Ricky,

the arrow in the notation denotes John Conway's chained arrow notation which is much much larger than knuth's up-arrow notation.

In fact, The chained-arrow notation here is pretty huge, although I'm not sure I really got the concept of the notation in full.

]]>As one of these people said, "there's room for improvement".

]]>There already exists a proof that (a^n-b^n) is divisible by (a-b).

Therefore, I used the word 'most'.

Like for example, 63 is divisible by 3, 7.

4095 has many prime factors.

These are numbers of the kind I have mentioned in my post #1.]]>

If n-1 is divisible by almost all prime numbers, n+1 should be prime.

Thats a hypothetic conclusion.

By hypothetic, do you mean one that remains to be unproven?

And what is meant by most?

]]>the arrow in the notation denotes John Conway's chained arrow notation which is much much larger than knuth's up-arrow notation.

If n-1 is divisible by almost all prime numbers, n+1 should be prime.

Thats a hypothetic conclusion.]]>

Let n=6->6->6->6->6

Let n1 equal to the smallest number apart from zero and one which is a perfect square, cube, fourth, fifth, sixth and nth power.

n1+1 is a prime number.

Proof:- n1-1 is divisible to almost any prime number, because of the fact that (a^n-b^n) is divisible by (a-b).

I don't understand your 6->6->6->6 notation.

I also don't see how stating n1-1 is divible by almost any prime number proves n1+1 is prime.

]]>Let n1 equal to the smallest number apart from zero and one which is a perfect square, cube, fourth, fifth, sixth and nth power.

n1+1 is a prime number.

Proof:- n1-1 is divisible to almost any prime number, because of the fact that (a^n-b^n) is divisible by (a-b).

This is a better proof than Graham's Number for Ramsay theory, he he

Such numbers are enormously large.

For example, the smallest number apart from zero and one which is a perfect square, cube, fourth, fifht and sixth power is 1152921504606846976.

(That is how many bytes make an exabyte).

And extrapolating this to tenths power, the result is 3.940842x10^758, a number containing 759 digits.

If this is extrapolated to 20th power, the result is 2.125219 x 10^70077543 approximately, containg 70077544 digits.

And when this extrapolated to 1000th power, the result is 10^10^433, much much larger than a googolplex ]]>