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CRGreathouse · 2014-08-01, 07:18

I asked a question on stats.stackexchange about the factorization of 2015⁴ + 4¹³⁴⁵ (a number I just 'happened upon') because I was struck by the somewhat unusual factorization. At the time I was hoping for an algebraic factorization that I had missed, though this seems unlikely since 2015⁴ + x¹³⁴⁵ is irreducible. But is there any reason for this behavior? If it was just a typical number of its size the chance that it would have so many factors so (relatively) close together is something like .3% (which, I was reminded, corresponds to an alpha of about .006 since a priori I could have been surprised in either direction).

I did not cherry pick this number -- it was the only number I examined, and I suspected something funny -- algebraic factorization or other -- before I attempted the factorization.

It could be simple chance but I think not -- I think it shows a lack of understanding of factorizations on my part. Educate me!

2014-08-01, 07:18	#1
CRGreathouse Aug 2006 13512₈ Posts	Strange factorization I asked a question on stats.stackexchange about the factorization of 2015⁴ + 4¹³⁴⁵ (a number I just 'happened upon') because I was struck by the somewhat unusual factorization. At the time I was hoping for an algebraic factorization that I had missed, though this seems unlikely since 2015⁴ + x¹³⁴⁵ is irreducible. But is there any reason for this behavior? If it was just a typical number of its size the chance that it would have so many factors so (relatively) close together is something like .3% (which, I was reminded, corresponds to an alpha of about .006 since a priori I could have been surprised in either direction). I did not cherry pick this number -- it was the only number I examined, and I suspected something funny -- algebraic factorization or other -- before I attempted the factorization. It could be simple chance but I think not -- I think it shows a lack of understanding of factorizations on my part. Educate me!