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# How many positive integers less than 500 are the product of exactly

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How many positive integers less than 500 are the product of exactly
two distinct (meaning different) primes, each of which is greater than 10?

Guest Mar 5, 2015

#1
+18835
+5

How many positive integers less than 500 are the product of exactly
two distinct (meaning different) primes, each of which is greater than 10 ?

$$\small{\text{  \begin{array}{r|rcl|r} \hline n & p_1 & & p_2 & p_1\cdot p_2 \\ \hline 1 & 11 & \cdot & 13 & = 143 \\ 2 & 11 & \cdot & 17 & = 187 \\ 3 & 11 & \cdot & 19 & = 209 \\ 4 & 11 & \cdot & 23 & = 253 \\ 5 & 11 & \cdot & 29 & = 319 \\ 6 & 11 & \cdot & 31 & = 341 \\ 7 & 11 & \cdot & 37 & = 407 \\ 8 & 11 & \cdot & 41& = 451 \\ 9 & 11 & \cdot & 43 & = 473 \\ 10 & 13 & \cdot & 17 & = 221 \\ 11 & 13 & \cdot & 19 & = 247 \\ 12 & 13 & \cdot & 23 & = 299 \\ 13 & 13 & \cdot & 29& = 377 \\ 14 & 13 & \cdot & 31 & = 403 \\ 15 & 13 & \cdot & 37 & = 481 \\ 16 & 17 & \cdot & 19 & = 323 \\ 17 & 17 & \cdot & 23 & = 391 \\ 18 & 17 & \cdot & 29 & = 493 \\ 19 & 19 & \cdot & 23 & = 437 \\ \hline \end{array}  }}$$

heureka  Mar 5, 2015
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#1
+18835
+5
$$\small{\text{  \begin{array}{r|rcl|r} \hline n & p_1 & & p_2 & p_1\cdot p_2 \\ \hline 1 & 11 & \cdot & 13 & = 143 \\ 2 & 11 & \cdot & 17 & = 187 \\ 3 & 11 & \cdot & 19 & = 209 \\ 4 & 11 & \cdot & 23 & = 253 \\ 5 & 11 & \cdot & 29 & = 319 \\ 6 & 11 & \cdot & 31 & = 341 \\ 7 & 11 & \cdot & 37 & = 407 \\ 8 & 11 & \cdot & 41& = 451 \\ 9 & 11 & \cdot & 43 & = 473 \\ 10 & 13 & \cdot & 17 & = 221 \\ 11 & 13 & \cdot & 19 & = 247 \\ 12 & 13 & \cdot & 23 & = 299 \\ 13 & 13 & \cdot & 29& = 377 \\ 14 & 13 & \cdot & 31 & = 403 \\ 15 & 13 & \cdot & 37 & = 481 \\ 16 & 17 & \cdot & 19 & = 323 \\ 17 & 17 & \cdot & 23 & = 391 \\ 18 & 17 & \cdot & 29 & = 493 \\ 19 & 19 & \cdot & 23 & = 437 \\ \hline \end{array}  }}$$