[seqfan] prime conjecture

[Dmitry Kamenetsky]

Hello all,

First of all Happy New Year to everyone! Now for some serious stuff. I have
the following conjecture:

For every n>=1 and k (1<=k<=n) there is at least one prime in the interval
[k*n!+1, k*n!+n*n].


I've checked that this conjecture works for all n<=18, but I cannot prove it
for all n. Can anyone help me? Also it would be nice to get a tighter bound
on the upper range.


Sincerely,
Dmitry Kamenetsky