Explanation

Reading the exponents as printed (2¹²²+4⁶²+8⁶⁴+2¹³⁰): modulo 5, 2 has order 4, giving residues 4, 1, 1, 4 whose sum 10 ≡ 0 — so the number is divisible by 5. Modulo 11 the residues are 4, 5, 4, 1 (sum 14 ≡ 3), so 11 does not divide it; 3 and 7 fail similarly. The stored key D is therefore corrected to option B.