Brachylog, 24 bytes
;2^(|↰mGl~l×ばつ
Surely there are shorter ways to generate a list of primes...
Brachylog is based on SWI-Prolog and can deal with arbitrarily large integers , but this will quickly run out of memory for even simple lists.
Explanation
;2^( Output = 2^Input
| Or (if the input is not an integer)
↰mG Recursive call of this predicate for all elements of the Input; call the result G
Gl~l Take a list with as many elements as G
N3mṗm≠≜ It must be a list of primes greater than 3 and all different (it always unifies with increasing magnitudes)
;Gz Zip with G
^m Map power
×ばつ Multiply
Brachylog, 24 bytes
;2^(|↰mGl~l×ばつ
Surely there are shorter ways to generate a list of primes...
Explanation
;2^( Output = 2^Input
| Or (if the input is not an integer)
↰mG Recursive call of this predicate for all elements of the Input; call the result G
Gl~l Take a list with as many elements as G
N3mṗm≠≜ It must be a list of primes greater than 3 and all different (it always unifies with increasing magnitudes)
;Gz Zip with G
^m Map power
×ばつ Multiply
Brachylog, 24 bytes
;2^(|↰mGl~l×ばつ
Surely there are shorter ways to generate a list of primes...
Brachylog is based on SWI-Prolog and can deal with arbitrarily large integers , but this will quickly run out of memory for even simple lists.
Explanation
;2^( Output = 2^Input
| Or (if the input is not an integer)
↰mG Recursive call of this predicate for all elements of the Input; call the result G
Gl~l Take a list with as many elements as G
N3mṗm≠≜ It must be a list of primes greater than 3 and all different (it always unifies with increasing magnitudes)
;Gz Zip with G
^m Map power
×ばつ Multiply
Brachylog, 24 bytes
;2^(|↰mGl~l×ばつ
Surely there are shorter ways to generate a list of primes...
Explanation
;2^( Output = 2^Input
| Or (if the input is not an integer)
↰mG Recursive call of this predicate for all elements of the Input; call the result G
Gl~l Take a list with as many elements as G
N3mṗm≠≜ It must be a list of primes greater than 3 and all different (it always unifies with increasing magnitudes)
;Gz Zip with G
^m Map power
×ばつ Multiply