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**Definition:**Proth number is a number of the form :

[itex]k\cdot 2^n+1[/itex]

where [itex]k[/itex] is an odd positive integer and [itex]n[/itex] is a positive integer such that : [itex]2^n>k[/itex]

My question : If Proth number is prime number are there some other known relations in addition to [itex]2^n>k[/itex] , between exponent [itex]n[/itex] and coefficient [itex]k[/itex] ?