  Define a "nuclear partition" to be an integer partition with no part equal to
one. In this study we prove a simple formula to compute the partition function
$p(n)$ by counting only the nuclear partitions of $n$, a vanishingly small
subset by comparison with all partitions of $n$ as $n\to \infty$. Variations on
the proof yield other formulas for $p(n)$, as well as Ramanujan-like
congruences and an application to parity of the partition function.
