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Old 2015-01-17, 18:37   #1
davar55
 
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May 2004
New York City

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Default On Leyland Primes

Let's call a prime p that can be written in the form p = x^y + y^x for integral x > y > 1 (or x=y=1 or x=2,y=1) a Leyland-alpha prime.

Let's call a prime p that can be written in the form p = x^y - y^x > 0 for integral x,y a Leyland-beta prime.

Find primes p that can be expressed as both an L-alpha and L-beta prime simultaneously (with different x,y).
Find primes p that can be expressed in at least two different ways as L-alpha or L-beta primes (with different x,y).

I don't currently know if there are any.

Last fiddled with by davar55 on 2015-01-17 at 19:23
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