Hunt for the 3 primes

primerange is a generator that, in this case, supplies all of the two-digiti primes. combinations is another generator that, in this case, supplies all of the three-combinations of these primes. The code simply sifts through the combinations to identify any that satisfy the required conditions.

Since the average of any number of two-digit numbers will also be a two-digit number, apart from the decimals, I could have checked whether the averages are primes using table lookup. However, this approach, using isprime seemed more straightforward.

I split the if statement up into pieces in the misapprehension that this would be faster. Of course, if I had put all of the conditions together the interpreter would have stopped executing them as soon as one of them failed.

We wrote this program in python and we got the output as 129

def prime(x):

z=x**0.5

a=1

while (a<=z):

    a+=1

    if (x % a == 0):

        return False

return True

l=[]

for a in range(10,100):

if prime(a)==True:

    l.append(a)

for s in l:

for t in l:

    for u in l:

        if (s!=t) and (t!=u) and (s!=u):

            w=(s+t+u)/3

            q=(s+t)/2

            r=(t+u)/2

            y=(s+u)/2

            if (prime(w)==True) and (prime(q)==True) and (prime(r)==True) and (prime(y)==True):

                print(s+t+u)

Hence the answer is 129