f = b0110011001110111111000100000000101000110010100001000111110110111 f = 0x6677e20146508fb7 f = 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

v₀ = x⁰ (mod f)
v₀ = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 v₀ = 0x00000000000000000000000000000001 v₀ = 1
v₁ = x² (mod f)
v₁ = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100 v₁ = 0x00000000000000000000000000000004 v₁ = x²
v₂ = x⁴ (mod f)
v₂ = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000 v₂ = 0x00000000000000000000000000000010 v₂ = x⁴
v₃ = x⁶ (mod f)
v₃ = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000 v₃ = 0x00000000000000000000000000000040 v₃ = x⁶
v₄ = x⁸ (mod f)
v₄ = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000 v₄ = 0x00000000000000000000000000000100 v₄ = x⁸
v₅ = x¹⁰ (mod f)
v₅ = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000 v₅ = 0x00000000000000000000000000000400 v₅ = x¹⁰
v₆ = x¹² (mod f)
v₆ = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000 v₆ = 0x00000000000000000000000000001000 v₆ = x¹²
v₇ = x¹⁴ (mod f)
v₇ = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000 v₇ = 0x00000000000000000000000000004000 v₇ = x¹⁴
v₈ = x¹⁶ (mod f)
v₈ = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000 v₈ = 0x00000000000000000000000000010000 v₈ = x¹⁶
v₉ = x¹⁸ (mod f)
v₉ = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000 v₉ = 0x00000000000000000000000000040000 v₉ = x¹⁸
v₁₀ = x²⁰ (mod f)
v₁₀ = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000 v₁₀ = 0x00000000000000000000000000100000 v₁₀ = x²⁰
v₁₁ = x²² (mod f)
v₁₁ = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000 v₁₁ = 0x00000000000000000000000000400000 v₁₁ = x²²
v₁₂ = x²⁴ (mod f)
v₁₂ = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000 v₁₂ = 0x00000000000000000000000001000000 v₁₂ = x²⁴
v₁₃ = x²⁶ (mod f)
v₁₃ = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000 v₁₃ = 0x00000000000000000000000004000000 v₁₃ = x²⁶
v₁₄ = x²⁸ (mod f)
v₁₄ = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000 v₁₄ = 0x00000000000000000000000010000000 v₁₄ = x²⁸
v₁₅ = x³⁰ (mod f)
v₁₅ = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000 v₁₅ = 0x00000000000000000000000040000000 v₁₅ = x³⁰
v₁₆ = x³² (mod f)
