MathNovatory/Pure Maths/Prime Numbers/2

2 The first Prime Number

As the first prime number, 2 will produce its exterminating composites, all the even numbers, leaving only the odd numbers as potential primes, 1/2 of the original prime population.

It will be essential here to broaden the current concept of "producing a Prime Number by adding 1" with the symmetrical, complementary operation of subtracting 1 which is just as reliable and more complete. This will lead us to replace the expression "+ 1" by "+/- 1" after any composite point of reference.

Even and Odd
The current habit of defining an odd number as "2n + 1" now seems incomplete and should be replaced by "2n +/- 1". Completely aware of the fact that, as long as we are dealing with a binary concept of even/odd, this change does not seem particularly relevant. However, if we wish to establish the even/odd concept in ternary groupings, the expression "3n +/- 1" would be required to denote the (ternary) odd number on each side of its (ternary) even "3n". Even as odd as this might seem, as long as "n" is a binary odd number, the two ternary odd numbers expressed by "3n +/- 1" would obviously both be binary even numbers. Needless to add that, unless otherwise stated, the terms "even" and "odd" would be interpreted as being binary.


The red (binary) even numbers "4", "6", "8", "10", "12", "14" are all exterminating composites of the original prime 2, part of "2n". The odd numbers 3, 5, 7 are certified successive primes, whose sequence is terminated by the square "9" of blue prime 3. Other following odd numbers, 11 and 13 are also prime, but "15" is another blue exterminating composite of prime "3" (3x5) which obviously comes after the square.

To Primes 3 and 5