Ginger, yes that is the wild - or weed, depending on how you look at it - purslane. It is delicious and very nutritious, too. I used to have tons of it; I let it grow as a natural mulch for a bed I'm no longer using. It really helps to keep the soil moist below and when there's too much, just pinch off the newest, tender stems and cook or cut up in a salad.
I'll look at Lowe's to see if they have any. I haven't ever seen the edible variety in a nursery, though.