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Wikipedia gives it as

Remove the ISBN 10 check digit from the end
Add 978 to the front
Add the ISBN-13 check digit to the end

The check digit is calculated as per Wikipedia

Take each digit as an element in in an array x_ i.e. the ith digit i the ISBN is x_i e.g. x4 is the 4th digit.
Multiply the even digits by 3 and sum these.
add these to the sum of the odd digits
find the remainder mod 10
subtract from 10 (you have a number 1-10)
This is the result as a number between 1 and 10, unless the figure is 10 then the result is 0

x_13 = (10 - (x_1 + 3x_2 + x_3 + 3x_4 + ... + x_11 + 3x_12) mod10 ) mod 10


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