[AntonioLao]

Guille,
your numbers are base 10. I am using base 2. There is a big difference.

[Guille]

Originally Posted by AntonioLao Guille, your numbers are base 10. I am using base 2. There is a big difference.

My ideas aren't limited to my math. They don't care if you use a base 2, or a base pi, or a base from a maths of another civilisation, or from another galaxy.

ZERO AND INFINITY ARE AND ONLY ARE THE LIMITS OF QUANTITIES AND EXISTENCE.

[AntonioLao]

Infinity is a prime in base 2. Try to work out the math.

[Guille]

Originally Posted by AntonioLao Infinity is a prime in base 2. Try to work out the math.

But it doesn't make any sense, no matter what the math says. Infinity is not a quantity.

[AntonioLao]

Originally Posted by GUILLE Infinity is not a quantity.

It is not necessary to reach the end of infinity to prove that it is a prime. All we have to do is prove that the 1st digit '1' is prime.

[Guille]

But 1 is consider to NOT be a prime. At least this is what they teach us in school. Isn't right?

[AntonioLao]

I decided to do all the dirty works in showing at the least by the process of induction how infinity can be a prime number. The binary notations for few nonconsecutive primes are the following (reds are not prime but fully occupied in their binary power bases).

2 is 10
3 is 11
5 is 101
7 is 111
11 is 1011
15 is 1111
13 is 1101
17 is 10001
19 is 11101
31 is 11111
63 is 111111
127 is 1111111
255 is 11111111
511 is 111111111
1023 is 1111111111
2047 is 11111111111

As you can see, it is obvious that primes in binary notations have 1 in the 0-power base and the fully loaded bases of 11111...'s are more of primes than not prime. Based on these, the chance or probability that infinity is a prime number is almost 1. For me, it is exactly one. Furthermore, infinity plus one is also a prime.

[phoenixthoth]

Theorem: If p is prime and p>2, then p+1 is composite.

Proof: p is odd since p>2. If p is not odd and >2, then 2 is a factor of p besides p and 1. That can't be, so p is odd. Now p=2k+1 for some integer k. p+1=2k+2=2(k+1) shows that p+1 is even. Also note that as p>2, p+1>2. Thus 2 is a factor of p+1 besides p+1 and 1 as p+1 is even. Then p+1 is composite.

[AntonioLao]

Originally Posted by phoenixthoth Theorem: If p is prime and p>2, then p+1 is composite.

What happens when P = ∞ ? Would ∞ + 1 be composite?

[hanzoganz]

Originally Posted by AntonioLao Who are the intuitionists? The logicists and the formalists? Are there anyone here belonging to any of this groups? Once you identify as a member of one the groups, this post is requesting enlightenment from whoever you are concerning your philosophical stand why math is useful to the progress of science and the humanities.

i believe this classification is not longer valid, at least in terms of general mathematical research. the ones that still fight about it are the logicists, philosophers of science and pretty much that's it. Oh, and maybe some school teacher.
As for maths, we try to take as much as we can from all possible sources, including other sciences.