Medium #1
Number Theory
Level
3
How many integers are the product of two different primes? (Note that is not prime.)
The answer is 25.
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Let list the primes < 47, 2,3,5,7,11,13,17,19,23,29,31,37,41,43. There are 14 primes. From 2,3,5,7,11 : we can make products of two different primes. There are 5C2 = 10 pairs.But 2 x 3 is less than 10. So 9 pairs remain. 13 , 17 can be paired with 2,3,5. There are 6 pairs. 19, 23, 29 can be paired with 2, and 3. There are 6 pairs. 31,37,41,43 can be paired with 2. There are 4 pairs.There are 25 pairs in total