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You need to unlock a safe by typing in the correct password. All you have is the following note:

5101216429918933541175819375754311977470728893977974053502952628004830200066913358490313939657011283996554248679751960067799456833385973491180810546439419511054758188819591642086783446840805291939266542651397802763957203603872522037468171369937150488334327367887021211651743386426815128607541508758043216285865873671575671600533540790034686766260273498787830380052705630254574619771306940252220669399877490534732311208332493719176748171146266754890481517914627070988337499999999999999999999999999999999999999999999999999999999999999999999999999996611

Sincerely,

C. Goldbach

What is the password?

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1 Answer 1

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Adding

3389 to the number given (to get to the next multiple of a large power of ten) yields:
$$2^{80}\cdot 3^{65}\cdot 5^{83}\cdot 7^{83}\cdot 11^{87}\cdot 13^{79}\cdot 17^{82}\cdot 19^{68}$$

Translating the exponents from decimal to ASCII gives:

PASSWORD

The title "Goldbach's safe" and name "C. Goldbach" likely refers to:

  • Goldbach's conjecture, which deals with expressing numbers as sums of two prime numbers (the large number and 3389 are both prime).
  • Goldbach's theorem and other results by Goldbach that deal with perfect powers.

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2
  • $\begingroup$ The code to the safe could be not the word but the number that leads to it. $\endgroup$
    – Florian F
    Commented Apr 16 at 20:16
  • $\begingroup$ @FlorianF Maybe, but the question does ask for a password and not a code... $\endgroup$
    – 2012rcampion
    Commented Apr 17 at 12:27

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