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II
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Number properties: Prime Numbers ... 01 Jan 2008, 15:42
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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.
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eschn3am
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Number properties: Prime Numbers ... 02 Jan 2008, 05:07
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I don't know of a way that's any faster. Just write them out.

41, 43, 47, 53, 59

You only have 10 odd numbers to choose from and some of those are obviously not prime like 45, 49, 55.

you can check your work using the divisibility rules like if the sum of integers adds up to 3 it's divisible by 3 sort of thing.
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Number properties: Prime Numbers ... 02 Jan 2008, 09:23
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i would list them out as well, i cant see a quicker way to do it
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maratikus
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Number properties: Prime Numbers ... 02 Jan 2008, 12:15
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Euler method can be used. It's typically used for identifying all prime numbers from 2 to n. Write numbers 1 through n. Then mark every 2 (2,4,6,etc) as non-prime numbers, mark every 3 (3,6,9,etc), every 5 (5,10,15,etc) and continue the process until the square of the prime number k exceeds n (don't have to mark every k). It can be quickly modified to the set of numbers 40 through 60. Start with 40 (divisible by 2) and mark every 2 (42, 44, etc), then start with 42 (divisible by 3) and mark every 3 (45, 48, etc), start with 40 (divisible by 45) and mark every 5, finally, start with 42 (divisible by 7) and mark every 7 (49, 56, etc). You don't have to go any higher because 11^2 = 121>60 (k = 11, n = 60).



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