Lucky numbers can vary based on culture, personal belief and theory. In math, lucky numbers can refer to the lucky numbers of Euler or the numbers that survive the sieving process. In China, even numbers are considered more auspicious than odd, with exceptions for the numbers 4 and 3.
The lucky numbers of Euler are 2, 3, 5, 11, 17 and 41.
The sieved numbers are essentially infinite, but the first few are 1, 3, 7, 9 and 13. They are obtained by listing all odd numbers. The first odd number greater than 1 is 3, so every third number is struck out. Out of the remaining list, the next odd number greater than 3 is 7, so every seventh number is struck out. The process repeats for as long as desired to produce the lucky numbers.
In China, even numbers are considered lucky, with the number 8 being extremely lucky and associated with wealth and fortune. The number 3 represents Buddha, Dharma and Bonze in Buddhism, and so the number 9 has come to represent longevity and eternity, with a loose association with love. However, 4 in Chinese is phonetically similar to the word for "death," making it an extremely unlucky number and an exception to the rule.