gf(2) Iterate until all irreducible factors of f₀ are found

f₀ = b0110011001110111111000100000000101000110010100001000111110110111
f₀ = 0x6677e20146508fb7
f₀ = x⁶² + x⁶¹ + x⁵⁸ + x⁵⁷ + x⁵⁴ + x⁵³ + x⁵² + x⁵⁰ + x⁴⁹ + x⁴⁸ + x⁴⁷ + x⁴⁶ + x⁴⁵ + x⁴¹ + x³² + x³⁰ + x²⁶ + x²⁵ + x²² + x²⁰ + x¹⁵ + x¹¹ + x¹⁰ + x⁹ + x⁸ + x⁷ + x⁵ + x⁴ + x² + x + 1

Find at least one irreducible factor of f₀, if it exists.

Remove f₀ from list of resulting factors.
Add:

f₁ = b0000000000000000000000000000000010110000110000010101001011111001 f₁ = 0x00000000b0c152f9 f₁ = x³¹ + x²⁹ + x²⁸ + x²³ + x²² + x¹⁶ + x¹⁴ + x¹² + x⁹ + x⁷ + x⁶ + x⁵ + x⁴ + x³ + 1
f₂ = b0000000000000000000000000000000011101011111100101000001100011111 f₂ = 0x00000000ebf2831f f₂ = x³¹ + x³⁰ + x²⁹ + x²⁷ + x²⁵ + x²⁴ + x²³ + x²² + x²¹ + x²⁰ + x¹⁷ + x¹⁵ + x⁹ + x⁸ + x⁴ + x³ + x² + x + 1

f₁ = b0000000000000000000000000000000010110000110000010101001011111001
f₁ = 0x00000000b0c152f9
f₁ = x³¹ + x²⁹ + x²⁸ + x²³ + x²² + x¹⁶ + x¹⁴ + x¹² + x⁹ + x⁷ + x⁶ + x⁵ + x⁴ + x³ + 1

f₂ = b0000000000000000000000000000000011101011111100101000001100011111
f₂ = 0x00000000ebf2831f
f₂ = x³¹ + x³⁰ + x²⁹ + x²⁷ + x²⁵ + x²⁴ + x²³ + x²² + x²¹ + x²⁰ + x¹⁷ + x¹⁵ + x⁹ + x⁸ + x⁴ + x³ + x² + x + 1

f₀ = (b10110000110000010101001011111001)(b11101011111100101000001100011111) f₀ = (0xb0c152f9)(0xebf2831f) f₀ = (x³¹ + x²⁹ + x²⁸ + x²³ + x²² + x¹⁶ + x¹⁴ + x¹² + x⁹ + x⁷ + x⁶ + x⁵ + x⁴ + x³ + 1)(x³¹ + x³⁰ + x²⁹ + x²⁷ + x²⁵ + x²⁴ + x²³ + x²² + x²¹ + x²⁰ + x¹⁷ + x¹⁵ + x⁹ + x⁸ + x⁴ + x³ + x² + x + 1)

gf(2) Iterate until all irreducible factors of f0 are found

gf(2) Iterate until all irreducible factors of f₀ are found