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 The final quantity (Posted on 2015-02-18)
Given a list of all composite numbers below 1000, how many will remain after erasure of numbers divisible by 2,3 or 5?

Rem1: "or" is inclusive i.e. and/or.
Rem2: number 1 is neither prime nor composite, so it does not appear on the initial list.

 No Solution Yet Submitted by Ady TZIDON No Rating

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 re: Two methods by hand | Comment 3 of 4 |
(In reply to Two methods by hand by Jer)

I used the 2nd method and of course got the same result i.e 100.

My reasoning  was:  Since 7*7*7*7 > 1000 and should not be included we will count:

a. All semiprime numbers  below 1000 (created by coupling 7 with (7,11,13,  ...  139), 11 with (11,13,  ...  89)...
...31 with(31);  totaling  94  semiprime numbers .
b. 6 triplets:   7*7 *(7,11,13,17,19)  and 11*11*(7).

Clearly  7,11,13 is out and there are no quadruplets.

This morning I was about to post my compilation as a verification of Charlie's program (which actually performs the erasure) and was more than pleased to see Jer's comment, isomorphic to mine.

 Posted by Ady TZIDON on 2015-02-19 00:11:05

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