2. Make a conjecture about the sum of primes based on the following pattern: 4= 2+2 6=3+3 8=3+5 10=3+7 12=5+7 and so on. The sum of primes is equal to the multiple of the primes. The sum of primes is between 4 and 12. The sum of primes is equal to an even number. The sum of primes is equal to primes.

N= {1,2,3,...}. The prime numbers P = {2,3,5,7...}. True or false? The natural numbers are are ØCN True False

3. Kate was given the following number pattern by her teacher. 22+1=5 42+1=17 62+1=37 102+1=101 14²+1=197 Kate made the following conjecture based solely on the number patterns shown. "When an even number is squared and one is added to it, the resulting number is a prime number". In the examples above 5, 17, 37, 101, and 197 are prime numbers because the only factors of these numbers are 1 and the number itself. a) Is Kate's conjecture True or False, based solely on the numbers shown? Use your understanding of even numbers and prime numbers to explain your answer. b) Determine a counterexample to the pattern above to show that Kate's conjecture is false.

Which of the following is the set P for all prime numbers less than 14? P={2,3,5,7,11,13}   P={1,2,3,5,7,11,13}   P={2,4,6,8,10,12}   P={2,4,6,8,10,12,14}