### Instruction: As $p$ ranges over the primes greater than $5$, how many different remainders can $p^2$ leave upon division by $120$? Let's write a Python program.### Response: import sympy as sp

# Define the range of primes
lower_bound = 6
upper_bound = 500  # Chose a large number to cover a wide range of primes

# Generate all primes in the range
primes = list(sp.primerange(lower_bound, upper_bound))

remainders = set()

# Calculate the remainder of each prime squared divided by 120
for p in primes:
    remainder = (p**2) % 120
    remainders.add(remainder)

# Print the number of unique remainders
print(len(remainders))