I understand I can sell my prime residence without incurring income
tax on the capital gain, provided I have lived in the house two of the
past five years.  My question is this:  If I sell the house on
contract, taking monthly payments for the next 15 years, will I still
be exempt from tax on the entire capital gain?    Second part= Would
their be income tax on the interest received over the contract term,
or would it qualify as part of the tax free capital gain?

To clarify, you will not pay capital gains ont he first $250k of gains
 $500k if you are married.

Interest you earn is interest income.

Think of this transaction as having 2 distinct pieces.  
First you sell your house.  (and pay taxes on the gains subject to the
Internal revenue Code's prvisions)
Second, you loan somebody money secured by a piece of property.  (When
you purchase debt, the interest is income.  Also, that interest is not
taxed at capital gain tax rates, but at regular income tax rates
{which is much higher}.