Lucky Numbers

Lucky Numbers

There are several types of numbers that are commonly termed "Lucky Numbers"

In number theory, a lucky number is a natural number in a set which is generated by a "sieve" similar to the Sieve of Eratosthenes that generates the primes.

The first is the lucky numbers of Euler. The second is obtained by writing out all odd numbers 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, ....

The first odd number > 1 is 3, so strike out every third number from the list: 1, 3, 7, 9, 13, 15, 19, ....

The first odd number greater than 3 in the list is 7, so strike out every seventh number: 1, 3, 7, 9, 13, 15, 21, 25, 31

Numbers remaining after this procedure has been carried out completely are called lucky numbers. The first few are 1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37

A Lucky Prime Number is a lucky number that is prime. It is not known whether there are infinitely many lucky primes. The first few are 3, 7, 13, 31, 37, 43, 67, 73, 79, 127, 151, 163, 193