By the way, here’s something I just thought of with the factor field. First, check out this graphic:

As you can see, the red cells are there to highlight gaps in the line with the lines that come off in both directions on the arms of the “starburst.” Now here’s the thing about that: wherever a factor exists on the 6-spike, it blocks the same area at whatever distance that is above and below the line. This means that if there’s a factor at 5, then 5 above and 5 below that 6-spike cannot be prime.

Here’s what I thought of. Whenever you have factorial numbers, then these arms will block primes from appearing. So if you have 10 factorial (10!), for instance (which would occur at 3628800 (which is 10 x 9 x 8 x 7 x 6…), then there cannot be any prime numbers occuring for 10 ahead and 10 after. It’s impossible, because the arms that branch off would block them.

So then…if you have 100!, then it blocks 100 before and 100 after. 1000! would block 1000 before and 1000 after. And so on. The bigger the number you’re doing the factorial for, the more numbers before and after get blocked. Which means there are huge sections of numbers that cannot possibly be prime.

Which really makes you wonder about infinity factorial… Because an infinite number of numbers before and after it would be blocked from being primes….