Hardy Ramanujam theorem states that the number of prime factors of n will approximately be log(log(n)) for most natural numbers n
5192 has 2 distinct prime factors and log(log(5192)) = 2.1615
51242183 has 3 distinct prime facts and log(log(51242183)) = 2.8765
As the statement quotes, it is only an approximation. There are counter examples such as
510510 has 7 distinct prime factors but log(log(510510)) = 2.5759
1048576 has 1 prime factor but log(log(1048576)) = 2.62922
This theorem is mainly used in approximation algorithms and its proof lead to bigger concepts in probability theory.
The number of distinct prime factors is/are 3 The value of log(log(n)) is 2.8765
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- Chinese Remainder Theorem | Set 1 (Introduction)
- Wilson's Theorem
- Zeckendorf's Theorem (Non-Neighbouring Fibonacci Representation)
- Compute nCr % p | Set 2 (Lucas Theorem)
- Chinese Remainder Theorem | Set 2 (Inverse Modulo based Implementation)
- Combinatorial Game Theory | Set 4 (Sprague - Grundy Theorem)
- Using Chinese Remainder Theorem to Combine Modular equations
- Corollaries of Binomial Theorem
- Fermat's little theorem
- Nicomachus’s Theorem (Sum of k-th group of odd positive numbers)
- Midy's theorem
- Extended Midy's theorem
- Fermat's Last Theorem
- Nicomachu's Theorem
- Rosser's Theorem
- Euclid Euler Theorem
- Lagrange's four square theorem
- Vantieghems Theorem for Primality Test
- Dilworth's Theorem
- An application on Bertrand's ballot theorem
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