Legendre's Conjecture is an unproven statement regarding the distribution of prime numbers; it asserts there is at least one prime number in the interval \$(n^2,(n+1)^2)\$ for all natural \$n\$.
Make a program which only halts if Legendre's conjecture is false. Equivalently, the program will halt if there exists \$n\$ which disproves the conjecture.
This is code-golf so the shortest program in bytes wins.
No input shall be taken by the program.
The program only needs to halt or not halt in theory; memory and time constraints shall be ignored.
One may use methods other than checking every \$n\$ if they can prove their program will still only halt if Legendre's conjecture is false.