Is 1000000027 prime?

[Jingle47]

I am doing a little digging and am working with prime factorizations.
What I reall want to know is how YOU figure out if the following number is prime.
100000000000000000207

I actually already know whether it is prime or not, I am more interested in your approach(es).
I would appreciate any help I can get and who knows you might find it fun to do anyway!

[Chuck]

I used a program called PRNTEST1.UB that came with the UBasic programming language that I found online somewhere months ago. I don't know how it works. It says 100,000,000,000,000,000,207 is prime.

[ctrlaltdel]

is there a way 'around' the problem?

say i look at the big number and say:

207 is not a prime, 207 = 23 x 3 x 3

now if 10000000000000000000 is divisible by either 23 or 3 then the whole number is not a prime

if its not tho... then i guess i don't know yet

anyways an approach like this maybe totally misleading only because of the bunch of zeros i try to enforce it on the problem. if the number was something like 13215746545135464316545207 i'd be stuck with the brute force efforts.

[This message has been edited by ctrlaltdel (edited 04-16-2002 03:39 AM).]

[groza528]

It may be a difference of two squares, in which case it is not prime. That's probably the first thing I'd check is what's the next square, and then find the difference between the two. Unfortunately I'm too lazy to do that.
Is that supposed to be ...00207 or ...027?

[groza528]

If ...027 there's probably a difference of two cubes formula

[mole]

13215746545135464316545207 is not prime.

[CrystyB]

Groza, except 10^20 is not a cube

[Quailman]

If it had nine or fewer digits, I would look here.

[CzarJ]

Oh, I read about stuff like this in a book! I don't really understand how it works, though

------------------
Speaking of which, describe your favorite pair of pants.

[Jingle47]

I found out the answer using a program called Maple 6.
But I am kind of curious how Maple found the answer.

[SaberKitty]

I don't knwo the answer, but I just wanted to post this site because it's really cool The Great Internet Mersenne Prime Search(GIMPS Homepage)
-admits she's a geek -

[Griffin]

Jingle - It probably used one of the "primality tests" found at this site:

http://www.utm.edu/research/primes/prove/proving.html

[jamesshuang]

TI-89 calculators rule. They are great for finding primes. 100000000000000000207 is actually prime, by the way.

[extropalopakettle]

Here's a java program to test if any integer is prime or not:

code:

---

import java.math.BigInteger;





class testPrime


{


   public static void main(String[] args)


   {


      BigInteger n =  new BigInteger(args[0]);


      if (n.isProbablePrime(30))


         System.out.println("PRIME");


      else


         System.out.println("COMPOSITE");


   }


} 

---

The constant 30 can be changed. The higher it is, the less likely it is you'll get a false positive (positive=prime). You'll never get a false negative. For a value of X, the probability that a positive result is false is less than 1/2^X.