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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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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

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  • $\begingroup$ Correct! I'd recommend hiding the steps you used to reach the password to not spoil it for people that scroll down. (P.S. notice that the given number is prime, and that "Goldbach" was a mathematician...) $\endgroup$ – Vepir Aug 31 at 0:16

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