A191858 The greatest integer M for which there are no primes between M^(1+1/n) and (M+1)^(1+1/n).

0, 1051, 6776941, 50904310155, 833954771945899

Offset: 1

Author

Alexei Kourbatov, Jun 18 2011

Keywords

• nonn
• hard

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.

Examples

			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.
		

Links

• Thomas R. Nicely, First occurrence prime gaps [For local copy see A000101]
• Tomás Oliveira e Silva, Gaps between consecutive primes

Crossrefs

Cf. A144140, A192870.