Would there be a rule that a prime number must be reducible to a quarc factors. For instance, lets think about p =(qc1)(qc2)..(qcn). Can we say anything about the structure of the quarc factors building up the original prime ?
Lets think of 1357531357531357. This is a prime number. What if we divided it like that?
1357 is not prime, so 13; 57 is not prime, 575 is not prime, 5753 is not prime, 57531 is not a prime, 575313 is not a prime, 5753135 is not a prime, 57531357 is also not a prime. Indeed, pretty difficult to find a prime in this sequence. Btw, a “quarc” would be: (13) (5753135) (7531357) (and many like that), each of the elements would be a q-factor (quarc factor) and actually we could mix up the factors to receive all the quarcs (as defined earlier, as a set of these, not a specifc one, which might be misleading, but this is chanelling for me, no time to think more).
How about deep diving there and thinking what concatenations of which types of numbers would have to build the prime. If that was the case that we could judge by the structure of the concatenations, ie. by the sizes of the corresponding building numbers that in the same time are quarc factors, it would mean that we could potentially a different approach to the connection between the size of the number and its geometrical structure (prime divisors).
So, the questions are:
– if there was a connection between the size of the numbers and their geometrical shape to be found (we know it is, for instance, that the higher the number the less likely it is that it is going to be prime), how would the concatenation of quarc factors (eleements of the numbers) of the same size (or maybe not only?) be interesting?
– how about quarc numbers of the same size? what about dividing a number into quarc factors and changing the sequence of the quarcs?
– how about turning every number into quarc with prime quarc factors only?
– a non-prime number cannot be turned into prime quarcs (assuming the 2 and 5 (one digit nums) would not be used itself), for instance, 238479623092, even if we are able to divide it into prime quarcs we are going to bump into the last digit which is 2, and which we don’t use”!