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Playing Perpelx City does not require you to solve every card. This particular card does require you to prove the Riemann Hypothesis which, to date, no one on Earth has succedded in doing. However, someday this hypthothesis may be solved, enabling you to enter the answer to the card.
We hope that you'd don't stop playing Perplex City because of this, as part of the game is to showcase as yet unsolved puzzled in the hopes that they may one day be solved. We are aware that this card has caused a lot of frustration and debate and will bear this in mind when designing future cards.
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Prime numbers are numbers that cannot be divided by any other number except themselves and 1. For example, 2, 3, 5, 7, 11, 13 and 17 are all prime numbers. Aside from their theoretical interest, large prime numbers have become increasingly important in day to day life since they underpin the cryptography that allows secure transactions to take place on the internet (such as encrypting your credit card details when you buy online). While there are standard techniques to discover new primes, and more importantly, check whether a number really is a prime, mathematicians have not been able to discover if there is any order to the way in which primes are distributed. However, the German mathematician G.F.G. Riemann (1826-1866) noticed that the frequency of primes is highly related to the Zeta Function, now known as the Riemann Zeta Function.
The Riemann Hypothesis is that "The real part of any non-trivial zero of the Riemann Zeta Function is 1/2." It sounds complicated (and it is!) but a lot rests on whether his hypothesis is true. There are many equations in abstract mathematics that have been solved on the assumption that the hypothesis is true--and if it isn't, then not only would we have to look at those equations again, but it would aso imply that there is a certain order to primes.
(As of 2004, the largest known prime was 7235733 digits long!)
BOTTOM RIGHT: $1,000,000 prize offered upon solving this puzzle see http://www.claymath.org/millennium/Riemann_Hypothesis/