A Study to Assess the Safety and Efficacy of Oral Armour Thyroid Compared to Synthetic T4 for the Treatment of Primary Hypothyroidism in Adult Participants

* Have a diagnosis of primary hypothyroidism made \>= 12 months prior to Screening. * Be on continuous thyroid replacement therapy of synthetic T4 for primary hypothyroidism for at least 12 months immediately prior to the Screening Visit. * Be on a stable FDA-approved daily dose of synthetic T4 prior to the Screening visit, and must be taking synthetic T4 dose of at least 25 mcg at Screening visit. Must enter the study using the same stable dose to determine dose conversion. * Documentation of 1 in-range thyroid-stimulating hormone (TSH) (i.e., within 0.45 - 4.12 mIU/L, inclusive) at Screening and at least 1 additional in range TSH (i.e., within 0.45 - 4.12 mIU/L, inclusive) taken at a minimum of 6 weeks and a maximum of 12 months prior to Screening.

* Any clinical condition or previous surgery that might affect the absorption, distribution, biotransformation, or excretion of Armour Thyroid or synthetic T4. * History of alcohol or other substance abuse within the previous 6 months prior to the Screening. * Known or suspected allergy or intolerance to any ingredients of Armour Thyroid, including its excipients, synthetic T4, other thyroid replacement medications, or pork products.