SCP-1941

SCP-1941现象（由LRO提供），像网格一样的黑色区域是正在进行的建造过程的结果。

$\large 2^{2^{79}} + 3^{2^{83}} + 5^{2^{89}} + 7^{2^{97}}$

Given this development, interest has been renewed in attempting to factor the mathematical expression in the primary message. Investigations into leveraging the processing power of SCP-155 were made (SCP-155 being a computer capable of an asymptotic number of computations in finite amounts of time), as well as investigations into the attendant risks of doing so (参见文件以查阅SCP-155).

Estimates have been made on the amount of energy that would be released by SCP-155 during this attempt, and whether or not provisions should be made to relocate it off the Earth should it prove necessary to safeguard against a PK-class event, or the sterilization of all life on the planet.

The lower-bound placed on the amount of energy released is 4.2 x 1018 Joules, deemed acceptable (roughly equivalent to a gigaton nuclear explosion). The upper-bound, however, has been placed at 3.1 x 1044 Joules, or roughly the amount of energy released by the average supernova. Research is currently underway to refine these bounds.

Mathematical Supplement:
The secondary message is as follows:

(1)
\begin{align} \large f(): f(n) = {p_1}^{a_1}{p_2}^{a_2} \dotsb {p_k}^{a_k} , \forall p \neg \exists a,b : a>1, b>1, p=ab \end{align}
(2)
\begin{align} \large \Omega = 2^{2^{79}} + 3^{2^{83}} + 5^{2^{89}} + 7^{2^{97}} \end{align}
(3)
\begin{align} \large f(n) \Rightarrow \left\{ \begin{array}{rl} n=∅ &\mbox{-> e} \\ n=Ω &\mbox{-> 0} \end{array} \right. \end{align}

Which has been interpreted to mean the following:

(1): Definition of the function f() which yields the prime factors of an integer.
(2): Definition of Ω, the intractably large number.
(3): The condition, where the prime factors of the empty set f(∅) yields the base of the natural logarithm, e (interpreted to mean continued exponential growth) while the prime factors of the intractable number f(Ω) yields 0, (interpreted to mean the cessation of growth).

Upper and Lower bounds:
The lower bound is estimated using the expectation that, on average, as the number Ω approaches infinity, Ω will have $\ln\ln$ Ω number of prime factors. The upper bound is estimated using the assumption that the number Ω represents the pathological case and is itself prime.