Can you solve this captcha?

Question

I found the following problem in a captcha: (and I was really surprised, I expected just regular blurred or distorted text)

enter image description here

What does that mean, and what would the solution be?

EDIT: It looks, from comments and answers, that this is a consequence of Riemann Hypothesis. I would appreciate if someone could outline the proof of that fact. Cheers!

The equation displayed is a consequence of the Riemann Hypothesis, but strictly weaker. The validity of the RH (and as far as I know, also of the displayed equation) is unknown, so maybe the expected answer is "unknown"? Or, more likely IMHO, this is just a hoax ... — Hagen von Eitzen, Oct 15 '14 at 11:24
This has been around at least since 2008. See http://www.hojohnlee.com/weblog/archives/2005/02/09/page/28/ currently at the bottom of the page. — Gerry Myerson, Oct 15 '14 at 12:24
The examples in the first update are not of the same kind as this -- they are actually answerable by most people with a reasonable mathematical background, freshman calculus in the first two and elementary-school arithmetic in the last. Update 2 (unfolded dodecahedron) must be either another joke or an attempt to make it really cumbersome for non-premium users. — hmakholm left over Monica, Oct 15 '14 at 14:34
"I just found some pics on the internet" does not make a good question. — , Oct 15 '14 at 14:50
Thanks @The-Game for the edit, the post is as clear as it initially was now ! :) — Traklon, Oct 15 '14 at 15:06
@HagenvonEitzen: What on earth does "strictly weaker than RH" mean? If RH is true then there is nothing strictly weaker than RH... But we don't know whether RH is true or not. — user21820, Aug 15 '16 at 12:28

Traklon · Answer 1 · 2014-10-15T11:27:58.723

14

The Riemann hypothesis is one of the seven Clay Mathematics Institute Millennium Prize Problems. It hasn't been solved as of today and the resolution of this is way beyond your average Internet user knowledge of mathematics. You can tell how difficult this problem is with the enormous hype that surrounded the resolution of Poincaré's Conjecture, the only Millenium Problem that has been solved.

So my guess is that it is joke, either on your friend's side (a montage), or on the webpage's side (like a way to tell you that as a non-premium user, you can't access the file).

edited Oct 15 '14 at 11:27

answered Oct 15 '14 at 11:22

Traklon

2,838

12

To be honest, anything more complex $(a+b)^2 = a^2 + 2ab + b^2$ is way beyond your average internet user knowledge of mathematics – Ant Oct 15 '14 at 13:00
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The average internet user knows for a fact that $(a+b)^2=a^2+b^2$. – Did Oct 15 '14 at 17:00
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@Did average MSE users knows for a fact that $(a+b)^2=a^2+b^2$ Only when a and b is 0 :) – M.S.E Oct 16 '14 at 14:27
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@Tharindu Actually when $a$ or $b$ are $0$. – Oct 21 '14 at 04:45
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Actually when $a$ and $b$ are elements of a field of characteristic $2$! (This is the so-called freshman's dream or biologist's rule.) – Peter Humphries Jan 05 '15 at 07:15
actually when multiplication is anticommutative, what is ab = - ba. – moudrick Dec 10 '16 at 22:12

score 10 · Accepted Answer · edited Oct 17 '14 at 02:57

The Riemann Hypothesis is arguably the most famous problem in mathematics. Its usual statement involves the zeroes of a function $\zeta:\mathbb C\to\mathbb C$ defined by $$\zeta(s)=\sum_{n=1}^\infty \frac{1}{n^s}.$$ Although it looks like it's only in the world of complex numbers, it turns out to have much deeper implications in number theory and exaplaining the behavior of the prime numbers. It's an open problem, however - nobody has solved it yet. We have however proved that many things assuming it, and the statement here is one of these.

The symbol $\pi(x)$ is the prime counting function, it counts the number of prime numbers less than or equal to $x$. So for instance $\pi(6) = 3$, because of the $3$ primes $2,3,5$. I assume you understand the integral. The $O(x^{1/2+\varepsilon})$ is just saying that the expression roughly acts like $x^{1/2+\varepsilon}$ as $x$ grows.

The problem is very hard - it's even worth a million dollars. I would go ahead and assume it's a scam or a joke.

Can you solve this captcha?

2 Answers2