I N T R O D U C T I O N

It is my ambition to say in ten sentences what others say in a whole book.
--> Friedrich Nietzsche

For this reason there isn't introduction. There is a story instead:

(...) in 1903 F. N. Cole (1861-1927) proved that M67 [=(2^67)-1] is not prime.(...) At the October,1903, meeting in New York of the American Mathematical Society, Cole had a paper on the program with the  modest title "On the factorization of large numbers". When the chairman called on him for his paper, Cole - who was always a man of very few words - walked to the board and, saying nothing, proceeded to chalk up the arithmetic for raising 2 to the  sixty- seventh power. Then he carefully subtracted 1. Without  a word he moved over to a clear space on the board and multiplied out, by longhand, 193, 707, 721  *  761, 838, 257, 287.  The two calculations agreed. Mersenne's conjecture - if such  it was - vanished into the limbo of mathematical mythology. For the first and only time on record, an audience of the American Mathematical Society vigorously applauded the author of a paper delivered before it. Cole took his seat without having uttered a word. Nobody asked him a question.                           
--> Eric Temple Bell. 
In: James R. Newman (ed.), Volume I-IV The World of Mathematics. Simon and Schuster, New York 1956, p. 503