Let's say both of you noticed each other and made eye contact. Then let's say at least one of the two of you has the courage to introduce yourself and exchange names, then speak for only 5 more minutes.
You don't know if you will see each other again, but the most courageous one asks for your number. Would you give it, after only 5 minutes of speaking?
maybe. it depends on the vibe I'm getting from the guy. but probably not. maybe just because where I live there tends to be a lot of drunk creeper tourists, so I put my guard up. my best guy friend was asked for his number once when we were out...by a straight and wasted guy. haha.