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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)



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.


Table of n, a(n) for n=1..5.

T. R. Nicely, List of prime gaps

Tomás Oliveira e Silva, Gaps between consecutive primes


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.


Cf. A144140, A192870.

Sequence in context: A020389 A252609 A185680 * A090005 A225714 A158692

Adjacent sequences:  A191855 A191856 A191857 * A191859 A191860 A191861




Alexei Kourbatov, Jun 18 2011



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Last modified December 16 14:48 EST 2018. Contains 318167 sequences. (Running on oeis4.)