What is the use of the convolution theorem in multiplying large numbers?

[John Creighto]

I had this dumb though the other day. I can't help wonder if there would ever be a reason to use the convolution theorem to multiply large numbers. It is used to multiply polynomials. But you would need an awful lot of digits to get any efficiency advantages from it and it would not take care of the carry part of the operation.

 

[HallsofIvy]

You might also want to look at this Wikipedia article:
http://en.wikipedia.org/wiki/Fourier_analysis

 

[John Creighto]

You might also want to look at this Wikipedia article:
http://en.wikipedia.org/wiki/Fourier_analysis

Okay, interesting. It seems that they use something like it for a prime number search.

http://en.wikipedia.org/wiki/Great_Internet_Mersenne_Prime_Search

However, there are perhaps superior methods since number theoretic transforms avoid rounding errors:
http://en.wikipedia.org/wiki/Multiplication_algorithm#Fourier_transform_methods