A Leyland prime is a Leyland number that is a prime number. Under the strict definition 
with integers 
, the first values are 17, 593, 32993, 2097593,
.... For example, 
and 
. The OEIS sequence OEIS A094133 prepends 3 as an exception to this strict
definition.
For a prime number of this form, 
and 
must be relatively prime
and have opposite parity. A greatest
common divisor greater than 1 would divide both powers,
while bases of the same parity give an even
number greater than 2. Equal bases give the composite
number 
,
so 
is necessary. These conditions
are not sufficient: 
is a composite number.
."