| Line 1: | Line 1: | ||
| + | Proof by contradiction. | ||
| − | |||
| − | |||
| − | + | Assume that there are only a finite number of prime number <math>p_1,p_2,......,p_n</math> | |
| + | . Then by using the fact from exercise 18 (Let <math>p_1,p_2,....,p_n </math> be primes. Then <math>p_1p_2.....p_n +1 </math> is divisible by none of these primes), <math>p_1p_2p_3....p_n +1</math> is not divisible by any prime.) This means <math>p_1p_2...p_n +1 </math> (which is larger than our initial conditions) is itself prime. This contradicts the assumption that <math>p_1,p_2,...p_n </math> is the list of all primes. | ||
| + | |||
| + | --Angela [[User:Akcooper|Akcooper]] 20:09, 6 September 2008 (UTC) | ||
Revision as of 15:09, 6 September 2008
Proof by contradiction.
Assume that there are only a finite number of prime number $ p_1,p_2,......,p_n $
. Then by using the fact from exercise 18 (Let $ p_1,p_2,....,p_n $ be primes. Then $ p_1p_2.....p_n +1 $ is divisible by none of these primes), $ p_1p_2p_3....p_n +1 $ is not divisible by any prime.) This means $ p_1p_2...p_n +1 $ (which is larger than our initial conditions) is itself prime. This contradicts the assumption that $ p_1,p_2,...p_n $ is the list of all primes.
--Angela Akcooper 20:09, 6 September 2008 (UTC)
