E26 -- Observationes de theoremate quodam Fermatiano aliisque ad numeros primos spectantibus

(Observations on a theorem of Fermat and others on looking at prime numbers)


Euler shows that the fifth Fermat number, 225 +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.

According to the records, it was presented to the St. Petersburg Academy on September 26, 1732.

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