Last year, in Happy 0 0 1 0 0 1 0 0 0 0 1!, I discussed an interesting way to represent numbers based on their prime factorization. For example, 63 is represented by **0 2 0 1 **because 63 = 2^{0} x 3^{2} x 5^{0} x 7^{1}.

In the prime power representation, 2015 was **0 0 1 0 0 1 0 0 0 0 1**. However, with 2016 = 2^{5} x 3^{2} x 5^{0} x 7^{1}, this year can be represented by the more concise **5 2 0 1**.

I doubt you can express next year’s greeting in a single breath. Because 2017 is the 306th prime, it will take the form “**Happy 0 0 0 … 0 0 0 1!**“, where the one is preceded by 305 zeros.

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