v₁₆ = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000 v₁₆ = 0x00000000000000000000000100000000 v₁₆ = x³²
v₁₇ = x³⁴ (mod f)
v₁₇ = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000 v₁₇ = 0x00000000000000000000000400000000 v₁₇ = x³⁴
v₁₈ = x³⁶ (mod f)
v₁₈ = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000 v₁₈ = 0x00000000000000000000001000000000 v₁₈ = x³⁶
v₁₉ = x³⁸ (mod f)
v₁₉ = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000 v₁₉ = 0x00000000000000000000004000000000 v₁₉ = x³⁸
v₂₀ = x⁴⁰ (mod f)
v₂₀ = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000 v₂₀ = 0x00000000000000000000010000000000 v₂₀ = x⁴⁰
v₂₁ = x⁴² (mod f)
v₂₁ = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000 v₂₁ = 0x00000000000000000000040000000000 v₂₁ = x⁴²
v₂₂ = x⁴⁴ (mod f)
v₂₂ = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000 v₂₂ = 0x00000000000000000000100000000000 v₂₂ = x⁴⁴
v₂₃ = x⁴⁶ (mod f)
v₂₃ = b00000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000 v₂₃ = 0x00000000000000000000400000000000 v₂₃ = x⁴⁶
v₂₄ = x⁴⁸ (mod f)
v₂₄ = b00000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000 v₂₄ = 0x00000000000000000001000000000000 v₂₄ = x⁴⁸
v₂₅ = x⁵⁰ (mod f)
v₂₅ = b00000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000 v₂₅ = 0x00000000000000000004000000000000 v₂₅ = x⁵⁰
v₂₆ = x⁵² (mod f)
v₂₆ = b00000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000 v₂₆ = 0x00000000000000000010000000000000 v₂₆ = x⁵²
v₂₇ = x⁵⁴ (mod f)
v₂₇ = b00000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000 v₂₇ = 0x00000000000000000040000000000000 v₂₇ = x⁵⁴
v₂₈ = x⁵⁶ (mod f)
v₂₈ = b00000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000 v₂₈ = 0x00000000000000000100000000000000 v₂₈ = x⁵⁶
v₂₉ = x⁵⁸ (mod f)
v₂₉ = b00000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000 v₂₉ = 0x00000000000000000400000000000000 v₂₉ = x⁵⁸
v₃₀ = x⁶⁰ (mod f)
v₃₀ = b00000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000 v₃₀ = 0x00000000000000001000000000000000 v₃₀ = x⁶⁰
v₃₁ = x⁶² (mod f)
v₃₁ = b00000000000000000000000000000000000000000000000000000000000000000010011001110111111000100000000101000110010100001000111110110111 v₃₁ = 0x00000000000000002677e20146508fb7 v₃₁ = 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
v₃₂ = x⁶⁴ (mod f)
