  Through computation and analyses, we show that a non-trivial cycle number
must be infinite as the cycle length goes to infinity and bounded low and above
(10 times lower bounds) dependent on the cycle length. A cycle number must be
$m_1\geq978$ at the cycle length $s=485$; as the cycle length goes up to
$s=17087915$, the cycle number must be $m_1\geq46449769^{821013301}$, which is
approximately equal to $2^{2\times10^{10}}$, or $10^{6\times10^{9}}$.
