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 first known proof for this statement is attributed to him. Many more proofs of the infinitude of primes are known, including an analytical proof by Euler, Goldbach's proof based on Fermat numbers, Furstenberg's proof using general topology, and Kummer's elegant proof. Euclid's proof shows that every finite list of primes is incomplete. The key idea is to multiply together the primes in any given list and add formula_42. If the list consists of the primes formula_43, this gives the number By the fundamental theorem, formula_45 has a prime factorization with one or more prime factors. formula_45 is evenly divisible by