Give an example of three or more consecutive odd primes p1

Give an example of three or more consecutive odd primes p_1, ... ,p_t such that 2 * p_1 ... p_t + 1 is not prime.

Solution

Answer is 5,7,11

Let p₁ = 5,p₂= 7, p₃ = 11 which are three consecutive odd primes.

now

2.p_1.p_2.p₃ +1 = 2.5.7.11 + 1 = 770+1 = 771, which is not a prime.