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math.NT2014
Primes in the intervals between primes squared
Kolbjørn Tunstrøm
The set of short intervals between consecutive primes squared has the pleasant---but seemingly unexploited---property that each interval is full…
math.NT2013
The origin of the logarithmic integral in the prime number theorem
Kolbjørn Tunstrøm
We establish why li(x) outperforms x/log x as an estimate for the prime counting function pi(x). The result follows from subdividing the natural numbers into the intervals s_k :={p…