if p,qandr are prime numbers such that r=q+2andq=p+2,then the no. of triplets of the form(pqr)

Answer 1

We can start by substituting the values of r and q in terms of p:
r = q+2 = (p+2)+2 = p+4
q = p+2

So, we have p, p+2, and p+4 as three prime numbers that form a triplet.

We know that p cannot be 2, since all other primes are odd and adding 2 to an odd number gives an even number, which isn't a prime. So, let's assume p > 2.

If p is an odd prime, then both p+2 and p+4 are even and hence not primes.

Therefore, p must be an even prime, which means p=2. Substituting this in the equations for q and r, we get:
q = p+2 = 2+2 = 4 (not a prime)
r = q+2 = 4+2 = 6 (not a prime)

Hence, there are no triplets of the form (pqr) that satisfy the given conditions.

Answer 2

AAAaannndd the bot gets it wrong yet again!

This statement is clearly false:
If p is an odd prime, then both p+2 and p+4 are even and hence not primes.