Fundamental theorem of number theory refuted and corrected

THE PRIME NUMBER SERIES 30

Fundamental theorem of number theory refuted and corrected

The fundamental theorem of number theory is:

Any natural number n > 1 can be represented as a product of prime numbers. And this prime factorization is unambiguous except for the order of the factors.

Proof of the incorrectness: Even the first natural number n > 1, namely the 2, cannot be represented as a product of prime numbers.

The product representation of 2, and this applies to all prime numbers, can only be represented by a factor of 1.

And 1 is not a prime number according to the prime number definition, because a prime number is always greater than 1.

Which had to be proven.

The following is the corrected fundamental theorem of number theory:

Any natural number n > 1 is either a prime number or a composite number. If n is not prime, n can be represented as a product of prime numbers. And this prime factorization is unambiguous except for the order of the factors.

Munich, 13 November 2024

Gottfried Färberböck