v₃₂ = b00000000000000000000000000000000000000000000000000000000000000000011001101000111101011100000011011010011101100111010111000000101 v₃₂ = 0x00000000000000003347ae06d3b3ae05 v₃₂ = x⁶¹ + x⁶⁰ + x⁵⁷ + x⁵⁶ + x⁵⁴ + x⁵⁰ + x⁴⁹ + x⁴⁸ + x⁴⁷ + x⁴⁵ + x⁴³ + x⁴² + x⁴¹ + x³⁴ + x³³ + x³¹ + x³⁰ + x²⁸ + x²⁵ + x²⁴ + x²³ + x²¹ + x²⁰ + x¹⁷ + x¹⁶ + x¹⁵ + x¹³ + x¹¹ + x¹⁰ + x⁹ + x² + 1
v₃₃ = x⁶⁶ (mod f)
v₃₃ = b00000000000000000000000000000000000000000000000000000000000000000000000111110001011111000001100111000010011011111010011101111010 v₃₃ = 0x000000000000000001f17c19c26fa77a v₃₃ = x⁵⁶ + x⁵⁵ + x⁵⁴ + x⁵³ + x⁵² + x⁴⁸ + x⁴⁶ + x⁴⁵ + x⁴⁴ + x⁴³ + x⁴² + x³⁶ + x³⁵ + x³² + x³¹ + x³⁰ + x²⁵ + x²² + x²¹ + x¹⁹ + x¹⁸ + x¹⁷ + x¹⁶ + x¹⁵ + x¹³ + x¹⁰ + x⁹ + x⁸ + x⁶ + x⁵ + x⁴ + x³ + x
v₃₄ = x⁶⁸ (mod f)
v₃₄ = b00000000000000000000000000000000000000000000000000000000000000000000011111000101111100000110011100001001101111101001110111101000 v₃₄ = 0x000000000000000007c5f06709be9de8 v₃₄ = x⁵⁸ + x⁵⁷ + x⁵⁶ + x⁵⁵ + x⁵⁴ + x⁵⁰ + x⁴⁸ + x⁴⁷ + x⁴⁶ + x⁴⁵ + x⁴⁴ + x³⁸ + x³⁷ + x³⁴ + x³³ + x³² + x²⁷ + x²⁴ + x²³ + x²¹ + x²⁰ + x¹⁹ + x¹⁸ + x¹⁷ + x¹⁵ + x¹² + x¹¹ + x¹⁰ + x⁸ + x⁷ + x⁶ + x⁵ + x³
v₃₅ = x⁷⁰ (mod f)
v₃₅ = b00000000000000000000000000000000000000000000000000000000000000000001111100010111110000011001110000100110111110100111011110100000 v₃₅ = 0x00000000000000001f17c19c26fa77a0 v₃₅ = x⁶⁰ + x⁵⁹ + x⁵⁸ + x⁵⁷ + x⁵⁶ + x⁵² + x⁵⁰ + x⁴⁹ + x⁴⁸ + x⁴⁷ + x⁴⁶ + x⁴⁰ + x³⁹ + x³⁶ + x³⁵ + x³⁴ + x²⁹ + x²⁶ + x²⁵ + x²³ + x²² + x²¹ + x²⁰ + x¹⁹ + x¹⁷ + x¹⁴ + x¹³ + x¹² + x¹⁰ + x⁹ + x⁸ + x⁷ + x⁵
v₃₆ = x⁷² (mod f)
v₃₆ = b00000000000000000000000000000000000000000000000000000000000000000001101000101000111001000111000111011101101110010101000100110111 v₃₆ = 0x00000000000000001a28e471ddb95137 v₃₆ = x⁶⁰ + x⁵⁹ + x⁵⁷ + x⁵³ + x⁵¹ + x⁴⁷ + x⁴⁶ + x⁴⁵ + x⁴² + x³⁸ + x³⁷ + x³⁶ + x³² + x³¹ + x³⁰ + x²⁸ + x²⁷ + x²⁶ + x²⁴ + x²³ + x²¹ + x²⁰ + x¹⁹ + x¹⁶ + x¹⁴ + x¹² + x⁸ + x⁵ + x⁴ + x² + x + 1
v₃₇ = x⁷⁴ (mod f)
v₃₇ = b00000000000000000000000000000000000000000000000000000000000000000000111011010100011100111100011000110000101101011100101101101011 v₃₇ = 0x00000000000000000ed473c630b5cb6b v₃₇ = x⁵⁹ + x⁵⁸ + x⁵⁷ + x⁵⁵ + x⁵⁴ + x⁵² + x⁵⁰ + x⁴⁶ + x⁴⁵ + x⁴⁴ + x⁴¹ + x⁴⁰ + x³⁹ + x³⁸ + x³⁴ + x³³ + x²⁹ + x²⁸ + x²³ + x²¹ + x²⁰ + x¹⁸ + x¹⁶ + x¹⁵ + x¹⁴ + x¹¹ + x⁹ + x⁸ + x⁶ + x⁵ + x³ + x + 1
