#### English Title

Observations on a theory of Fermat and others on looking at prime numbers

#### Enestrom Number

26

#### Fuss Index

23

#### Original Language

Latin

#### English Summaries

Euler shows that the fifth Fermat number, 2^{25} +1 = 4,294,967,297, is not prime because it is divisible by 641, though he does not give any clues about how he discovered this fact. He also tacks on a few "theorems" but says that he does not yet know how to prove them.

#### Published as

Journal article

#### Published Date

1738

#### Written Date

1732

#### Content Summary

Euler shows that the fifth Fermat number, 2^{25}+1 = 4,294,967,297, is not prime because it is divisible by 641, though he does not give any clues about how he discovered this fact. He also tacks on a few "theorems" but says that he does not yet know how to prove them.

#### Original Source Citation

Commentarii academiae scientiarum Petropolitanae, Volume 6, pp. 103-107.

#### Opera Omnia Citation

Series 1, Volume 2, pp.1-5.

#### Record Created

2018-09-25