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
400 (number) = 2 × 101, Mertens function returns 0, nontotient, noncototient. 405 = 3 × 5, Mertens function returns 0, Harshad number; 406 = 2 × 7 × 29, sphenic number, triangular number, centered nonagonal number, nontotient 407 = 11 × 37, 408 = 2 × 3 × 17 409 is a prime number, Chen prime, centered triangular number. 410 = 2 × 5 × 41, sphenic number, sum of six consecutive primes (59 + 61 + 67 + 71 + 73 + 79), nontotient, Harshad number 411 = 3 × 137, self number, 412 = 2 × 103, nontotient, noncototient,