Class of whole numbers introduced in 1956 by the Polish mathematician Stanislav Ulam with properties that resemble those of prime numbers.

Lucky numbers are sometimes called **Ulam numbers**.

### Property

**Ulam’s sieve**

- Ulam’s sieve is similar to the sieve of Eratosthenes.

The first number is 1; then in the sequence of whole numbers that remain, we remove one number out of 2, which is all of the even numbers. The first number that remains is 3 and then we remove one number out of 3 that remain, which are 6, 11, 17, etc. The first number that remains is 7 and then we remove one number out of 7, which are 19, 39, 61, etc. And so on. - A
**lucky prime number**is a number that is both prime and lucky. - According to Ulam, it seems that every even number is the sum of two lucky numbers.

Here is a list of the ten first lucky numbers: 1, 3, 7, 9, 13, 15, 21, 25, 31, 33.