prime number tricks

slimsohn wrote:Hi all,

I was wondering if there are any special tricks or formulas involving problems with prime numbers and/or if a number is/should be divisible by a prime. (ex: when they have some HUGE number and you have to see if its divisible by a prime or if they want the largest prime factor.)



thanks

well if to check if a number is divisible by a prime u will have to do it the old fashioned way... dividing it by the prime number..... but about the largest prime factor thing ... i do remember reading something about it in my old "hall & knight " .... will dig out the book and get back to u if i find something useful...

To check there isnt any method...or may be i dont know....but what I know is pretty useful.

Here it goes... to find the number is prime or not you can use this...
lets say the no. is x. find out the nearest perfect square lower than the number. and get its square root. check for all the prime numbers less than that (the square root).

example:

lets take 109...is it a prime number or whats the greatest prime factor?
nearest perfect square is 100. 10^2

so now check for 2, 3, 5, 7..thats it..after that 11 is greater than 10.

109 is divisible by 2? no
3? no
5? no
7? no

so it is a prime...109

i hope this simplifies to a great extent.

lets take 119

nearest square...100 again
10
so take 2, 3, 5, 7
its divisible by 7
so 7 is the greatest prime factor.

I think this is the shortest method.

Hope that helps!