Little known fact: 22 is the smallest prime that can be formed from the product of smaller primes in four different ways (7x3, 3x7, and 7x1x3). Anyway, check out the 22nd skeptics circle.
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Little known fact: 21 is the smallest prime that can be formed from the product of smaller primes in four different ways (7x3, 3x7, and 7x1x3). Anyway, the 21st skeptics circle is here. Check it out.
In my last math post I casually mentioned that the sum of the reciprocals of the primes diverges. That is
\[
\frac{1}{2}+\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+\frac{1}{11}+\frac{1}{13}+ \dots=\infty
\]
That seems like a hard thing to prove. Certainly none of the traditional convergence tests…
There's one kind of semi-mathematical crackpottery that people frequently send to me, but which i generally don't write about. Given my background, I call it gematria - but it covers a much wider range than what's really technically meant by that term. Another good name for it would be numeric…
In this week's edition of Monday Math we look at what I regard as one of the prettiest equations in number theory. Here it is:
\[
\sum_{n=1}^\infty \frac{1}{n^s} = \prod_p \left( \frac{1}{1-\frac{1}{p^s}}\right)
\]
Doesn't it just make your heart go pitter-pat?
You are probably familiar with…
Is this a snare for the unthinking (let's see how widely copied through the net this gets?) or a typo or an unthinking moment?
My grasp of mathematics is fairly rudimentary but surely -
no prime is the product of any other primes except itself and one,
22 is divisable by 11 and 2, thus not a prime,
7x3 equals 21 not 22,
7x3 is the same as 3x7 and 7x3x1 not different amd represents one way to get ...21 and zero ways to get 22.
ok... so space is a spiral, and time is a curve. Have I got that right?
Ken,
You forgot to mention that Tim says "four" ways and then only lists 3. Without going out too far on a limb here, I think we can say this is a joke.
Nope :-) but try any of these:
wikipedia on 22