the first bidecade of numbers (1-20), there are precisely 8 prime numbers (2,3,5,7,11,13,17,19).

Are there other such bidecades with 8 prime numbers?

No. The only numbers in a decade, other than the first decade, that can be prime are the numbers ending in 1, 3, 7, or 9. Therefore, to get 8 primes in a bidecade, there must be 2 consecutive decades with 4 primes ending in 1, 3, 7, and 9. However, then there would be 4 consecutive odd numbers that are prime, but 1 of every 3 consecutive odd numbers is divisible by 3. Therefore, it is impossible to have 8 prime numbers in a bidecade, other than 2, 3, 5, 7, 11, 13, 17, 19.

Posted by Math Man on 2025-03-10 20:46:37