"On being requested to give the factors which would produce the
number 247,483, he immediately named 941 and 263, which are the only
two numbers from the multiplication of which it would result. On
171,395 being proposed, he named 5 x 34,279, 7 x 24,485, 59 x 2905,
83 x 2065, 35 x 4897, 295 x 581, and 413 x 415.

"He was then asked to give the factors of 36,083, but he immediately
replied that it had none, which was really the case, this being a
prime number. Other numbers being proposed to him indiscriminately,
he always succeeded in giving the correct factors except in the case
of prime numbers, which he generally discovered almost as soon as
they were proposed to him. The number 4,294,967,297, which is 2^32 +
1, having been given him, he discovered, as Euler had previously
done, that it was not the prime number which Fermat had supposed it
to be, but that it is the product of the factors 6,700,417 x 641.
The solution of this problem was only given after the lapse of some
weeks, but the method he took to obtain it clearly showed that he had
not derived his information from any extraneous source.

"When he was asked to multiply together numbers both consisting of
more than these figures, he seemed to decompose one or both of them
into its factors, and to work with them separately. Thus, on being
asked to give the square of 4395, he multiplied 293 by itself, and
then twice multiplied the product by 15. And on being asked to tell
the square of 999,999 he obtained the correct result,
999,998,000,001, by twice multiplying the square of 37,037 by 27. He
then of his own accord multiplied that product by 49, and said that
the result (viz., 48,999,902,000,049) was equal to the square of
6,999,993. He afterwards multiplied this product by 49, and observed