Question

The number of primes of the form |n2 - 6n + 5/ where n is an integer is
a.
b.
0
1
2.
3
C.
d.​

Answer 1

2 prime numbers are of the form  | n² - 6n + 5 |

Given:

| n² - 6n + 5 | where n is integer

To Find:

The number of primes of the form | n² - 6n + 5 |

Solution:

| n² - 6n + 5 |

Factorize

| (n - 1)(n - 5) |

To be prime number one factor must be 1

Hence

| (n - 1) |  = 1  or | (n - 5) |  = 1

Solving | (n - 1) |  = 1

n = 2  , n  = 0

Substituting n = 2

| n² - 6n + 5 | = | 4 - 12 + 5 | = 3

3 is prime

Substituting n = 0

| n² - 6n + 5 | = | 0 - 0 + 5 | = 5

5 is prime

| (n - 5) |  = 1

=> n = 6 ,  4

Substituting n = 6

| n² - 6n + 5 | = | 36 - 36 + 5 | = 5

5 is prime

Substituting n = 4

| n² - 6n + 5 | = | 16 - 24 + 5 | = 3

3 is prime

Hence prime numbers are 3 and 5 which are of form | n² - 6n + 5 |

Hence 2 prime numbers are of the form  | n² - 6n + 5 |

Correct option is  c) 2