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 A191858 The greatest integer M for which there are no primes between M^(1+1/n) and (M+1)^(1+1/n) 1
 0, 1051, 6776941, 50904310155, 833954771945899 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Terms are conjectural, even under the Riemann Hypothesis. (1) The initial term a(1)=0 gives a simple restatement of Legendre's conjecture: There are no primes between 0^2 and 1^2, but there is a prime between m^2 and (m+1)^2 for m>0. (2) Lists of known maximum prime gaps and known first occurrences of prime gaps help verify the initial terms in this sequence. However, a lengthy computation would be needed for subsequent terms. LINKS T. R. Nicely, List of prime gaps Tomás Oliveira e Silva, Gaps between consecutive primes EXAMPLE The second term is a(2)=1051 because there are no primes between 1051^(3/2) and 1052^(3/2), but there is at least one prime between m^(3/2) and (m+1)^(3/2) for m>1051. CROSSREFS Cf. A144140, A192870. Sequence in context: A020389 A252609 A185680 * A090005 A225714 A158692 Adjacent sequences:  A191855 A191856 A191857 * A191859 A191860 A191861 KEYWORD nonn,hard AUTHOR Alexei Kourbatov, Jun 18 2011 STATUS approved

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Last modified October 23 16:46 EDT 2019. Contains 328373 sequences. (Running on oeis4.)