposite c is exactly 90 degrees AND the converse also holds.
Fewer than 20 percent of the positive integers from 1 to 1000 are prime.
The positive root of x² - x - 1 = 0 is exactly (1 + √5)/2.
The Goldbach conjecture holds for every even integer greater than 2.