Prime Numbers Between Two Quadratics: A Useful Result?

[nocat2]

Would it be a useful result to know there is at least one prime between
16x^2+4x-1 and 16x^2+8x-5 for any odd natural number x?

 

[fresh_42]

I'm too lazy to work it out by myself and I'm no expert in number theory neither. But it might help in connection with the following conjecture:[/PLAIN] https://en.wikipedia.org/wiki/Andrica's_conjecture[/URL]
But to be honest. If it's true I doubt that it's unknown.