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 instance the Solovay–Strassen primality test on a given number formula_20 chooses a number formula_34 randomly from formula_42 to formula_210 and uses modular exponentiation to check whether formula_211 is divisible by formula_20. If so, it answers yes and otherwise it answers no. If formula_20 really is prime, it will always answer yes, but if formula_20 is composite then it answers yes with probability at most 1/2 and no with probability at least 1/2. If this test is repeated formula_1 times on the same number, the probability that a composite number could pass the test every time is at most formula_216. Because