Question

What is the sum of all integer values of n satisfying 1≤n≤100, such that n^2−1 is a product of exactly two distinct prime numbers?

Answer 1

those prime numbers are in the interval between 1 and 100?

Answer 2

yes prime numbers are between 1 and 100

Answer 3

please show me the step!

Answer 4

*steps!!

Answer 5

i found out, there are 26 prime numbers between 1 and 100, and only 15 prime numbers satisfy thee condition n^2-1

Answer 6

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

Answer 7

just add all the numbers to find the sum

Answer 8

I don't see why prime numbers have to be between 1 and 100, because:
let the prime numbers be p and q, then \(n^2-1=pq\) or \(n=\sqrt{pq+1}\le 100 \)
this means that \(pq \le 9999\)

Answer 9

you can't treat prime numbers like that, prime numbers don't have a particular rule to follow, so i think it's best to do it manually

Answer 10

my point is that the prime numbers are not only in the interval from 1 to 100

Answer 11

but, she/he said that it lies between 1 and 100

Answer 12

@SerikMB , so what is the next? I don't think by listing them out and "try and check" to get the answer is the way to solve the problem.

Answer 13

the asker is offline, but I am eager to know what happen next.

Answer 14

@Hoa , i really don't know, but, in my opinion it is the only way to solve this, as prime numbers don't obey any rules

Answer 15

OK, friend, I am ok with that. I will wait for someone gives out the solution.

Answer 16

sorry but 15 is not the answer !!