My naive implementation without using heap. It is still good to try this way at least once I guess :)

import sys sys.setrecursionlimit(3500)

def add_a_vertex(covered, uncovered, edges, distance):

for i, j, w in edges[:]:
    if i in uncovered and j in covered:
        distance[i] = min(distance[i], w)
    if j in uncovered and i in covered:
        distance[j] = min(distance[j], w)

weight = min([i for i in distance.values()])

for k in distance.keys():
    if distance[k] == weight:
        next_vertex = k
        break

covered.add(next_vertex)
uncovered.remove(next_vertex)
del distance[next_vertex]

if len(distance) == 0:
    return weight
else:
    return weight + add_a_vertex(covered, uncovered, edges, distance)

def prims(n, edges, start): # Write your code here

weight = 0

covered = set()
covered.add(start)
uncovered = set(range(1,n+1))
uncovered.remove(start)

distance = {}
for i in uncovered:
    distance[i] = float('inf')

# print(f'distance {distance}')

weight += add_a_vertex(covered, uncovered, edges, distance)

return weight