I cannot speak to the exact correspondence of 313 or other numbers within that specific system but, I have a feeling that it is of some significance. Nearly every religion or spiritual practice has some repetitive method of meditation. The number is almost always significant.
There are the many names of shiva, allah, yhvh, and the practice of the rosary.
In all of these cases I have found some reason for the numbers of the repitition. For catholics( among Franciscans) the rosary is usually a number of "Hail Marys" equal to the length of Mary's life(in this case 72) and five "Our Fathers" for the five wounds of Christ.
As to the vast amount of repetition I feel it works as both a self-hypnosis and trance creating practice. It is easy to note the use of Mantras by various new age groups where the meaning is not even known but the mood established is noticed.
Purists may frown but I have found that even the repetition of gibberish can have an affect on the mind. (Try chanting randomly created barborous enochian names)
Ending, I think that the number is important in setting the mood and this is the reason it is a practice that crosses culture and religion. Prayer beads for mantra chanting have been found in Buddhist, Christian, Islamic, Hindu, and ancient Peruvian cultures.
My own personal belief is that the number of prayers or recitations set different moods so that with each a different "vision" or "face" of god is seen and this accounts for so many of the similarities yet small differences in various gods.
I'm turning into a Kantian (help!).
If you haven't already you should check the wikipedia entry for Mantra.
Mantra Wiki Entryit explains the psychology and variations far better than I can.