1,1

For any n>0 is there always at least one prime p such that 2^n<=p<=2^n+prime(n)? (checked until n=250 ) In this case, that would be stronger than the Schinzel conjecture : "for m >1 there's at least one prime p such that m<=p<=m+ln(m)^2" since for n >2 prime(n)<ln(2^n)^2=n^2*ln(2).

(PARI) for(n=1, 65, print1(sum(i=2^n, 2^n+prime(n), isprime(i)), ", "))

Cf. A014210.

Sequence in context: A127240 A097561 A048689 this_sequence A095840 A131343 A089051

Adjacent sequences: A069920 A069921 A069922 this_sequence A069924 A069925 A069926

easy,nonn

Benoit Cloitre (benoit7848c(AT)orange.fr), May 05 2002