p, q, r are prime number such that
p<q<r<13.
∴ p can take the values
2,3,5,7,11.
q can take the values
3,5,7,11.
r can take the values
5,7,11.
For
p=3,q=5,r=7,p+q+r=3+5+7=15
, which is not a prime number
For
p=3,q=5,r=11,p+q+r=3+5+11=19
, which is a prime number
For
p=3,q=7,r=11,p+q+r=3+7+11=21
, which is not a prime number
For
p=5,q=7,r=11,p+q+r=5+7+11=23
, which is a prime number
So, there are 2 cases where,
p+q+r is also a prime number