[AI] formula for prime numbers

Kartik Sawhney sawhney.kartik at gmail.com
Thu Sep 2 05:01:28 EDT 2010


Divisibility test for 7

Sir, the divisibility test for 7 is as mentioned below:

• Take the last digit in a number.
• Double and subtract the last digit in your number from the rest of the digits.
• Repeat the process for larger numbers.
• Example: 357 (Double the 7 to get 14. Subtract 14 from 35 to get 21
which is divisible by 7 and we can now say that 357 is divisible by 7.

Further, we cannot simply use these divisibility tests to determine if
a No. is prime. For instance, a number might not be divisible by 2, 3,
4, 5, 6, 7, 8, 9, 10 or 11. However, the same number might be
divisible by some other No. Therefore, it is imparative that we work
out all the steps as given in my previous mail.

Regards,
-Kartik

On 9/2/10, Zujar Shabbir Kanchwala <zujarbright at gmail.com> wrote:
> Divisibility test for 9:
>
> If the one-digit sum total of the digits of a number is 9 then the the
> number is divisible by 9. For example,
>
> Let's take the number 2471913
> Total of digits = 2 + 4 + 7 + 1 + 9 + 1 + 3 =27
> once more, total of digits = 2 + 7 = 9
> Hence, the number 2471913 is divisible by 9.
>
> NB: This divisibility test is similar to the one for 3 except that the
> result for divisibility by 3 should be 3, 6 or 9.
>
> hth...
>
> --
> Best Regards,
> Zujar...
>
> An optimist laughs to forget, whereas a pessimist forgets to laugh!
>
>
> On 9/2/10, Amiyo Biswas <amiyo.biswas at gmail.com> wrote:
>> Hello,
>>
>> There are some similar tricks for determining if a number is a prime one.
>> If
>> you add the last two digits and the previous ones and the result is
>> divisible by 11, the number is divisible by 11. In this case of Kartik's
>> example, 21 +23 = 44 which is divisible by 11. I have forgotten some
>> tricks
>> which can determine dibisibility by 7.
>>
>> In C / C++ lessons, you may be asked to write a utility for finding out a
>> prime number.
>>
>> With best regards,
>> Amiyo Biswas.
>> Cell: 9433464329
>> ----- Original Message -----
>> From: "Kartik Sawhney" <sawhney.kartik at gmail.com>
>> To: <accessindia at accessindia.org.in>
>> Sent: Thursday, September 02, 2010 11:01 AM
>> Subject: Re: [AI] formula for prime numbers
>>
>>
>>> Hi,
>>>
>>> In order to compute and determine if a large number is
>>> prime/composite, adopt the following method:
>>>
>>> For example sake I'll use the number 2,321
>>>
>>> 1) Find the square root of the number - The Square root of 2,321 is
>>> 48.176...
>>>
>>> 2) remember that if the square root results in an integer it is
>>> automatically composite
>>>
>>> 3) if your number ends in a 0,2,4,5,6,8 it is NOT PRIME
>>> - 2,321 ends in a 1, so we keep going
>>>
>>> 4) add up the digits of your number, if the sum is divisible by 3,
>>> your number is composite (basically testing the divisibility of the
>>> number by 3)-2+3+2+1= 8 3 does not go into 8 evenly- onto the next
>>> step
>>>
>>> 5) Divide the number by all the prime numbers less than the square
>>> root (you can skip 2, 3, and 5)
>>> -since the square root of 2,321 is 48.176..., we need to
>>> try dividing 2,321 by primes less than 48
>>> (7,11,13,17,19,23,29,31,37,41,43,47) since 2,321 is
>>> divisible by 11, it is NOT prime and therefore composite.
>>>
>>> 6) If a number is not divisible by any of the prime numbers less than
>>> the square, it is PRIME, if it is, it's COMPOSITE.
>>>
>>> I hope this will help you.
>>>
>>> -Kartik
>>>
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>>
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>
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