# Euler and 1,000,009

Here’s a tale of one the great mathematicians of all time that I heard for the first time this year: the great mathematician published a mistake… which, when it occurs today, is highly professionally embarrassing to modern mathematicians. From Mathematics in Ancient Greece:

In a paper published in the year 1774, [Leonhard] Euler listed [1,000,009] as prime. In a subsequent paper Euler corrected his error and gave the prime factors of the integer, adding that one time he had been under the impression that the integer in question admitted of the unique partition

$1,000,009 = 1000^2 + 3^2$

but that he had since discovered a second partition, namely

$1,000,009 = 235^2 + 972^2$,

which revealed the composite character of the number.

See Wikipedia and/or Mathworld for the details of how this allowed Euler to factor $1,000,009$.