Fortunate number numbers are prime. 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
Prime number so is every element in the sequence. Therefore, this progression contains only one prime number, 3 itself. In general, the infinite progression can have more than one prime only when its remainder formula_34 and modulus formula_107 are relatively prime. If they are relatively prime, Dirichlet's theorem on arithmetic progressions asserts that the progression contains infinitely many primes. The Green–Tao theorem shows that there are arbitrarily long finite arithmetic progressions consisting only of primes. Euler noted that the function yields prime numbers for formula_109, although composite numbers appear among its later values. The search for an explanation for this phenomenon led