**Core Concept**
Prolactin is a hormone produced by the pituitary gland, playing a crucial role in lactation, reproductive processes, and various physiological functions. The synthesis and secretion of prolactin are regulated by the hypothalamic-pituitary axis, involving the action of dopamine as a prolactin-inhibiting factor.

**Why the Correct Answer is Right**
Prolactin is synthesized in the lactotroph cells of the anterior pituitary gland. This process involves the transcription and translation of the prolactin gene, resulting in the production of a preprohormone that is then processed and secreted as mature prolactin. The lactotroph cells are responsive to dopamine, which inhibits the secretion of prolactin by binding to D2 receptors.

**Why Each Wrong Option is Incorrect**
**Option A:** The hypothalamus is involved in the regulation of prolactin secretion, but it is not the primary site of synthesis. The hypothalamus produces dopamine, which inhibits prolactin release, but it does not synthesize prolactin itself.
**Option B:** The anterior pituitary gland is the correct location, but the specific cell type is lactotroph cells, not somatotroph cells. Somatotroph cells produce growth hormone.
**Option C:** The posterior pituitary gland is primarily involved in the storage and release of antidiuretic hormone (ADH) and oxytocin, not prolactin.
**Option D:** The thyroid gland is not involved in the synthesis of prolactin, which is a hormone produced by the pituitary gland.

**Clinical Pearl / High-Yield Fact**
The dopamine agonist bromocriptine is used to treat conditions such as hyperprolactinemia by inhibiting the secretion of prolactin from the pituitary gland. This highlights the importance of the dopamine-pituitary axis in regulating prolactin levels.

**Correct Answer:** C. The anterior pituitary gland, specifically the lactotroph cells, is the primary site of prolactin synthesis.