Question

The number of ordered pairs of different prime numbers whose sum is not exceeding 26 and difference between second number and first number cannot be less than 10..

Answer 1

Step-by-step explanation:

We take the following prime numbers in a way that the sum of any two numbers will not exceed 26.

2, 3, 5, 7, 11, 13, 17, 19, 23

Condition 1. Sum ≤ 26

Of these numbers, the pairs with sum ≤ 26 are

(2, 3), (2, 5), (2, 7), (2, 11), (2, 13), (2, 17), (2, 19), (2, 23),

(3, 5), (3, 7), (3, 11), (3, 13), (3, 17), (3, 19), (3, 23),

(5, 7), (5, 11), (5, 13), (5, 17), (5, 19),

(7, 11), (7, 13), (7, 17), (7, 19),

(11, 13).

Condition 2. Difference ≮ 10

Of the pairs above, the pairs with difference ≮ 10 are

(2, 13), (2, 17), (2, 19), (2, 23),

(3, 13), (3, 17), (3, 19), (3, 23),

(5, 17), (5, 19),

(7, 17), (7, 19).

We see that the number of pairs which fulfill both condition 1 and condition 2 is 12.

Answer:

Hence there are 12 ordered pairs of different prime numbers whose sum is not exceeding 26 and difference between second number and first number cannot be less than 10.