The 2nd First Order Logic Statement of "Infinitely Many Primes" is a mathematical statement that claims there are infinitely many prime numbers. In other words, there is no largest prime number and the list of prime numbers goes on forever.
The 2nd First Order Logic Statement of "Infinitely Many Primes" is considered wrong because it was proven to be a fallacy by the mathematician Euclid. He showed that there are infinitely many prime numbers by contradiction, meaning that assuming there is a largest prime number leads to a contradiction.
The 1st First Order Logic Statement of "Infinitely Many Primes" is a correct statement that states there are infinitely many prime numbers. The 2nd First Order Logic Statement, on the other hand, is a false statement that claims there is a largest prime number. They differ in their truth value and validity.
The 2nd First Order Logic Statement of "Infinitely Many Primes" has no impact on the study of prime numbers because it has been proven to be false. Mathematicians continue to use the 1st First Order Logic Statement, which has been proven to be true, in their research and calculations related to prime numbers.
The proof that the 2nd First Order Logic Statement of "Infinitely Many Primes" is wrong can be understood by studying Euclid's proof of the infinitude of prime numbers by contradiction. This proof uses basic principles of number theory and logic, and can be easily understood with some background knowledge in these areas. There are also many resources available online and in books that explain the proof step by step for a deeper understanding.