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Fermat$501553$ - translation to English
POSITIVE INTEGER OF THE FORM (2^(2^N))+1
Fermat prime; Fermat numbers; 4294967297 (number); Fermat primes; Fermat Numbers; Generalized Fermat number; Generalized Fermat prime; Fermat Primes; Fermat Prime; 4294967297; Primality of Fermat numbers; Factorization of Fermat numbers; Generalized Fermat numbers; Generalized Fermat primes; Generalized Fermat
Fermat
n. Pierre de Fermat (1601-1665), matematico francese, il primo ad applicare il calcolo differenziale nella ricerca delle tangenti. Condivise con Pascal la scoperta del calcolo delle probabilità.
Pierre de Fermat
![The 1670 edition of [[Diophantus]]'s ''[[Arithmetica]]'' includes Fermat's commentary, referred to as his "Last Theorem" (''Observatio Domini Petri de Fermat''), posthumously published by his son](https://commons.wikimedia.org/wiki/Special:FilePath/Diophantus-II-8-Fermat.jpg?width=200 "The 1670 edition of [[Diophantus]]'s ''[[Arithmetica]]'' includes Fermat's commentary, referred to as his \"Last Theorem\" (''Observatio Domini Petri de Fermat''), posthumously published by his son")
![Place of burial of Pierre de Fermat in Place Jean Jaurés, [[Castres]]. Translation of the plaque: in this place was buried on January 13, 1665, Pierre de Fermat, councillor at the Chambre de l'Édit (a court established by the [[Edict of Nantes]]) and mathematician of great renown, celebrated for his theorem, an + bn ≠ cn for n>2](https://commons.wikimedia.org/wiki/Special:FilePath/Fermat burial plaque.jpg?width=200 "Place of burial of Pierre de Fermat in Place Jean Jaurés, [[Castres]]. Translation of the plaque: in this place was buried on January 13, 1665, Pierre de Fermat, councillor at the Chambre de l'Édit (a court established by the [[Edict of Nantes]]) and mathematician of great renown, celebrated for his theorem, an + bn ≠ cn for n>2")
![Monument to Fermat in [[Beaumont-de-Lomagne]] in [[Tarn-et-Garonne]], southern France](https://commons.wikimedia.org/wiki/Special:FilePath/Beaumont-de-Lomagne - Monument à Fermat.jpg?width=200 "Monument to Fermat in [[Beaumont-de-Lomagne]] in [[Tarn-et-Garonne]], southern France")
![Bust in the Salle Henri-Martin in the [[Capitole de Toulouse]]](https://commons.wikimedia.org/wiki/Special:FilePath/Capitole Toulouse - Salle Henri-Martin - Buste de Pierre de Fermat.jpg?width=200 "Bust in the Salle Henri-Martin in the [[Capitole de Toulouse]]")
![[[Holographic will]] handwritten by Fermat on 4 March 1660, now kept at the Departmental Archives of [[Haute-Garonne]], in [[Toulouse]]](https://commons.wikimedia.org/wiki/Special:FilePath/Fermats will.jpg?width=200 "[[Holographic will]] handwritten by Fermat on 4 March 1660, now kept at the Departmental Archives of [[Haute-Garonne]], in [[Toulouse]]")
FRENCH MATHEMATICIAN AND LAWYER
Fermat; PierreDeFermat; Pierre Fermat; P. Fermat; Pierre De Fermat; Pierre de fermat
n. Pierre de Fermat (1601-1665), matematico francese autore con Pascal della teoria del numero e della teoria della probabilità
Definition
Fermat prime
<mathematics> A prime number of the form 2^2^n + 1. Any
prime number of the form 2^n+1 must be a Fermat prime.
Fermat conjectured in a letter to someone or other that all
numbers 2^2^n+1 are prime, having noticed that this is true
for n=0,1,2,3,4.
Euler proved that 641 is a factor of 2^2^5+1. Of course
nowadays we would just ask a computer, but at the time it was
an impressive achievement (and his proof is very elegant).
No further Fermat primes are known; several have been
factorised, and several more have been proved composite
without finding explicit factorisations.
Gauss proved that a regular N-sided polygon can be
constructed with ruler and compasses if and only if N is a
power of 2 times a product of distinct Fermat primes.
(1995-04-10)
Wikipedia
Fermat number
In mathematics, a Fermat number, named after Pierre de Fermat, who first studied them, is a positive integer of the form
where n is a non-negative integer. The first few Fermat numbers are:
- 3, 5, 17, 257, 65537, 4294967297, 18446744073709551617, ... (sequence A000215 in the OEIS).
If 2k + 1 is prime and k > 0, then k must be a power of 2, so 2k + 1 is a Fermat number; such primes are called Fermat primes. As of 2023, the only known Fermat primes are F0 = 3, F1 = 5, F2 = 17, F3 = 257, and F4 = 65537 (sequence A019434 in the OEIS); heuristics suggest that there are no more.