v₃₈ = x⁷⁶ (mod f)
v₃₈ = b00000000000000000000000000000000000000000000000000000000000000000011101101010001110011110001100011000010110101110010110110101100 v₃₈ = 0x00000000000000003b51cf18c2d72dac v₃₈ = x⁶¹ + x⁶⁰ + x⁵⁹ + x⁵⁷ + x⁵⁶ + x⁵⁴ + x⁵² + x⁴⁸ + x⁴⁷ + x⁴⁶ + x⁴³ + x⁴² + x⁴¹ + x⁴⁰ + x³⁶ + x³⁵ + x³¹ + x³⁰ + x²⁵ + x²³ + x²² + x²⁰ + x¹⁸ + x¹⁷ + x¹⁶ + x¹³ + x¹¹ + x¹⁰ + x⁸ + x⁷ + x⁵ + x³ + x²
v₃₉ = x⁷⁸ (mod f)
v₃₉ = b00000000000000000000000000000000000000000000000000000000000000000010000110101000111110000110000110000111111111011010100111011110 v₃₉ = 0x000000000000000021a8f86187fda9de v₃₉ = x⁶¹ + x⁵⁶ + x⁵⁵ + x⁵³ + x⁵¹ + x⁴⁷ + x⁴⁶ + x⁴⁵ + x⁴⁴ + x⁴³ + x³⁸ + x³⁷ + x³² + x³¹ + x²⁶ + x²⁵ + x²⁴ + x²³ + x²² + x²¹ + x²⁰ + x¹⁹ + x¹⁸ + x¹⁶ + x¹⁵ + x¹³ + x¹¹ + x⁸ + x⁷ + x⁶ + x⁴ + x³ + x² + x
v₄₀ = x⁸⁰ (mod f)
v₄₀ = b00000000000000000000000000000000000000000000000000000000000000000010110000111011110001111000010111010101000001110011011110100001 v₄₀ = 0x00000000000000002c3bc785d50737a1 v₄₀ = x⁶¹ + x⁵⁹ + x⁵⁸ + x⁵³ + x⁵² + x⁵¹ + x⁴⁹ + x⁴⁸ + x⁴⁷ + x⁴⁶ + x⁴² + x⁴¹ + x⁴⁰ + x³⁹ + x³⁴ + x³² + x³¹ + x³⁰ + x²⁸ + x²⁶ + x²⁴ + x¹⁸ + x¹⁷ + x¹⁶ + x¹³ + x¹² + x¹⁰ + x⁹ + x⁸ + x⁷ + x⁵ + 1
v₄₁ = x⁸² (mod f)
v₄₁ = b00000000000000000000000000000000000000000000000000000000000000000001101001110111001110000001010010011110111011010100111001011101 v₄₁ = 0x00000000000000001a7738149eed4e5d v₄₁ = x⁶⁰ + x⁵⁹ + x⁵⁷ + x⁵⁴ + x⁵³ + x⁵² + x⁵⁰ + x⁴⁹ + x⁴⁸ + x⁴⁵ + x⁴⁴ + x⁴³ + x³⁶ + x³⁴ + x³¹ + x²⁸ + x²⁷ + x²⁶ + x²⁵ + x²³ + x²² + x²¹ + x¹⁹ + x¹⁸ + x¹⁶ + x¹⁴ + x¹¹ + x¹⁰ + x⁹ + x⁶ + x⁴ + x³ + x² + 1
v₄₂ = x⁸⁴ (mod f)
v₄₂ = b00000000000000000000000000000000000000000000000000000000000000000000111110101011000000100101001100111101111001011011011011000011 v₄₂ = 0x00000000000000000fab02533de5b6c3 v₄₂ = x⁵⁹ + x⁵⁸ + x⁵⁷ + x⁵⁶ + x⁵⁵ + x⁵³ + x⁵¹ + x⁴⁹ + x⁴⁸ + x⁴¹ + x³⁸ + x³⁶ + x³³ + x³² + x²⁹ + x²⁸ + x²⁷ + x²⁶ + x²⁴ + x²³ + x²² + x²¹ + x¹⁸ + x¹⁶ + x¹⁵ + x¹³ + x¹² + x¹⁰ + x⁹ + x⁷ + x⁶ + x + 1
v₄₃ = x⁸⁶ (mod f)
v₄₃ = b00000000000000000000000000000000000000000000000000000000000000000011111010101100000010010100110011110111100101101101101100001100 v₄₃ = 0x00000000000000003eac094cf796db0c v₄₃ = x⁶¹ + x⁶⁰ + x⁵⁹ + x⁵⁸ + x⁵⁷ + x⁵⁵ + x⁵³ + x⁵¹ + x⁵⁰ + x⁴³ + x⁴⁰ + x³⁸ + x³⁵ + x³⁴ + x³¹ + x³⁰ + x²⁹ + x²⁸ + x²⁶ + x²⁵ + x²⁴ + x²³ + x²⁰ + x¹⁸ + x¹⁷ + x¹⁵ + x¹⁴ + x¹² + x¹¹ + x⁹ + x⁸ + x³ + x²
