5 Jun
2003
5 Jun
'03
2 a.m.
David Wilson writes: << Propp's conjecture* would imply a prime between n^2 and (n+1)^2, which conjecture I believe is stil outstanding.
*That for any n >=2 and for each k in [0,n-1], there is at least one prime in the "row" of n consecutive numbers [kn+1,(k+1)n]. ------------------------------------------------------------------------------ ---------------------------------- I guess David Wilson's point is that the interval of 2n numbers [(n-1)^2, n^2], forms the last two rows in Propp's conjecture. But obviously, there's a prime in the first row, and there's one in the second row guaranteed by Bertrand's Postulate. Question: Where does the conjectural territory first begin? [2n+1,3n] ? [3n+1,4n] ? Etc. --Dan