Surely, a month is possible to go up from $6k to $20k, but the odds are way in the slim arena.
Most past bitcoin bull runs contain a decent amount of ramping up before they go parabolic.
Of course, every bull run will be different, and each one will have its underlying dynamics that causes it to run up.
The last one took nearly two years from late 2015 and then had its final run up that took nearly two months to play out, of course, with an increasing upwards slope in the end.
Surely, if there is going to be an upsurge now, then the second half of 2013 that had finished off the double surge for the year would be the closest approximate model.. and even that one had a bit of ramping up for about a month before really going up the second month...
An upwards surge from here to the end of the year, and even shooting past $20k is not out of the question, but seems a bit pie in the sky, at the moment..... but surely, in bitcoinlandia, we need to almost be ready for anything, and surely I would love to see BTC shorts getting reckt and a large number of BTC naysayers and alt coin pumpers running after the BTC train.. though I am kind of suspecting that if a BTC pump were to take place in the coming month or two, there are going to be a lot of frothy altcoin projects coming along for the ride, and perhaps a number of them outperforming bitcoin in the short-term, even though their long term fundamentals don't even add up to the value of a pile of crap.