Question

The smallest whole number n for which n^2+n+11 is not a prime is

Answer 1

if we put n =1
then 1+1+11=13 is prime
let n=2
=4+2+11=17 is prime
let n = 3
=9+3+11=23 is prime
let n =4
= 16+4+11=31 is prime
let n =5
25+5+11=41 is prime
let n =6
36+6+11=53 is prime
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let n=11
121+11+11=143 is not prime..
so n =11 such that n²+n+11 is non prime
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reason
by fundamental theorem of arithmetic a composite number (not prime) can be written as a product of unique prime numbers ignoring the order in which they are taken
so here n²+n+11 should be non prime
n×n+n+11
n(n+1)+11
so here if we take n=11 then only it can be written as product of primes..