The Ramanujan hypothesis is a conjecture in mathematics that relates to the distribution of prime numbers. It was proposed by the Indian mathematician Srinivasa Ramanujan in the early 20th century.
The hypothesis states that the number of prime numbers less than a given number N is approximately equal to the logarithm of N divided by the difference between the logarithm of N and 1. This can be expressed mathematically as:
π(N) ≈ (log N)/(log N - 1),
where π(N) denotes the number of prime numbers less than or equal to N.
The Ramanujan hypothesis is closely related to the famous Riemann hypothesis, which is considered one of the most important unsolved problems in mathematics. The Riemann hypothesis provides a more precise statement about the distribution of prime numbers, and its proof would also imply the truth of the Ramanujan hypothesis.
Despite much effort by mathematicians, the Ramanujan hypothesis remains unproven. However, it is widely believed to be true, and many results have been established that support its validity.
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