As a Sunday reflection, this from the first volume of Greg Ross's Futility Closet:
"In 1643, Marin Mersenne wrote to Pierre de Fermat asking whether 100895598169 were a prime number.
Fermat replied immediately that it's the product of 898423 and 112303, both of which are prime.
To this day, no one knows how he knew this. Has a powerful factoring technique been lost?"
[Additionally, be sure to check out my interview this morning at MathTango with Dr. Mircea Pitici, editor of "The Best Writing on Mathematics" series.]