David Wilson writes:

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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].
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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