Weird Spread

One of the things that drive people nuts that enjoy puzzles are Primes. Primes are any number that can be divided evenly by only itself and 1. If you ever look at a Table Of Primes, you will see they seem to have a pattern but there isn’t any readily recognizable rhyme or reason to it. Logically, you would think that the spaces that would separate Primes would be even or at the most not far off even. Here’s what I mean. The simplest Primes are the single digits 1, 2, 3, 5, 7. Looks relatively simple to me, but the larger the numbers, the more the Primes’ locations seem to be completely disorganized. Since Primes are defined as numbers divisible by themselves and 1 you can eliminate some numbers immediately. Two (2) divides evenly into any number that has 0, 2, 4, 6, 8 in the far right column ( 10, 12, 24, 36, 48, for example ). Five (5) is the only other number that divides evenly into any number that has 5 or 0 in the far right column (125, 155, 175 ), ( 120, 150, 180). The remaining prime numbers are 1, 3, 7. They may or may not divide evenly into any number that has a 1, 3, 7 in the far right column. The only other number not discussed is 9 which isn’t a prime number because it’s divisible by 3 ( 9 / 3 = 3 ) Weird as it is, you will find that the numbers 1, 3, 7, and 9 are in the farthest right column of Prime Numbers. For example, ( 11, 13, 17, 19 ) are all Prime Numbers. If you divide any number ending in 1, 3, 7, 9 in the far right column into any number ending in ( 1, 3, 7, 9 ) in the far right column sometimes it divides evenly which means that particular number that ends in ( 1, 3, 7, 9 ) isn’t a Prime Number, For example, ( 21, 33, 27, 39 ) are all divisible by 3. You will see that the Prime Number locations would now start to spread out because not all numbers ending in ( 1, 3, 7, 9 ) in the far right column are only divisible by themselves and 1. The final randomizer is due to the fact that, except for single digit prime number 3, the total of the digits forming a Prime number ending in 1, 3, 7, 9, will never total 3 or a multiple of 3. For instance 69 is not a Prime because its’ digits 6 and 9 total 15 which is divisible evenly by 3. ( 69, 6 + 9 = 15, 15 / 3 = 5 ).

So, in summary, randomizing occurs because:

Prime Numbers have 1, 3, 7, 9 in their farthest right column leaving spaces of 1, 2, multiples of 2 or even odd or even powers of 2 between Prime Numbers.

Not all numbers having 1, 3, 7, 9 in their farthest right column are Prime Numbers ( 21, 33, 27, 39 ).

Except for Prime Number 3, the sum of the digits of Prime Numbers never total 3 or multiples of 3. ( 21, 33, 27, 39 )