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Apocalyptic number

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Apocalyptic numbers are numbers of the form 2n containing the digits 666 in their decimal expansions. 2157 is the smallest apocalyptic number: 182687704666362864775460604089535377456991567872 2n is an apocalyptic number for n = 157, 192, 218, 220, 222, ... (OEIS A007356). These values of n become increasingly dense, and as \(n ightarrow \infty\), the probability of \(2^n\) being apocalyptic becomes 1. Thus, when sufficiently large, apocalyptic numbers cease to be interesting and non-apocalyptic powers of two become more of a novelty.

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Apocalyptic numbers are numbers of the form 2n containing the digits 666 in their decimal expansions. 2157 is the smallest apocalyptic number: 182687704666362864775460604089535377456991567872 2n is an apocalyptic number for n = 157, 192, 218, 220, 222, ... (OEIS A007356). These values of n become increasingly dense, and as \(n ightarrow \infty\), the probability of \(2^n\) being apocalyptic becomes 1. Thus, when sufficiently large, apocalyptic numbers cease to be interesting and non-apocalyptic powers of two become more of a novelty. There are 3716 non-apocalyptic numbers of the form 2n for \(0 \le n \le 1000000\), the largest of which is \(2^{29784}\). From heuristic considerations, \(2^{29784}\) is very likely the largest one.