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 a product of prime numbers is called a "prime factorization" of the number. For example: The terms in the product are called prime factors. The same prime factor may occur more than once; this example has two copies of the prime factor formula_28. When a prime occurs multiple times, exponentiation can be used to group together multiple copies of the same prime number: for instance, in the second way of writing the product above, formula_29 denotes the square or second power of formula_28. The central importance of prime numbers to number theory and mathematics in general stems from the "fundamental