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
Largest known prime number the progression of the largest known prime number in ascending order. Here M = 2 − 1 is the Mersenne number with exponent "n". The longest record-holder known was M = 524,287, which was the largest known prime for 144 years. No records are known before 1456. GIMPS found the fourteen latest records (all of them Mersenne primes) on ordinary computers operated by participants around the world. A list of the 5,000 largest known primes is maintained by Chris K. Caldwell, of which the twenty largest are listed below. Largest known prime number The largest known prime number () is