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The 15-Year-Old Who Discovered the Law of Primes

The phrase “The 15-Year-Old Who Discovered the Law of Primes” refers to Carl Friedrich Gauss, who, at age 15 or 16 in 1792 or 1793, discovered that the density of prime numbers decreases logarithmically as numbers increase.  This observation led to the Prime Number Theorem, which approximates the number of primes up to a number $n$ as $n / \ln(n)$.  While Gauss