English Title

On various ways of examining very large numbers, for whether or not they are primes

Authors

Leonhard Euler

Enestrom Number

715

Fuss Index

20

Original Language

Latin

Published as

Journal article

Published Date

1802

Written Date

1778

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.

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

Included in

Mathematics Commons

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