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Primes of the form [pc] and related questions
Published online by Cambridge University Press: 18 May 2009
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Much interest has been shown in determining the range of values of c for which the sequence [n]c contains infinitely many primes. The result is an elementary deduction from the prime number theorem, of course, of 0<c≤l. In 1953, Piatetski–Shapiro [9] showed that
for 1<c<12/11, where xc(X) stands for the number of primes in the set {[nc]n≤x}.
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- Copyright © Glasgow Mathematical Journal Trust 1995
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