Fortunate number Fortunate number A Fortunate number, named after Reo Fortune, is the smallest integer "m" > 1 such that, for a given positive integer "n", "p"# + "m" is a prime number, where the primorial "p"# is the product of the first "n" prime numbers. For example, to find the seventh Fortunate number, one would first calculate the product of the first seven primes (2, 3, 5, 7, 11, 13 and 17), which is 510510. Adding 2 to that gives another even number, while adding 3 would give another multiple of 3. One would similarly rule out the integers up to
Prime number arts and literature. They have also been used in evolutionary biology to explain the life cycles of cicadas. Fermat primes are primes of the form with formula_64 a natural number. They are named after Pierre de Fermat, who conjectured that all such numbers are prime. The first five of these numbers – 3, 5, 17, 257, and 65,537 – are prime, but formula_236 is composite and so are all other Fermat numbers that have been verified as of 2017. A regular formula_1-gon is constructible using straightedge and compass if and only if the odd prime factors of formula_1 (if any)