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Number properties: Prime Numbers ...

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by II » Tue Jan 01, 2008 2:44 pm
Hi All

How many prime numbers are there which are greater than 40 and less than 60?

Is there a quicker way of working this out, instead of listing all the numbers between 40 and 60 and removing all the numbers which have factors other than themselves and one leaving us with the primes ?

Thanks.
II
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by Auzbee » Tue Jan 01, 2008 6:17 pm
IMO, for such small ranges it is quicker to just enumerate the numbers and list the prime numbers.

At a general level, in a set of any ten consecutive numbers (like 11-20, 32-40, 151-160 etc) there will be 2 number divisible by 5, 4 number divisible by 2 (taking the one's ending with 0 under divisible by 5 category), and 3 number divisible by 3. Out of these these, 3 number divisible by 3, at most 2 can overlap with the ones already considered under divisible by 2 category. THis makes it 7~9 numbers non-prime leaving 1~3 numbers as prime.
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