Find the prime numbers in dictionaries?

Output should be only prime numbers in list of values.

data_input = {'number_1': [3,6,9], 'number_2': [4,10,11,21,23], 'number_3': [10,12,15]}
for x,y in data_input.items():
    for num in y:
        if num>1:
            for i in range(1,num):
                if(num%i)==0:
                    break
                else:
                    data_input.append(num)

data_input.update()
print(data_input)

This is wrong. The program is not showing any prime numbers, printing all numbers.