以下の式はLPer NATTOの『SCP-1941-Ω mod 487811 計算過程』に基づき抜粋・清書した物となります。
\( \pmod{487811-1} \\ 2^{79}=2^{62}\times2^{17}\equiv432344\times131072\equiv280688=(01000100100001110000)_{2} \\ 2^{83}=2^{62}\times2^{21}\equiv432344\times145912\equiv100718=(00011000100101101110)_{2} \\ 2^{89}=2^{62}\times2^{27}\equiv432344\times\hspace{0.5em}69978\equiv104422=(00011001011111100110)_{2} \\ 2^{97}=2^{62}\times2^{35}\equiv432344\times353208\equiv390292=(01011111010010010100)_{2} \)
\( \pmod{487811} \\ 2^{2^{79}}\equiv2^{280688}=2^{2^{4}}\times2^{2^{5}}\times2^{2^{6}}\times2^{2^{11}}\times2^{2^{14}}\times2^{2^{18}} \\ 2^{2^{4}}=65536 \\ 2^{2^{5}}=64294967296\equiv279252 \\ 2^{2^{6}}=77981679504\equiv213044 \\ 2^{2^{11}}\equiv44368367044\equiv5350 \\ 2^{2^{14}}\equiv187134108100\equiv52280 \\ 2^{2^{18}}\equiv135449025156\equiv8219 \)
\( 2^{280688}\pmod{487811} \\ \equiv(279252\times65536)\times213044\times5350\times52280\times8290 \\ \equiv18301059072\times213044\times5350\times52280\times8290 \\ \equiv(341596\times213044)\times5350\times52280\times8290 \\ \equiv72774978224\times5350\times52280\times8290 \\ \equiv(406378\times5350)\times52280\times8290 \\ \equiv2174122300\times52280\times8290 \\ \equiv(436484\times52280)\times8290 \\ \equiv22819383520\times8290 \\ \equiv72751\times8290 \\ \equiv597940469 \\ \equiv371994 \)