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Math Help - Determine a number is prime or not

  1. #1
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    Determine a number is prime or not

    Hi,

    I was aked to check whether 241 is prime or not. The time given was 40 sec. But I took a lot of time to determine this.

    Is there any tricks avialble to quickly determine whether a number is prime or not?

    Thanks!
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  2. #2
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    Quote Originally Posted by ManuLi View Post
    Hi,

    I was aked to check whether 241 is prime or not. The time given was 40 sec. But I took a lot of time to determine this.

    Is there any tricks avialble to quickly determine whether a number is prime or not?

    Thanks!
    Have you heard of the divisibility tests?

    Divisibility rule - Wikipedia, the free encyclopedia


    Otherwise you can draw a factor tree:

    Integer factorization - Wikipedia, the free encyclopedia

    (see Prime Factorisation).
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  3. #3
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    Hello,

    First, see roughly that 15=225, so if a prime number divides 241, it must be less than 16.
    Immediate known rules exclude 2 (and hence any even number), 5, 3 & 9 (sum of numbers), 11 (we know that 21*11=231)
    now there remain 7 and 13, that's all...

    7*10=70, 7*30=210. So is 241-210=31 divisible by 7 ? No. So 7 doesn't divide 241.

    13*20=260. So is 260-241=19 divisible by 13 ? No. So 13 doesn't divide 13.

    So 241 is a prime number


    (took me less than 30 sec to find it out, so it's feasible)
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  4. #4
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    An important thing to know, as Moo mentioned, is some basics about what numbers divide a numbers. The rule with summing the digits for 3 and 9 are important, as well as understanding why one can eliminate 2, 5, 10 and 11.
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