Is there an age when the pap test is not necessary? The mammogram? I am seventy one and wondered if there is an age when these tests are no longer necessary.

It depends. Your previous history determines the age at which one can stop getting pap smears, but even then you still need an annual pelvic exam.
It depends. If someone is in relatively good health, no matter what their age, it is probably appropriate to continue screening mammography in order to detect early, and potentially curable, cancers. If someone has a terminal condition, or other severe medical problems resulting in a relatively short term expectation of survival, mammography probably adds no benefit.
It. It is recommended that woman age 50 (some say age 40) and over get mammograms to screen for breast cancer for as long as they are in good health. It is prudent you continue to get mammograms. Women age 70 and over who have had 3 normal pap smears in a row (and no abnormal results in the last 10 years) may choose to stop getting pap smears, per current national recommendations. Always follwo the advice of your health care provider.