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.