An iteration produces all the prime numbers

[ttw]

One doesn't (for really big stuff) use the same wheel. When possible, one switches to a bigger wheel. Most of those I've seen use 30030 to store 5760 for an efficiency of 192/1001. Of course, the last time I did this seriously, I had a 100 megaword Cray YMP for computation (I didn't use the SSD) for 100,000,000 words *64 bits or 6,400,000,000 bits. Using 8 bits for 30 numbers (easy coding) gave me N=24,000,000,000.

The density of primes is about ln(N)/N which means the spacing is ln(n) on the average.
This clearly increases as N gets large. For N=6,400,000,000 the average spacing is /Ln( 6,400,000,000 or about 22. The 30-wheel has uses 30 numbers for 8 prime so the spacing is 15/4 or 3.75. A list of spacings is better.

To make things more complicated, Yitang Zhang proved that there are infinitely many prime pairs with gap less than 70,000,000, the first result related to prime pairs. Of course,70,000,000 is bigger than 2. (The latest number gap which occurs infinitely often is 246.)

https://online.kitp.ucsb.edu/online/coll...m_KITP.pdf