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 factorizations are based on Euclid's lemma: If formula_20 is a prime number and formula_20 divides a product formula_33 of integers formula_34 and formula_35, then formula_20 divides formula_34 or formula_20 divides formula_35 (or both). Conversely, if a number formula_20 has the property that when it divides a product it always divides at least one factor of the product, then formula_20 must be prime. There are infinitely many prime numbers. Another way of saying this is that the sequence of prime numbers never ends. This statement is referred to as "Euclid's theorem" in honor of the ancient Greek mathematician Euclid, since the