If n = x+1 where x is the product of three consecutive positive integers?

Question

then
is n a prime number
If yes how and if no how

Answer 1

n*(n+1)*(n+2)+1 generates composite numbers and prime numbers. In the set n=1 to 100 are 34 primes while in the set
1 to 100 are 25 primes.

Here at least, you get a more primes for your buck

Answer 2

2*3*4 + 1 = 24+1 = 25 not a prime number.
11*12*13+1 = 1717 = 17*101.

Answer 3

1*2*3 = 6
n = 6 + 1 = 7 is a prime number

Answer 4

let the 1st no. a, then the 2nd is a+1 & the 3rd is a+2
n=(a*(a+1)*(a+2))+1
n= a^3+3a^2+2a+1
let a^3+3a^2+2a=b
n=b+1
so n is prime number