- The folowing is just a curio, and of no great import, but anyway...
Motivated by the fact that the integer part of (3^33/33^3) is prime,
I looked at the integer part of (33333333/3^3)^3+k.(333/3^3), and
found it prime when k=4. The left part of the equation is just the
integer part of repunit(n)^3/(3^6), and the right part is just 12.k.
So here is the curio: between 8 an 18, whenever the left part was not
even, I could find a small k such that the equation was prime, viz.,
I didn't look beyond 18. Seems like a curiously high density of
prime numbers to me, but then again...