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
Prime number theorem the notion that the "density" of primes around should be . This function is related to the logarithm by the asymptotic expansion So, the prime number theorem can also be written as . In fact, in another paper in 1899 de la Vallée Poussin proved that for some positive constant , where is the big notation. This has been improved to Because of the connection between the Riemann zeta function and , the Riemann hypothesis has considerable importance in number theory: if established, it would yield a far better estimate of the error involved in the prime number theorem than