Primes between consecutive powers

Abstract

This paper updates the explicit interval estimate for primes between consecutive powers. It is shown that there is least one prime between $n^{155}$ and $(n+1{)}^{155}$ for all $n\ge 1$. This result is in part obtained with a new explicit version of Goldston's 1983 estimate for the error in the truncated Riemann--von Mangoldt explicit formula.

This is the published version

References in corpus (3)

• Explicit Interval Estimates for Prime Numbers
• Two explicit divisor sums
• Medium-sized values for the Prime Number Theorem for primes in arithmetic progression

Cited by in corpus (1)

• An algorithm and computation to verify Legendre's Conjecture up to $3.33\cdot 10^{13}$