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 a special form, including the special number field sieve. the largest number known to have been factored by a general-purpose algorithm is RSA-768, which has 232 decimal digits (768 bits) and is the product of two large primes. Shor's algorithm can factor any integer in a polynomial number of steps on a quantum computer. However, current technology can only run this algorithm for very small numbers. the largest number that has been factored by a quantum computer running Shor's algorithm is 21. Several public-key cryptography algorithms, such as RSA and the Diffie–Hellman key exchange, are based on large prime numbers