The mathematical paradox of a formula that calculates primes
In short: Can you actually write down a single equation to find the nth prime number? While a precise formula exists, its complexity reveals a profound truth about the nature of prime numbers.
In 1964, C. P. Willans engineered an exact formula to determine the nth prime number. The expression involves nested summations, factorials, and trigonometric functions. However, the video explores why this formula is largely impractical for calculation.
The formula is technically correct but computationally inefficient. Because it relies on operations that scale exponentially, it serves more as a theoretical curiosity than a functional tool. It highlights the tension between mathematical existence and practical utility in number theory.
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Sources
- Summary by Intellect · source: An Exact Formula for the Primes: Willans' Formula
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