Note: the question was changed after this answer was posted. The first two queries work for the original question. The last query (in the addendum) works for the updated question.
This should do the trick, though it will be a bit slow for larger tables:
SELECT prikey, authnum FROM myTable
WHERE prikey <> (SELECT MAX(prikey) FROM myTable)
ORDER BY prikey
This query is longer but for a large table it should faster. I'll leave it to you to decide:
SELECT * FROM (
SELECT
prikey,
authnum,
ROW_NUMBER() OVER (ORDER BY prikey DESC) AS RowRank
FROM myTable)
WHERE RowRank <> 1
ORDER BY prikey
Addendum There was an update to the question; here's the updated answer.
SELECT
common,
SUM(miles)
FROM (
SELECT
common,
miles,
ROW_NUMBER() OVER (PARTITION BY common ORDER BY prikey DESC) AS RowRank
FROM myTable
)
WHERE RowRank <> 1
GROUP BY common