Prime Numbers

I believe you already explained it. It's the rules of the game. You circle a number, you get the points for that number, your opponent gets points for its factors.

17 is a prime number. Its factors are 17 and 1. Circle it. You get 17 points, your opponent gets 1.

The prime factorization of -116 is: -2 x -2 x -29

2 x 2 x 2 x 2 x 3 = 48

23*5*13

You can't get something that was never there and never existed.

1994 = 2 x 997

Sorry, but both of these have direct and relatively simple proofs. To prove the infinity of primes, let p1, p2, p3, ... pn be the first n primes. Form the product p1 x p2 x p3 ... x pn. Clearly it is divisible by all the prime numbers up to pn. Then add 1 to that sum. The new value cannot be divisible by any of the preceding primes so it must be a new prime number. Because you can do this for any value of n, the number of primes must be infinite. The proof of the irrationality of the square root of 2 is similarly easy and should be available in any high-school math book at the level of Algebra 2 or above.

Where in the world are you finding 100 watt CFLs? 32-35 watts is about where those things top out, which is a pretty bright light, the equivalent of about 150 watts incandescent. Or -- perhaps you mean 23 watt CFLs or something, which have about a 100-watt equivalent when compared with incandescents. At least at the beginning of their life they do. So if that's the case then eight 400-watt halogens can be changed out with sixteen 23-watt fluorescents, which will end up at about half the brightness, and have a greenish / bluish tinge to the light over time. You may want to splurge and get 32 watt bulbs, which will look like roughly 150 watts of incandescent light. One of the really cool things about using CF is less heat in the summertime, so the A/C doesn't have to work as hard. what is what Wat is what misspelled.

In number theory, the fundamental theorem of arithmetic, also called the unique factorization theorem or the unique-prime-factorization theorem, states that every integergreater than 1 either is prime itself or is the product of prime numbers, and that this product is unique, up to the order of the factors.

3100000

45 = 3 * 3 * 5

The prefix oct- means eight.

That's an infinite list.

All composite numbers can be expressed as unique products of prime numbers. This is accomplished by dividing the original number and its factors by prime numbers until all the factors are prime. A factor tree can help you visualize this.

Example: 210

210 Divide by two.

105,2 Divide by three.

35,3,2 Divide by five.

7,5,3,2 Stop. All the factors are prime.

2 x 3 x 5 x 7 = 210

That's the prime factorization of 210.

70

2 x 32 = 18

1323 is not prime. 1323 = 3 * 3 * 3 * 7 * 7

18 has two prime factors: 2 and 3

On Jan. 25, 2013, the largest known prime number was discovered on Great Internet Mersenne Prime Search (GIMPS) volunteer Curtis Cooper's computer. The new prime number, 2 multiplied by itself 57,885,161 times, less one, has 17,425,170 digits.

The prime factorization of 2670 is: 2x3x5x89.

Prime factors are 7, 7, 19

Other factors are combinations of the primes, i.e.

7 x 7 = 49

7 x 19 = 133

6 and -5

All numbers that only have one and itself as factors are prime. So to tell if a number is prime simply find it's factors. If it has more than two factors than it is not a prime number.

Because its the closest prime number to 69 without going over.

369 is composite.