## Re: sufficent proof for primes ?

Expand Messages
• ... The concept of a cyclic group in the adjoined numbers , modulo a composite integer, has not been defined. In any case, the proof is clearly nonsense. It
Message 1 of 50 , Aug 8, 2010
• 0 Attachment
"bhelmes_1" <bhelmes@...> wrote:

> Please try to understand the mathematical proof, which i gave under
> http://beablue.selfip.net/devalco/suf_prime.html

The concept of "a cyclic group in the adjoined numbers",
modulo a composite integer, has not been defined.

In any case, the "proof" is clearly nonsense.
It invokes the trivial argument that if
n = f*g = -1 mod d with d > 2, then we cannot have
f = -1 mod d and g = -1 mod d.
However if
n = f*g*h = -1 mod d with d > 2, then we can have
f = -1 mod d, g = -1 mod d and h = -1 mod d.
Thus even if the author were able to explain
what he means he would be unable to exclude
the possibility that n is a composite number
with an odd number of prime factors.

David
• ... [4] is meaningless, as it stands. You should write a double mod: 4. (1+x)^p = 1-x mod(x^2-a,p) ... There is no reason whatsoever to believe that [1] to [4]
Message 50 of 50 , Sep 29, 2011
• 0 Attachment
"bhelmes_1" <bhelmes@...> wrote:

> 1. let a jacobi (a, p)=-1
> 2. let a^(p-1)/2 = -1 mod p
> 3. a^6 =/= 1 mod p
> 4. (1+sqrt (a))^p = 1-sqrt (a)

[4] is meaningless, as it stands.
You should write a double mod:

4. (1+x)^p = 1-x mod(x^2-a,p)

> 1. Is it possible that there are other exceptions

There is no reason whatsoever to believe that
[1] to [4] establish that p is prime. Morevoer,
some folk believe that, for every epsilon > 0,
the number of pseudoprimes less than x may
exceed x^(1-epsilon), for /sufficiently/ large x.

> 2....
> there is a cyclic order ...

> 3....
> there is a cyclic order ...

The group of units (Z/nZ)* is /not/ cyclic
if n has at least two distinct odd prime fators.

David
Your message has been successfully submitted and would be delivered to recipients shortly.