Generate P19 sequence

The P19 sequence consists of numbers that are coprime to 2, 3, 5, 7, 11, 13, and 17.

This means we only keep numbers up to a limit that are not divisible by any of these primes.

transform P19 elements for Sieve of Sundaram

Sieve of Sundaram works by removing numbers of the form i + j + 2ij ≤ n.

To map back to actual primes, we transform using: prime = 2 * i + 1

So, you subtract 1 from each P19 number and divide by 2:

This is the core logic. We mark the numbers of the form i + j + 2ij and eliminate them.

make an optimized sieve

The P19 version avoids all unnecessary operations on multiples of small primes.

NOTE: Use NumPy arrays instead of Python lists for memory-efficient boolean marking.

NOTE: Parallelize outer loops using numba or multiprocessing.

Dear Mr. Brandon Alexander,

Thanks for replying. I have noted your recommendation. There more possibilities to time and Space complexity by using higher Pn series.

The P19 Set E Sieve of Sundaram further optimizes this approach by leveraging numbers coprime to a large prime set, significantly reducing computational overhead. 2. Methodology Step 1: Constructing P19 Set E - Generate the first 1,658,880 numbers that are coprime to 2, 3, 5, 7, 11, 13, 17 (P19 sequence). - Extend the set to be coprime up to 223,092,870, forming P19 Set E. - The resulting numbers exclude all multiples of primes