202 Help with a prime number spiral which turns 90 degrees at each prime 64 Is it possible to draw this picture without lifting the pen? 38 Are the nontrivial zeroes of the Riemann zeta function countable? 30 Why is the rational number system inadequate for analysis? 26 Past open problems with sudden and easy-to-understand solutions

### Reputation (20,709)

 +10 Prove that, given any positive integer n, some multiple of it must be of the form 99…900…0 +5 $\forall n\in\mathbb N:n^x\in\mathbb Q$ implies $x\in\mathbb Z$ - elementary proof? +5 Conductor of $\mathbb Q(\omega,\sqrt{\pi})/\mathbb Q(\omega)$ for nonprimary $\pi$ +10 Does a maximal ideal of $\mathbb{Z}[X,Y]$ contain a prime number?

### Questions (56)

 29 $\forall n\in\mathbb N:n^x\in\mathbb Q$ implies $x\in\mathbb Z$ - elementary proof? 20 At most one divisor in $[\sqrt{n},\sqrt{n}+\sqrt{n}]$ 16 Are derivatives of geometric progressions all irreducible? 15 Function $\Bbb Q\rightarrow\Bbb Q$ with everywhere irrational derivative 13 There is a prime between $n$ and $n^2$, without Bertrand

### Tags (266)

 320 prime-numbers × 37 125 geometry × 30 291 number-theory × 75 105 recreational-mathematics × 5 202 visualization × 2 104 sequences-and-series × 30 202 pattern-recognition 92 elementary-set-theory × 18 166 elementary-number-theory × 46 88 real-analysis × 40

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