v₄₄ = x⁸⁸ (mod f)
v₄₄ = b00000000000000000000000000000000000000000000000000000000000000000011011001011111111000010011000101010010111110100111001101011110 v₄₄ = 0x0000000000000000365fe13152fa735e v₄₄ = x⁶¹ + x⁶⁰ + x⁵⁸ + x⁵⁷ + x⁵⁴ + x⁵² + x⁵¹ + x⁵⁰ + x⁴⁹ + x⁴⁸ + x⁴⁷ + x⁴⁶ + x⁴⁵ + x⁴⁰ + x³⁷ + x³⁶ + x³² + x³⁰ + x²⁸ + x²⁵ + x²³ + x²² + x²¹ + x²⁰ + x¹⁹ + x¹⁷ + x¹⁴ + x¹³ + x¹² + x⁹ + x⁸ + x⁶ + x⁴ + x³ + x² + x
v₄₅ = x⁹⁰ (mod f)
v₄₅ = b00000000000000000000000000000000000000000000000000000000000000000001010110010000010000001100011111000111010010001101001000010110 v₄₅ = 0x0000000000000000159040c7c748d216 v₄₅ = x⁶⁰ + x⁵⁸ + x⁵⁶ + x⁵⁵ + x⁵² + x⁴⁶ + x³⁹ + x³⁸ + x³⁴ + x³³ + x³² + x³¹ + x³⁰ + x²⁶ + x²⁵ + x²⁴ + x²² + x¹⁹ + x¹⁵ + x¹⁴ + x¹² + x⁹ + x⁴ + x² + x
v₄₆ = x⁹² (mod f)
v₄₆ = b00000000000000000000000000000000000000000000000000000000000000000011000000110110111000010001111001011011011100111100011111101111 v₄₆ = 0x00000000000000003036e11e5b73c7ef v₄₆ = x⁶¹ + x⁶⁰ + x⁵³ + x⁵² + x⁵⁰ + x⁴⁹ + x⁴⁷ + x⁴⁶ + x⁴⁵ + x⁴⁰ + x³⁶ + x³⁵ + x³⁴ + x³³ + x³⁰ + x²⁸ + x²⁷ + x²⁵ + x²⁴ + x²² + x²¹ + x²⁰ + x¹⁷ + x¹⁶ + x¹⁵ + x¹⁴ + x¹⁰ + x⁹ + x⁸ + x⁷ + x⁶ + x⁵ + x³ + x² + x + 1
v₄₇ = x⁹⁴ (mod f)
v₄₇ = b00000000000000000000000000000000000000000000000000000000000000000000110000110100010000000111101111100001011011100000000011010010 v₄₇ = 0x00000000000000000c34407be16e00d2 v₄₇ = x⁵⁹ + x⁵⁸ + x⁵³ + x⁵² + x⁵⁰ + x⁴⁶ + x³⁸ + x³⁷ + x³⁶ + x³⁵ + x³³ + x³² + x³¹ + x³⁰ + x²⁹ + x²⁴ + x²² + x²¹ + x¹⁹ + x¹⁸ + x¹⁷ + x⁷ + x⁶ + x⁴ + x
v₄₈ = x⁹⁶ (mod f)
v₄₈ = b00000000000000000000000000000000000000000000000000000000000000000011000011010001000000011110111110000101101110000000001101001000 v₄₈ = 0x000000000000000030d101ef85b80348 v₄₈ = x⁶¹ + x⁶⁰ + x⁵⁵ + x⁵⁴ + x⁵² + x⁴⁸ + x⁴⁰ + x³⁹ + x³⁸ + x³⁷ + x³⁵ + x³⁴ + x³³ + x³² + x³¹ + x²⁶ + x²⁴ + x²³ + x²¹ + x²⁰ + x¹⁹ + x⁹ + x⁸ + x⁶ + x³
v₄₉ = x⁹⁸ (mod f)
v₄₉ = b00000000000000000000000000000000000000000000000000000000000000000000111110101011110000111011110010011010010000010001001001001110 v₄₉ = 0x00000000000000000fabc3bc9a41124e v₄₉ = x⁵⁹ + x⁵⁸ + x⁵⁷ + x⁵⁶ + x⁵⁵ + x⁵³ + x⁵¹ + x⁴⁹ + x⁴⁸ + x⁴⁷ + x⁴⁶ + x⁴¹ + x⁴⁰ + x³⁹ + x³⁷ + x³⁶ + x³⁵ + x³⁴ + x³¹ + x²⁸ + x²⁷ + x²⁵ + x²² + x¹⁶ + x¹² + x⁹ + x⁶ + x³ + x² + x
