OR How soon do I need to use the profit from the sale of my primary resident to purchase another primary resident to avoid income tax?
The rule to which you are referring was eliminated inn 1997.
You no longer need to reinvest the proceeds to avoid income tax.
The rule has been replaced by the "last two out of five" rule, which is to say if you owned the residence and used it as your principal residence for the last two out of five years leading up to the sale, then you can exclude up to $250,000 in capital gain ($500,000 if married filing a joint return).
Purchasing another home is irrelevant. It has been irrelevant since 1997.
SALE OF HOUSE
If your gain was more than $250,000 filing Single, or more than $500,000 filing Married Filing Jointly the sale must be reported on your tax return. Whether you re-invested the gain in to another house is irrelevant. If you have a Form 1099-S go to Federal>Wages and Income>Less Common Income>Sale of Home (gain or loss)
If you owned and lived in the home as your primary residence for at least 2 of the last 5 years on the date of the sale, you do not have to report the home sale if the gain is less than $250K filing Single, or less than $500K filing Married Filing Jointly (and you both owned and lived in the home for at least 2 years).
NOTE: If you have ever used the home as rental property or claimed a home office, you have more information to enter