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# Mathspp Blog

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##### Problem #063 – arbitrarily many primes in arbitrarily big intervals

Can you prove that there are arbitrarily many primes in arbitrarily big intervals?

##### Problem #023 - guess the polynomial

In this problem you have to devise a strategy to beat the computer in a "guess the polynomial" game.

##### Twitter proof: consecutive integers are coprime

Let's prove that if $$k$$ is an integer, then $$\gcd(k, k+1) = 1$$. That is, any two consecutive integers are coprime.

##### Problem #022 - coprimes in the crowd

This simple problem is an example of a very interesting phenomenon: if you have a large enough "universe" to consider, even randomly picked parts exhibit structured properties.

##### Water buckets riddle

Can you measure exactly $$2$$L of water with two plain buckets with volumes of $$14$$L and $$5$$L? Of course you can!

##### Problem #002 - a bag full of numbers

Two friends were bored and decided to play a game... a mathematical game with a paper bag!

##### Solving diophantine equations with random walks

Here's how I like to solve my equations: just walk around randomly until I trip over a solution!