Maybe not every cat is the same, but my cats will sit on my lap for half an hour, never ever purring. Then only when I start petting them, will they purr. I think purring means "Wow, I feel good!" and not really "I am friendly". My big boy cat purrs the loudest and longest. He sleeps near my head, I pet him for as long as I can manage to stay awake and typically after I stop petting him he purrs for another minute or so... then he sighs very deeply and smacks his lips twice and goes to sleep. It's very cute.