Comment by Karliss

Comment by Karliss 8 days ago

1 reply

Nothing too surprising more or less same thing as all other vertical columns. 546=2*3*7*13 and all numbers in the range [242, 250] can be divided by one of those 4 primes same for [296, 304] . If x is divisor of a and b, then it will also divide a+n*b meaning you get an empty column. 2 and 3 already makes more than half the columns non primes, fill in the gaps with few more primes and you get the wide empty columns. If the width is multiple of many different small primes it's more likely to happen.

In a similar way 210=2*3*7*5 also gives wide empty columns (if you ignore ignore first row where 2,3,5,7 themselves are primes)

It helps if you think of it in terms of where the non primes are located instead of where the primes are. Multiples of 2, 3, 5 form a very regular pattern. Wrap it around in a grid and you get straight lines which are either straight vertical or slightly shifted depending on the divisors of width. Stack a couple of repetitive patterns and you still get a repetitive pattern. If the positions which are not primes form a regular pattern, the inverted image also forms recognizable pattern. Of course the primes don't form perfectly regular pattern and but most the visible repetition are result of small prime multiples.