The world largest known prime to the test!

With the Lucas–Lehmer primality test ,

${ a }_{ 74,207,279 }\left( mod\quad { 2 }^{ 74,207,281 }-1 \right) =0$

${ a }_{ 74,207,280 }\left( mod\quad { 2 }^{ 74,207,281 }-1 \right) ={ 0 }^{ 2 }-2\left( mod\quad { 2 }^{ 74,207,281 }-1 \right) \\ =-2\left( mod\quad { 2 }^{ 74,207,281 }-1 \right)$

${ a }_{ 74,207,281 }\left( mod\quad { 2 }^{ 74,207,281 }-1 \right) ={ \left( -2 \right) }^{ 2 }-2\left( mod\quad { 2 }^{ 74,207,281 }-1 \right) \\ =2\left( mod\quad { 2 }^{ 74,207,281 }-1 \right)$

${ a }_{ 74,207,282 }\left( mod\quad { 2 }^{ 74,207,281 }-1 \right) ={ 2 }^{ 2 }-2\left( mod\quad { 2 }^{ 74,207,281 }-1 \right) \\ =2\left( mod\quad { 2 }^{ 74,207,281 }-1 \right)$

Now we realise that we will keep getting $2$ .

So, the answer is $2$