### 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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