v₅₀ = x¹⁰⁰ (mod f)
v₅₀ = b00000000000000000000000000000000000000000000000000000000000000000011111010101111000011101111001001101001000001000100100100111000 v₅₀ = 0x00000000000000003eaf0ef269044938 v₅₀ = x⁶¹ + x⁶⁰ + x⁵⁹ + x⁵⁸ + x⁵⁷ + x⁵⁵ + x⁵³ + x⁵¹ + x⁵⁰ + x⁴⁹ + x⁴⁸ + x⁴³ + x⁴² + x⁴¹ + x³⁹ + x³⁸ + x³⁷ + x³⁶ + x³³ + x³⁰ + x²⁹ + x²⁷ + x²⁴ + x¹⁸ + x¹⁴ + x¹¹ + x⁸ + x⁵ + x⁴ + x³
v₅₁ = x¹⁰² (mod f)
v₅₁ = b00000000000000000000000000000000000000000000000000000000000000000011011001010011111111111100101100101000101100000011101110001110 v₅₁ = 0x00000000000000003653ffcb28b03b8e v₅₁ = x⁶¹ + x⁶⁰ + x⁵⁸ + x⁵⁷ + x⁵⁴ + x⁵² + x⁴⁹ + x⁴⁸ + x⁴⁷ + x⁴⁶ + x⁴⁵ + x⁴⁴ + x⁴³ + x⁴² + x⁴¹ + x⁴⁰ + x³⁹ + x³⁸ + x³⁵ + x³³ + x³² + x²⁹ + x²⁷ + x²³ + x²¹ + x²⁰ + x¹³ + x¹² + x¹¹ + x⁹ + x⁸ + x⁷ + x³ + x² + x
v₅₂ = x¹⁰⁴ (mod f)
v₅₂ = b00000000000000000000000000000000000000000000000000000000000000000001010110100000001110110010111000101110011000011111000101010110 v₅₂ = 0x000000000000000015a03b2e2e61f156 v₅₂ = x⁶⁰ + x⁵⁸ + x⁵⁶ + x⁵⁵ + x⁵³ + x⁴⁵ + x⁴⁴ + x⁴³ + x⁴¹ + x⁴⁰ + x³⁷ + x³⁵ + x³⁴ + x³³ + x²⁹ + x²⁷ + x²⁶ + x²⁵ + x²² + x²¹ + x¹⁶ + x¹⁵ + x¹⁴ + x¹³ + x¹² + x⁸ + x⁶ + x⁴ + x² + x
v₅₃ = x¹⁰⁶ (mod f)
v₅₃ = b00000000000000000000000000000000000000000000000000000000000000000011000011110111000011101011100111111111110101110100101011101111 v₅₃ = 0x000000000000000030f70eb9ffd74aef v₅₃ = x⁶¹ + x⁶⁰ + x⁵⁵ + x⁵⁴ + x⁵³ + x⁵² + x⁵⁰ + x⁴⁹ + x⁴⁸ + x⁴³ + x⁴² + x⁴¹ + x³⁹ + x³⁷ + x³⁶ + x³⁵ + x³² + x³¹ + x³⁰ + x²⁹ + x²⁸ + x²⁷ + x²⁶ + x²⁵ + x²⁴ + x²³ + x²² + x²⁰ + x¹⁸ + x¹⁷ + x¹⁶ + x¹⁴ + x¹¹ + x⁹ + x⁷ + x⁶ + x⁵ + x³ + x² + x + 1
v₅₄ = x¹⁰⁸ (mod f)
v₅₄ = b00000000000000000000000000000000000000000000000000000000000000000000111100110011111111101110010101110011111111000011010011010010 v₅₄ = 0x00000000000000000f33fee573fc34d2 v₅₄ = x⁵⁹ + x⁵⁸ + x⁵⁷ + x⁵⁶ + x⁵³ + x⁵² + x⁴⁹ + x⁴⁸ + x⁴⁷ + x⁴⁶ + x⁴⁵ + x⁴⁴ + x⁴³ + x⁴² + x⁴¹ + x³⁹ + x³⁸ + x³⁷ + x³⁴ + x³² + x³⁰ + x²⁹ + x²⁸ + x²⁵ + x²⁴ + x²³ + x²² + x²¹ + x²⁰ + x¹⁹ + x¹⁸ + x¹³ + x¹² + x¹⁰ + x⁷ + x⁶ + x⁴ + x
v₅₅ = x¹¹⁰ (mod f)
