A famous conjecture. There are many unproved conjectures
regarding prime numbers. One of these was made by Christian
Goldbach (1690-1764) in 1742 in a letter to the great Swiss
mathematician Euler. Goldbach had observed that every even
integer, except 2, seemed representable as the sum of two
primes. Thus 4 = 2 + 2, 6 = 3 + 3, 8 = 5 + 3,..., 48 = 29 +
19,..., 100 = 97 + 3, and so forth. Goldbach seems to have been
an industrious correspondent and to have had the respect of many
of the top mathematicians of his day. It was in a letter to
Goldbach in 1746, for example, that Euler first announced his
remarkable discovery thatii (where i= I/ - 1) is a real number.
But today, about the only mention of Goldbach in the history of
mathematics concerns his teasing conjecture given above.