Question

List all such pairs of primes upto 100 whose difference is 3​

Answer 1

Answer:

What are two prime numbers whose difference is 3?

2 and 5. The trick here is to try out all pairs of numbers, starting with 2 and 5, that are 3 apart from each other (since the difference of them must be 3). 2 and 5 works.

Let’s try going even further.

(2, 5)

(3, 6)

(4, 7) -- we can stop trying all multiples of 2 since they will be composite

(5, 8)

(7, 10)

(9, 12) -- we can stop trying all multiples of 3 since they will be composite

(11, 14)

(13, 16)

However, none of these work. The reason?

To make the two numbers have a difference of 3, we must add 3 to the first number to obtain the second number. However, 3 is an odd number, and all primes are odd (with the exception of 2). Therefore, excluding 2, if we add 3 (an odd number) to another odd number, we will always obtain an even number. All even numbers are composite (as always, except for 2). So none of these options will ever work… except for the pair (2, 5) because 2 is the only even prime number

Step-by-step explanation:

hope you can understand by it and it helps you in you studies

Answer 2

Answer:

2 and 5 are pair of prime numbers

Step-by-step explanation:

3, 6)

(4, 7) -- we can stop trying all multiples of 2 since they will be composite

(5, 8)

(7, 10)