# Lucky Primes

In number theory, a lucky number is a natural number in a set which is generated by a certain "sieve". This sieve is similar to the Sieve of Eratosthenes that generates the primes, but it eliminates numbers based on their position in the remaining set, instead of their value (or position in the initial set of natural numbers).

Begin with a list of integers starting with 1: | ||||||||||||||||||||||||

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 |

Every second number (all even numbers) in the remaining list is eliminated, leaving only the odd integers: | ||||||||||||||||||||||||

1 | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | 25 | ||||||||||||

The second term in this sequence is 3. Starting with 5, every third number which remains in the list is eliminated: | ||||||||||||||||||||||||

1 | 3 | 7 | 9 | 13 | 15 | 19 | 21 | 25 | ||||||||||||||||

The next surviving number is now 7. Every seventh remaining number is eliminated, starting with 19: | ||||||||||||||||||||||||

1 | 3 | 7 | 9 | 13 | 15 | 21 | 25 |

Lucky primes are such numbers which are also primes.

First 11: 2, 3, 7, 11, 29, 47, 199, 521, 2207, 3571, 9349

Checkout list of first: 10, 50 lucas primes. You can also check all lucas primes.

## External#

- OEIS: A031157
- Wikipedia: Lucky primes

## Tags#

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