Is there any number that isn't a prime number and can't be divided by any numbers from 1 to 9

Question

Number-theory-related

Answer 1

All numbers can be divided by 1 so do you mean 2-9?

2537 is not divisible by any numbers between 2 and 9 and its factors are 43 and 59.

Comments

How did I get a solution?

First, I found the least common denominator of the numbers between 2 and 9.

To get this, I found the product of 5, 7, 8 and 9=2520. I ignored 2, 3, 4 and 6 because 8 is a multiple of 4 and 2 (which will divide into everything that 8 divides into), and 6 divides into 8×9.

Then I wrote down 2521 and a set of numbers following that.

Next, I crossed off all the numbers which are the sum of 2520 and the numbers 2-9 and their multiples. So between 2521 and about 2540 I was left with:

2521, 2531, 2533, 2537, 2539.

Next, I crossed off the 3 prime numbers in this set leaving:

2533 and 2537.

So I could have also picked 2533=17x149.