v₅₅ = b00000000000000000000000000000000000000000000000000000000000000000011110011001111111110111001010111001111111100001101001101001000 v₅₅ = 0x00000000000000003ccffb95cff0d348 v₅₅ = x⁶¹ + x⁶⁰ + x⁵⁹ + x⁵⁸ + x⁵⁵ + x⁵⁴ + x⁵¹ + x⁵⁰ + x⁴⁹ + x⁴⁸ + x⁴⁷ + x⁴⁶ + x⁴⁵ + x⁴⁴ + x⁴³ + x⁴¹ + x⁴⁰ + x³⁹ + x³⁶ + x³⁴ + x³² + x³¹ + x³⁰ + x²⁷ + x²⁶ + x²⁵ + x²⁴ + x²³ + x²² + x²¹ + x²⁰ + x¹⁵ + x¹⁴ + x¹² + x⁹ + x⁸ + x⁶ + x³
v₅₆ = x¹¹² (mod f)
v₅₆ = b00000000000000000000000000000000000000000000000000000000000000000011111111010000001010100101010110110011011000100101001001001110 v₅₆ = 0x00000000000000003fd02a55b362524e v₅₆ = x⁶¹ + x⁶⁰ + x⁵⁹ + x⁵⁸ + x⁵⁷ + x⁵⁶ + x⁵⁵ + x⁵⁴ + x⁵² + x⁴⁵ + x⁴³ + x⁴¹ + x³⁸ + x³⁶ + x³⁴ + x³² + x³¹ + x²⁹ + x²⁸ + x²⁵ + x²⁴ + x²² + x²¹ + x¹⁷ + x¹⁴ + x¹² + x⁹ + x⁶ + x³ + x² + x
v₅₇ = x¹¹⁴ (mod f)
v₅₇ = b00000000000000000000000000000000000000000000000000000000000000000011001110101111011011010101010001000001001010000101011001010110 v₅₇ = 0x000000000000000033af6d5441285656 v₅₇ = x⁶¹ + x⁶⁰ + x⁵⁷ + x⁵⁶ + x⁵⁵ + x⁵³ + x⁵¹ + x⁵⁰ + x⁴⁹ + x⁴⁸ + x⁴⁶ + x⁴⁵ + x⁴³ + x⁴² + x⁴⁰ + x³⁸ + x³⁶ + x³⁴ + x³⁰ + x²⁴ + x²¹ + x¹⁹ + x¹⁴ + x¹² + x¹⁰ + x⁹ + x⁶ + x⁴ + x² + x
v₅₈ = x¹¹⁶ (mod f)
v₅₈ = b00000000000000000000000000000000000000000000000000000000000000000000001001010010011100010101001110001000000000000100011000110110 v₅₈ = 0x00000000000000000252715388004636 v₅₈ = x⁵⁷ + x⁵⁴ + x⁵² + x⁴⁹ + x⁴⁶ + x⁴⁵ + x⁴⁴ + x⁴⁰ + x³⁸ + x³⁶ + x³³ + x³² + x³¹ + x²⁷ + x¹⁴ + x¹⁰ + x⁹ + x⁵ + x⁴ + x² + x
v₅₉ = x¹¹⁸ (mod f)
v₅₉ = b00000000000000000000000000000000000000000000000000000000000000000000100101001001110001010100111000100000000000010001100011011000 v₅₉ = 0x00000000000000000949c54e200118d8 v₅₉ = x⁵⁹ + x⁵⁶ + x⁵⁴ + x⁵¹ + x⁴⁸ + x⁴⁷ + x⁴⁶ + x⁴² + x⁴⁰ + x³⁸ + x³⁵ + x³⁴ + x³³ + x²⁹ + x¹⁶ + x¹² + x¹¹ + x⁷ + x⁶ + x⁴ + x³
v₆₀ = x¹²⁰ (mod f)
v₆₀ = b00000000000000000000000000000000000000000000000000000000000000000010010100100111000101010011100010000000000001000110001101100000 v₆₀ = 0x00000000000000002527153880046360 v₆₀ = x⁶¹ + x⁵⁸ + x⁵⁶ + x⁵³ + x⁵⁰ + x⁴⁹ + x⁴⁸ + x⁴⁴ + x⁴² + x⁴⁰ + x³⁷ + x³⁶ + x³⁵ + x³¹ + x¹⁸ + x¹⁴ + x¹³ + x⁹ + x⁸ + x⁶ + x⁵
v₆₁ = x¹²² (mod f)
v₆₁ = b00000000000000000000000000000000000000000000000000000000000000000011111000000100011100101110000111001010111000000001110101011001 v₆₁ = 0x00000000000000003e0472e1cae01d59 v₆₁ = x⁶¹ + x⁶⁰ + x⁵⁹ + x⁵⁸ + x⁵⁷ + x⁵⁰ + x⁴⁶ + x⁴⁵ + x⁴⁴ + x⁴¹ + x³⁹ + x³⁸ + x³⁷ + x³² + x³¹ + x³⁰ + x²⁷ + x²⁵ + x²³ + x²² + x²¹ + x¹² + x¹¹ + x¹⁰ + x⁸ + x⁶ + x⁴ + x³ + 1

