A collection of some of the largest known [[Prime Number|Primes]]. $\huge 2^{p} - 1 $ Where $p$ is [[Prime Number|Prime]]. Not all numbers of this form produces a [[Prime Number|Prime]] (ex. $2^{11}-1$ is [[Composite Number|Composite]]). The cases where $2^{p}-1$ is not also prime, they are called a [[Mersenne Primes|Mersenne Number]]. >[!abstract] Thereom >For every [[Mersenne Primes|Mersenne Prime]], there corresponds a [[Perfect Number]]. >$\huge >\begin{align} >2^{p}-1 \text{{ is prime}} >\implies >2^{p-1}\pa{2^{p}-1} \text{{ is perf.}} >\end{align} $