4. Goodwill and Purchased Intangibles

Goodwill

The carrying value of goodwill at each of September 30, 2023 and December 31, 2022 was $0.

The following table presents details of our purchased intangible assets as of September 30, 2023 and December 31, 2022:

Intangible assets

Schedule of Goodwill and Intangible Assets 

The intangible assets are being amortized on a straight-line basis over their estimated useful lives of one year to twenty years.

Amortization expense for intangible assets was $28,689 and $107,211 for the nine months ended September 30, 2023 and 2022, respectively, and is included in depreciation and amortization on the accompanying unaudited condensed consolidated statements of operations and comprehensive loss.

Amortization expense for intangible assets was $10,747 and $35,724 for the three months ended September 30, 2023 and 2022, respectively.

The estimated future amortization expense of our intangible assets as of September 30, 2023 is as follows:

Schedule of Finite Lived Intangible Assets Future Amortization Expense