What makes the primeness of number 7 so real (to some) as to be comforting (to some) is the absolute and shared confidence in the law that 7 is a prime. Absolute confidence in a law is attainable when external consistency (i.e., applicability across time and space) is replaced by internal logical consistency, as occurs in mathematics. What constitutes the logical is a matter of instinct, and is perceived as the beautiful. By pursuing the beautiful one pursues knowledge---in addition to gratification---as the concepts of the logical and the beautiful share their aesthetic origins. In creative work, the acute sense of beauty can replace the foresight of the relevance of one's creations.
Individuals will acknowledge proved mathematical laws to be true as long as the individuals' inborn concepts of beauty are similar. The mathematical truth is a property of the brain in the same way as the physical truth is a property of the outside world. An individual has the sense of control over experiments in mathematics that does not apply to experiments in physics---which justifies the distinction between mathematics and physics, for now.