This article uses technical mathematical notation for logarithms. All instances of log(x) without a subscript base should be interpreted as a natural logarithm, also commonly written as ln(x) or loge(x).
Existence of a prime number between any number and its double
This statement was first conjectured in 1845 by Joseph Bertrand[2] (1822–1900). Bertrand himself verified his statement for all integers .
His conjecture was completely proved by Chebyshev (1821–1894) in 1852[3] and so the postulate is also called the Bertrand–Chebyshev theorem or Chebyshev's theorem. Chebyshev's theorem can also be stated as a relationship with , the prime-counting function (number of primes less than or equal to ):