Maier's theorem
In number theory, Maier's theorem is a theorem due to Helmut Maier about the numbers of primes in short intervals for which Cramér's probabilistic model of primes gives a wrong answer. The theorem states that if π {\displaystyle \pi } is the prime-counting function and λ > 1 {\displaystyle \lambda >1} , then π ( x + ( log x ) λ ) − π ( x ) ( log x ) λ − 1 {\displaystyle {\frac {\pi (x+(\log x)^{\lambda })-\pi (x)}{(\log x)^{\lambda -1}}}} does not have a limit as x {\displaystyle x} tends to infinity; more precisely the limit superior is greater than 1, and the limit inferior is less than 1.