Cunningly multiplied by two a nice prime number (8,3)

I believe the answer is:

american pie

'number' is the definition.
(1971 song or 'number')

'cunningly multiplied by two a nice prime' is the wordplay.
I cannot quite see how this works, but
'a' could be 'an' and 'an' is located in the answer.
This explanation may well be incorrect...

(Another definition for american pie that I've seen is " 1999 US film comedy".)

I've seen this clue in The Times.

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