Visualizing Prime Numbers as Sum of Other Unique Prime Numbers

Here, by unique I mean two of the same prime number can't be directly used to sum up to the prime number. The symbol (n), where n is an integer is used on edge to specify different groups that add up to the prime number.

---

Visualizations 1:

---

Visualizations 2:

---

Visualizations 3:

---

Visualizations 4:

---

Visualizations 5: