This is flat wrong!According to the definition of a burst, a character would get to choose the center of the burst anywhere within the range of the spell. The spell description contradicts itself. It gives a "Range" of 30 feet, and then says the burst is centered on the caster. For it to work the way I thought it did, the Range would have to be zero, and the area would be a 30' radius burst.
No part of a spell's effect may extend outside its range. See PHB p148, or this SRD page. "If any portion of the spell's area would extend beyond the range, that area is wasted."
If Prayer had a range of 0, then it would affect only the caster. Even if it still specified a 30' radius burst, the whole burst area would lie outside the range and would therefore be wasted.