A prize of 120 million JPY will be paid to those who have revealed the truth of the Collatz conjecture. The conjecture is also known as the $3x+1$ problem or the $3n+1$ problem. 120 million JPY in USD Collatz conjecture Repeatedly applying the function $f(x)$ defined below to any positive integers will eventually result in $1$. $$f(x)=\{\begin{array}{}x/2& (x\equiv 0(\mathrm{mod}2))\\ 3x+1& (x\equiv 1(\mathrm{mod}2))\end{array}$$