Let us consider the strong twin conjecture:
For all positive integer n there exist a prime p such that
[math]n+4<p<2^n2^4[/math] and p is a prime and p+2 is a prime
Since the inequalities and the set of primes are both diophantine, we can construct a polynomial P(X) such that the strong twin conjecture is equivalent to the following statement:
For all positive integer n there exist a prime p such that P(X)=0 where X is a vector of several variables.
Now, in a book by Matiyasevich's: https://mitpress.mit.edu/books/hilberts-10th-problem
The author claim that the strong twin conjecture can be transformed into the unsolvability of a particular Diophantine equation.
Then my question is: How one can find this Diophantine equation or I am asking about a reference containing this equation.
For all positive integer n there exist a prime p such that
[math]n+4<p<2^n2^4[/math] and p is a prime and p+2 is a prime
Since the inequalities and the set of primes are both diophantine, we can construct a polynomial P(X) such that the strong twin conjecture is equivalent to the following statement:
For all positive integer n there exist a prime p such that P(X)=0 where X is a vector of several variables.
Now, in a book by Matiyasevich's: https://mitpress.mit.edu/books/hilberts-10th-problem
The author claim that the strong twin conjecture can be transformed into the unsolvability of a particular Diophantine equation.
Then my question is: How one can find this Diophantine equation or I am asking about a reference containing this equation.