Prime products (H). Suppose we make a number by taking a product of prime numbers and then adding the number 1-for example, ( 2 × 5 × 7 ) + 1. Compute the remainder when any of the primes used is divided into the number. Show that none of the primes used can divide evenly into the number. What can you conclude about the primes that divide evenly into the number? Can you use this line of reasoning to give another proof that there are infinitely many prime numbers?
Prime products (H). Suppose we make a number by taking a product of prime numbers and then adding the number 1-for example, ( 2 × 5 × 7 ) + 1. Compute the remainder when any of the primes used is divided into the number. Show that none of the primes used can divide evenly into the number. What can you conclude about the primes that divide evenly into the number? Can you use this line of reasoning to give another proof that there are infinitely many prime numbers?
Prime products (H). Suppose we make a number by taking a product of prime numbers and then adding the number 1-for example,
(
2
×
5
×
7
)
+
1.
Compute the remainder when any of the primes used is divided into the number. Show that none of the primes used can divide evenly into the number. What can you conclude about the primes that divide evenly into the number? Can you use this line of reasoning to give another proof that there are infinitely many prime numbers?
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