3 Jul
2006
3 Jul
'06
6:18 p.m.
And Erdos proved the following refinement of Bertrand's postulate: the interval from n to 2n always contains both a 1 mod 4 and a 3 mod 4 prime. That'll do it.
Um ---- n = 0? n = 1? n = 2? By engineer's induction (only slightly modified), this needs to go back to the drawing board!
Yes, sorry, excessively brief: "For all sufficiently large n," and in particular, n>6 will do it. Which explains RKG's handful of solutions perfectly. --Michael -- It is very dark and after 2000. If you continue you are likely to be eaten by a bleen.