Let a *tough-to-test composite* be a positive integer that is composite, but not divisible by 2, nor 3, nor 5.

Given that there are 168 prime numbers between 1 and 1000, how many *tough-to-test composite* numbers are there between 1 and 1000?

**Notes**: 1 is neither prime nor composite. There are some *tough-to-test composite* numbers that many would recognize as composite. For example, 49 and 77.

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