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.
(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.
re: Two methods by hand
