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 are distinct Fermat primes. Likewise, a regular formula_1-gon may be constructed using straightedge, compass, and an angle trisector if and only if the prime factors of formula_1 are any number of copies of 2 or 3 together with a (possibly empty) set of distinct Pierpont primes, primes of the form formula_241. It is possible to partition any convex polygon into formula_1 smaller convex polygons of equal area and equal perimeter, when formula_1 is a power of a prime number, but this is not known for other values of formula_1. Beginning with the work of Hugh Montgomery and Freeman Dyson in