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 is also a sufficient condition for formula_20 to be prime. Wilson's theorem says that an integer formula_145 is prime if and only if the factorial formula_146 is congruent to formula_147 mod formula_20. For a composite this cannot hold, since one of its factors divides both and formula_149, and so formula_150 is impossible. The formula_20-adic order formula_152 of an integer formula_1 is the number of copies of formula_20 in the prime factorization of formula_1. The same concept can be extended from integers to rational numbers by defining the formula_20-adic order of a fraction formula_157 to be formula_158. The formula_20-adic absolute value