Problem 47950. Test the generalized Legendre conjecture

The Legendre conjecture states that for every integer n there is a prime number between n^2 and (n+1)^2. The generalized Legendre conjecture (GLC) is that there is a prime number between n^K and (n+1)^K; a further conjecture is that the smallest K possible is log(1151)/log(95).
Write a function that takes a value of K, which you can assume to be less than log(1151)/log(95), and determines the first value of n for which the GLC fails as well as the interval [n^K (n+1)^K].
Solve

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42.86% Correct | 57.14% Incorrect
Last Solution submitted on Aug 18, 2025

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