Academic journal article The Science Teacher

Academic journal article The Science Teacher

## Article excerpt

Q The number 23, portrayed in a recent movie, seems to have an eerie number of life connections. Is there anything special about it?

Chemistry Student Hastings-On-Hudson High School

A We can show that every integer is special using proof by contradiction. Suppose not every integer is special, and let N be the smallest nonspecial integer. Then N is indeed special, a contradiction. This argument alone answers the question.

However, perhaps more along the lines of what you had in mind, possible reasons the digits of 23 might appear to be linked to the numerals inherent in so many life events can be found by using the simple functions of arithmetic. Numbers 2 and 3 are the two smallest prime numbers and the only adjacent primes, making them the factors of many larger integers. These two numbers are also the smallest-possible natural number bases (computers use base 2, the metric system uses base 10, the Babylonians used base 60). Because 2 and 3 are so small, and adjacent, the numbers and their combinations (e.g., powers, differences, sums) cover many more integers than any other two integers do.

One genuinely special occurrence of 23 happens to be that it answers the birthday problem: "How many people must there be in a room so that the probability that at least two have the same birthday is 50%?" Many people are surprised at the low answer of "23."

This brings to mind another factor that may be at work: There are so many events in life it is likely that many of them, when considered together, will appear oddly coincidental. …

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