The Meaning of Life, the Universe, and Everything.
Another thing to note is that, in a sense, all things grow twice as fast when torches are placed around them. This is because the light from touches acts as a light supply when it turns night time, and growing does not progress at night because there is no potent light source. Just thought this is good to know, since it will help them grow faster.
1. The stem takes awhile to grow (wouldn't be surprised if it was 2 hours).
2. The more squares around the stem that are available for pumpkins to grow (up to 4), the faster the pumpkin will grow.
3. You need an air block above the block that the pumpkin would occupy if it grew there.
4. You need water (this one should be obvious) 4 blocks away from the pumpkin at most (diagonals count as 1 block, not 2).