A Fermat number is a specific type of integer that can be expressed in the form: \[ F_n = 2^{2^n} + 1 \] where \( n \) is a non-negative integer. Fermat numbers were named after Pierre de Fermat, a French mathematician, who studied these numbers in the 17th century.
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A Fermat number is for . Distinct Fermat numbers are coprime integers. Their prime divisors are constrained by the multiplicative order of modulo that prime; this remains useful whether or not the Fermat number itself is prime. The initial value must be distinguished when a statement restricts to positive indices.