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I want to appologize for lack of therms, because I just love math as hobby, not on professional level. We all know what prime number can't be split (by division) on two different numbers aside from 1 and itself. So, basicaly, this numbers is constructing blocks for all of the numbers what can be obtained by multiplication. But, something came to my mind, what if prime is not a property of concrete number but (number & operator)? For example, this hyperoperators:

  • N=x+y
  • N=x*y
  • N=x^y
  • N=H4(x,y)
  • ...

Gives various prime numbers:

|    | + | * | ^ | H4|
|----|---|---|---|---|
| 2  | O | + | + | + |
| 3  | O | + | + | + |
| 4  | O | O | O | + |
| 5  | O | + | + | + |
| 6  | O | O | + | + |
| 7  | O | + | + | + |
| 8  | O | O | O | + |
| 9  | O | O | O | + |
| 10 | O | O | + | + |
| 11 | O | + | + | + |
| 12 | O | O | + | + |
| 13 | O | + | + | + |
| 14 | O | O | + | + |
| 15 | O | O | + | + |
| 16 | O | O | O | O |

O - not prime.
+ - prime for i-th number and j-th operator.
H4 - tetration operator H4(a,b)=a^(a^...) b times

What is strange for me is the fact that lower tier primes becomes subset of higher tier. So, if number aquired prime property at some tier level it will pass this property across higher tiers. Eventually, all numbers will become primes at infinite hyperoperator.

Of course, in society we hunt down primes in third column, and theories/solutions appeared for that purpose. But, what about the others? Is there some literature about the other operator primes?

  • 0
    can you please clarify, with one simple example, how can 2 become a prime under * and ^. – 2017-02-11
  • 1
    2=2^1 and no way around, 3=3^1, but 4=2^2=4^1, just draw analogy with multiplication, basically you want to find number what can be expressed through multiplication/power/tetration only by itself – 2017-02-11
  • 0
    if we can have 2=2^1, why can't we have 2+1=3, a prime? – 2017-02-11
  • 0
    Sorry, I can't explain it in terms of math, but if I remeber correctly for operators there is exist identity opearator which map value to itself. For + it is x+0, for * it is x*1, for ^ it is x^1, etc. So, to your question 2+0=1+1=2 - so it is not prime for +, but 1+0=1 - is in fact prime – 2017-02-11

0 Answers 0