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nv₀ = b00000000000000000000000000000000000000000000000000000000000000000001001001110000010000101110001001010001010011001000101011011100 nv₀ = 0x0000000000000000127042e2514c8adc nv₀ = x⁶⁰ + x⁵⁷ + x⁵⁴ + x⁵³ + x⁵² + x⁴⁶ + x⁴¹ + x³⁹ + x³⁸ + x³⁷ + x³³ + x³⁰ + x²⁸ + x²⁴ + x²² + x¹⁹ + x¹⁸ + x¹⁵ + x¹¹ + x⁹ + x⁷ + x⁶ + x⁴ + x³ + x²
nv₁ = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 nv₁ = 0x00000000000000000000000000000001 nv₁ = 1

kf_o = b0110011001110111111000100000000101000110010100001000111110110111 kf_o = 0x6677e20146508fb7 kf_o = 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

nv₀ = b0001001001110000010000101110001001010001010011001000101011011100 nv₀ = 0x127042e2514c8adc nv₀ = x⁶⁰ + x⁵⁷ + x⁵⁴ + x⁵³ + x⁵² + x⁴⁶ + x⁴¹ + x³⁹ + x³⁸ + x³⁷ + x³³ + x³⁰ + x²⁸ + x²⁴ + x²² + x¹⁹ + x¹⁸ + x¹⁵ + x¹¹ + x⁹ + x⁷ + x⁶ + x⁴ + x³ + x²

New factor (nf) = f/gcd(f,nv₀)

nf = b0000000000000000000000000000000010110000110000010101001011111001 nf = 0x00000000b0c152f9 nf = x³¹ + x²⁹ + x²⁸ + x²³ + x²² + x¹⁶ + x¹⁴ + x¹² + x⁹ + x⁷ + x⁶ + x⁵ + x⁴ + x³ + 1
Search though known factors (kf) for which (nf) factors evenly

kf₀ = b0110011001110111111000100000000101000110010100001000111110110111 kf₀ = 0x6677e20146508fb7 kf₀ = 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
t = kf₀/nf

t_remainder = b0000000000000000000000000000000000000000000000000000000000000000 t_remainder = 0x0000000000000000 t_remainder = 0

t_remainder == 0, nf is a factor of kf₀

kf₀ = nf // Replace kf₀ with nf
kf₁ = t_quotient // Append t_quotient to known factors list

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

kf₀ = b0000000000000000000000000000000010110000110000010101001011111001 kf₀ = 0x00000000b0c152f9 kf₀ = x³¹ + x²⁹ + x²⁸ + x²³ + x²² + x¹⁶ + x¹⁴ + x¹² + x⁹ + x⁷ + x⁶ + x⁵ + x⁴ + x³ + 1
kf₁ = b0000000000000000000000000000000011101011111100101000001100011111 kf₁ = 0x00000000ebf2831f kf₁ = x³¹ + x³⁰ + x²⁹ + x²⁷ + x²⁵ + x²⁴ + x²³ + x²² + x²¹ + x²⁰ + x¹⁷ + x¹⁵ + x⁹ + x⁸ + x⁴ + x³ + x² + x + 1

f = (b10110000110000010101001011111001)(b11101011111100101000001100011111) f = (0xb0c152f9)(0xebf2831f) f = (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) Berlekamp Algorithm