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May 14, 2012

Carnival of Mathematics 86

Brent Yorgey:

Welcome to the 86th Carnival of Mathematics! is semiprime, nontotient, and noncototient. It is also happy since and . In fact, it is the smallest happy, nontotient semiprime (the only smaller happy nontotient is 68--which is, of course, 86 in reverse--but 68 is not semiprime).

However, the most interesting mathematical fact about 86 (in my opinion) is that it is the largest known integer for which the decimal expansion of contains no zeros! In particular, . Although no one has proved it is the largest such , every up to (which is quite a lot, although still slightly less than the total number of integers) has been checked to contain at least one zero. The probability that any larger power of 2 contains no zeros is vanishingly small, given some reasonable assumptions about the distribution of digits in base-ten expansions of powers of two.

Posted by Jim Zellmer at May 14, 2012 1:57 AM
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