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# Untitled

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May 17th, 2018
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__Sign Up__- # Prime numbers
- > To a number be considered as a prime number, it must be greater than 1 and only divisible by 1 and itself.
- > Every integer greater than 1 can be written uniquely as a prime or as the product of two or more primes (prime factorization) where the prime factors are written in order of nondecreasing size.
- 641 = 641
- 100 = 2 x 2 x 5 x 5 = 2^2 x 5^2
- 999 = 3 x 3 x 3 x 37 = 3^3 x 37
- ### Trial Division
- > If n is a composite integer (no-prime), then n has a prime divisor less than or equal to √n.
- Show that 101 is prime
- **Solution**
- √101 ~ 10, so 101 will be prime if none of the prime numbers below 10 can divide 101.
- The only primes not exceeding 101 are 2, 3, 5, and 7. Because 101 is not divisible by 2, 3, 5, or 7 (the quotient of 101 and each of these integers is not an integer), it follows that 101 is prime.

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