2^1000 mod 100?

gistfile1.txt

2^1  = 2  (mod 100)
-------------------
2^2  = 4  (mod 100) 
2^3  = 8  (mod 100) 
2^4  = 16 (mod 100)
2^5  = 32 (mod 100)
2^6  = 64 (mod 100)
2^7  = 28 (mod 100)
2^8  = 56 (mod 100)
2^9  = 12 (mod 100)
2^10 = 24 (mod 100)
2^11 = 48 (mod 100)
2^12 = 96 (mod 100)
2^13 = 92 (mod 100)
2^14 = 84 (mod 100)
2^15 = 68 (mod 100)
2^16 = 36 (mod 100)
2^17 = 72 (mod 100)
2^18 = 44 (mod 100)
2^19 = 88 (mod 100)
2^20 = 76 (mod 100)
2^21 = 52 (mod 100)
------------------
2^22 = 4  (mod 100) -> repeat the cycle except 2^1 

999 mod 20 = 19 

2^1000 = 2^20 = 76 (mod 76)