On Primes In Short Intervals

2008/12/29 by Carella, N. A.
#11A41 #11N05 #FOS: Mathematics #General Mathematics (math.GM) #and 11M26

paper · doi:10.48550/arxiv.0812.4965

Abstract

This note discusses the existence of prime numbers in short intervals. An unconditional elementary argument seems to prove the existence of primes in the short intervals [x, x + y], where y >= x^(1/2)(log x)^e, e > 0, and a sufficiently large number x > 0. Further, an extension of Bertrand's postulate to arithmetic progressions will be considered

Related

• Primes in short intervals: Heuristics and calculations
• Arithmetic progressions of primes in short intervals
• A Conditional Explicit Result for the Prime Number Theorem in Short Intervals
• Effective short intervals containing primes
• Note On Prime Gaps And Very Short Intervals