Solve (2+1)(2^{2}+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)

$$( 2 + 1 ) ( 2 ^ { 2 } + 1 ) ( 2 ^ { 4 } + 1 ) ( 2 ^ { 8 } + 1 ) ( 2 ^ { 16 } + 1 ) ( 2 ^ { 32 } + 1 )$$

Evaluate

$$18446744073709551615$$

Solution Steps

Add 2 and 1 to get 3.

$$3\left(2^{2}+1\right)\left(2^{4}+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)$$

Calculate 2 to the power of 2 and get 4.

$$3\left(4+1\right)\left(2^{4}+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)$$

Add 4 and 1 to get 5.

$$3\times 5\left(2^{4}+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)$$

Multiply 3 and 5 to get 15.

$$15\left(2^{4}+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)$$

Calculate 2 to the power of 4 and get 16.

$$15\left(16+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)$$

Add 16 and 1 to get 17.

$$15\times 17\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)$$

Multiply 15 and 17 to get 255.

$$255\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)$$

Calculate 2 to the power of 8 and get 256.

$$255\left(256+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)$$

Add 256 and 1 to get 257.

$$255\times 257\left(2^{16}+1\right)\left(2^{32}+1\right)$$

Multiply 255 and 257 to get 65535.

$$65535\left(2^{16}+1\right)\left(2^{32}+1\right)$$

Calculate 2 to the power of 16 and get 65536.

$$65535\left(65536+1\right)\left(2^{32}+1\right)$$

Add 65536 and 1 to get 65537.

$$65535\times 65537\left(2^{32}+1\right)$$

Multiply 65535 and 65537 to get 4294967295.

$$4294967295\left(2^{32}+1\right)$$

Calculate 2 to the power of 32 and get 4294967296.

$$4294967295\left(4294967296+1\right)$$

Add 4294967296 and 1 to get 4294967297.

$$4294967295\times 4294967297$$

Multiply 4294967295 and 4294967297 to get 18446744073709551615.

$$18446744073709551615$$

Factor

$$3\times 5\times 17\times 257\times 641\times 65537\times 6700417$$