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Goldbach's conjecture asserts that every even integer greater than two is the sum of two prime numbers.  For example: 4 = 2 + 2, 6 = 3 + 3, 8 = 3 + 5, and so on.

Goldbach's conjecture asserts that every even integer greater than two is the sum of two prime numbers.  For example: 4 = 2 + 2, 6 = 3 + 3, 8 = 3 + 5, and so on.

This conjecture is one of the oldest unsettled statements in mathematics.  For centuries mathematicians have attempted to prove this statement, without success.  The conjecture is known to hold for numbers less than 3 <math>\cdot</math>10¹⁷.

This conjecture is one of the oldest unsettled statements in mathematics.  For centuries mathematicians have attempted to prove this statement, without success.  The conjecture is known to hold for numbers up to at least 3 <math>\cdot</math>10¹⁷.

===Riemann hypothesis===

===Riemann hypothesis===