Atopic Dermatitis (Eczema): This is a common condition characterized by itchy, inflamed skin that can present as a generalized pruritic papular rash. The fact that it spares palms, soles, and genitals is consistent with atopic dermatitis, as these areas are less commonly involved.

Papular Urticaria: An allergic reaction to insect bites or other environmental allergens, leading to itchy papules. The distribution can be widespread but typically spares the palms, soles, and genitals.
Scabies: A parasitic infection caused by the mite Sarcoptes scabiei, leading to intense itching and a papular rash. While it can involve any part of the body, it often spares the face in adults and can have a predilection for areas like the finger webs, wrists, and genital area, though it doesn't exclusively spare palms, soles, and genitals.
Drug Eruption: A reaction to a medication that can cause a wide range of skin manifestations, including a pruritic papular rash. The distribution can be generalized but may spare certain areas like palms and soles.

Bullous Pemphigoid: An autoimmune disease that can initially present with a pruritic papular rash before progressing to blistering. It's crucial to diagnose early due to the potential for significant morbidity.
Cutaneous T-Cell Lymphoma (Mycosis Fungoides): A type of skin lymphoma that can present with a variety of skin lesions, including a pruritic papular rash. Early diagnosis is critical for treatment and prognosis.
HIV-Related Dermatoses: Certain skin conditions are associated with HIV infection, such as pruritic papular eruption, which can be an early sign of the disease. Identifying and treating HIV early is vital.

Pityriasis Lichenoides: A rare skin condition characterized by the appearance of small, raised spots that can be itchy. It's less common and might be considered if other diagnoses are ruled out.
Lichen Planus: An inflammatory condition that affects mucous membranes inside the mouth and can also affect the skin, presenting as purplish, itchy, flat bumps. While not typically described as sparing palms, soles, and genitals exclusively, it's a rare condition that could be considered in the differential diagnosis.
Erythroderma (Exfoliative Dermatitis): A condition characterized by widespread redness and scaling of the skin, which can be itchy. It's a rare but serious condition that requires prompt diagnosis and treatment.