Solve (2^{2}+1)(2^4+1)(2^8+1)(2^16+1)(2^22+1)+1

$$( 2 ^ { 2 } + 1 ) ( 2 ^ { 4 } + 1 ) ( 2 ^ { 8 } + 1 ) ( 2 ^ { 16 } + 1 ) ( 2 ^ { 22 } + 1 ) + 1$$

Evaluate

$$6004800933418326$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$\left(4+1\right)\left(2^{4}+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{22}+1\right)+1$$

Add 4 and 1 to get 5.

$$5\left(2^{4}+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{22}+1\right)+1$$

Calculate 2 to the power of 4 and get 16.

$$5\left(16+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{22}+1\right)+1$$

Add 16 and 1 to get 17.

$$5\times 17\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{22}+1\right)+1$$

Multiply 5 and 17 to get 85.

$$85\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{22}+1\right)+1$$

Calculate 2 to the power of 8 and get 256.

$$85\left(256+1\right)\left(2^{16}+1\right)\left(2^{22}+1\right)+1$$

Add 256 and 1 to get 257.

$$85\times 257\left(2^{16}+1\right)\left(2^{22}+1\right)+1$$

Multiply 85 and 257 to get 21845.

$$21845\left(2^{16}+1\right)\left(2^{22}+1\right)+1$$

Calculate 2 to the power of 16 and get 65536.

$$21845\left(65536+1\right)\left(2^{22}+1\right)+1$$

Add 65536 and 1 to get 65537.

$$21845\times 65537\left(2^{22}+1\right)+1$$

Multiply 21845 and 65537 to get 1431655765.

$$1431655765\left(2^{22}+1\right)+1$$

Calculate 2 to the power of 22 and get 4194304.

$$1431655765\left(4194304+1\right)+1$$

Add 4194304 and 1 to get 4194305.

$$1431655765\times 4194305+1$$

Multiply 1431655765 and 4194305 to get 6004800933418325.

$$6004800933418325+1$$

Add 6004800933418325 and 1 to get 6004800933418326.

$$6004800933418326$$

Factor

$$2\times 3\times 13\times 683\times 3881\times 29042879$$