Bertrand’s postulate

mathematics

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June 22, 2026

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Bertrand's postulate, also known as Bertrand's conjecture, is a theorem in number theory that states there is always at least one prime number between any integer n greater than 1 and its double, 2n. This was conjectured by Joseph Bertrand in 1845 and later proven by Pafnuty Chebyshev.1

A prime number is a positive integer greater than 1 that has only two divisors: 1 and itself. Examples include 2, 3, 5, 7, and 11. The distribution of prime numbers is a fundamental area of study in number theory, with theorems like the Prime Number Theorem and Dirichlet's theorem exploring their patterns.123

While Bertrand's name is associated with this postulate, he is also known for his work in differential equations, probability, and differential geometry.4

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Paul Erdős
…a stunningly simple proof of Bertrand’s postulate, which says that a prime can always be found between any integer (greater than 1) and its double. Even at this early point in his career, Erdős had definite ideas about mathematical elegance. He believed that God, whom he affectionately called the S.F.…
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…a stunningly simple proof of Bertrand’s postulate, which says that a prime can always be found between any integer (greater than 1) and its double. Even at this early point in his career, Erdős had definite ideas about mathematical elegance. He believed that God, whom he affectionately called the S.F.…
Read More