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 Aug26 comment Primality using $\Gamma(x)$ @Qiaochu Yuan My motive was not Wilson related so much as exploring the Gamma function, being new to it and all. Perhaps 'primality' is an unsuitable term? To Alex, I'll try to be careful =P $a+bi$ where $b$ is non-zero. Jul30 comment A prime number pattern Of course, it would also have to happen that the only $1s$ I have encountered in odd number chains correspond to $Z_t$ values, which end the sequence. If this is the only place $1s$ might occur (for odd numbers), the conjecture would fall to induction. Jul30 comment A prime number pattern My real bad. That aside, even numbers only get $Z_t\in\{-1,0,1\}$ while odd numbers have $\{0,1,2\}$. Let us assume above observation is true till $2n+1$. Then, we can prove if $2n+1$ never reaches $1$, it will not reach $-1$. Follows from the fact that $2n$ would have the same chain as $2n+1$, but for a displacement of $1$ in values. Hence, at the terminus, $Z_t({2n})$ would displace to $2$ (from $-1$) instead of $-2$. This won't work for for any odd number reaching $1$ in the middle of the sequence, of course. Jul29 comment A prime number pattern An elementary result that would follow if odd numbers don't have $−1$ as a terminal is that there always exists a prime between $p_2n+1$ and $−1+\sum_{i=1}^{{2n+}1}p_i$ where $p_n$ is the $n-th$ prime. For example, $-1 + 2 + 3 + 5 = 9$, if there is no prime $p$ such that \$5