Inquiring on whether or not the number 100009 is prime
Euler shows that 1,000,009 is not prime by showing that it can be written as the sum of two squares in more than one way. This corrected a published list of primes that had included 1,000,009. He also shows that 1,000,081 is prime by showing that it can be written as the sum of two squares in only one way. (Based on Jordan Bell's translation abstract.)
Original Source Citation
Nova Acta Academiae Scientiarum Imperialis Petropolitanae, Volume 10, pp. 63-73.
Opera Omnia Citation
Series 1, Volume 4, pp.245-254.