English Title
On various ways of examining very large numbers, for whether or not they are primes
Enestrom Number
715
Fuss Index
20
Original Language
Latin
Content Summary
Euler reviews the fact that a number with two representations of the form axx+byy cannot be prime, then demonstrates the theorem by applying it to 12091 = axx+byy for (x, y) = (40, 9) and (4, 33), and using this to factor 12091. He proves that if M and N are of the same form, then so is MN. He presents the problem: given a formula axx+byy and a number that can be written in that form in only one way, when can you conclude that the number must be prime? This reduces to a problem in congruent (idoneal) numbers, and Euler gets to repeat his table of 65 such numbers.
Published as
Journal article
Published Date
1802
Written Date
1778
Original Source Citation
Nova Acta Academiae Scientiarum Imperialis Petropolitanae, Volume 13, pp. 14-44.
Opera Omnia Citation
Series 1, Volume 4, pp.303-328.
Record Created
2018-09-25
