This is an initial post for quadsigma mathematical topic blog

First of all there are not too may definitions around stating what a number is or what numbers are. Many people might have difficulty in describing in plain language what is meant by a number. Lets say we have 6 pebbles. It could be said that this is 3 lots of 2 pebbles. But this is not so as It could also be stated that 6 pebbles is 2 lots of 3 pebbles or it could also be stated that 6 pebbles is 1 pebble plus 5 pebbles. Immediately numerically we have run into problems as there are many views of the same thing i.e 6 pebbles...

Its probably OK working from the top that is taking 6 pebbles and DIVIDING the 6 pebbles into groups of 2 or 3 pebbles. Here we can account for all the pebbles. However using pebbles as units and working the other way round and asking the question what is 2 x 1 pebble? most people would answer 2 pebbles. This answer is arrived at by Pure Magic. Initially we had 1 pebble, multiplied it by the NUMBER 2 and we now have 2 pebbles. Where did the extra pebble come from ? Now we can carry out more magic and ask what is 2 +1 and the most common answer is 3. There are now 3 pebbles when originally there was only one. So now two of the building blocks of prime numbers, the numbers 2 and 3, have been constructed by pure magic. It wouldn't be suprising that this is part of the reason that the mathematical puzzles surrounding prime numbers have not been resolved in thousands of years.

Much closer study of the relationships between the numbers 1, 2 and 3 probably needs to be carried out to create clarity in prime number theory before progressing. 1 is not a prime number but consideration of 1 has to be made when studying prime numbers, as 2 and 3 are contructed from units of 1. The numbers 1, 2 and 3 have fundamentally different properties. 1 can be looked at as possibly having replication properties otherwise how does 2 or 3 get into the picture i.e double 1 and 2 arrives out of nowhere. 2 can be looked at as having symmetrical properties with the two identical 1's that make up 2 being the basis of the symmetry. The number 3 really is getting relevant as far as prime numbers are concerned. Three consists of three points . . . and two consists of two points . . Exactly how the relationship between the numbers 2 and 3 is defined will determine how other prime numbers fit into the prime number superstructure, if such a superstructure exists.