In number theory, a Fortunate number such that, for a given positive integer is a prime number, where the primorial prime numbers. They are named after Reo Fortune.

For example, to find the seventh Fortunate number, one would first calculate the product of the first seven primes, which is

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 18. Adding 19, however, gives 510529, which is prime. Hence 19 is a Fortunate number.

The Fortunate numbers for the first primorials are:

. The Fortunate numbers sorted in numerical order with duplicates removed are

.

Fortune conjectured that no Fortunate number is composite. A Fortunate prime is a Fortunate number which is also a prime number. .

is divisible by the prime factors.

Paul Carpenter defines the less Fortunate numbers. These are also conjectured to be always prime.

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