TITLE: Do 4 consecutive primes always form a polygon?
QUESTION [10 upvotes]: Related to this question, if 4 segments have length of 4 consecutive primes, can they always form a 4-vertex polygon?
This question occurred to me out of sheer curiosity, but now I can't prove or disprove it, and I can't sleep knowing that.
According to one form of Bertrand's postulate, $p_ {n+1} < 1.1 \times  p_{n}$ for large enough $n$, so it is easy to prove that for large enough $n$, the statement about polygon is true. But how to know the value of "large enough $n$", so that the statement about polygon can be manually checked for smaller $n$?

REPLY [7 votes]: Yes.
To have the lengths be valid for a quadrilateral, any one side must have length less than the sum of the lengths of the other three sides.
Bertrand's Postulate ensures that this is easily satisfied for four consecutive primes.