Question

Determine whether each of these integers is prime, verifying some of mersenne's claims.

a.27 – 1
b.29 – 1

Answer 1

Both 27 - 1 (which equals 26) and 29 - 1 (which equals 28) are not prime numbers since they are even and divisible by numbers other than 1 and themselves.

Step-by-step explanation:

To determine whether each of the integers 27 - 1 and 29 - 1 are prime numbers, we perform the calculations and then verify their primality:

1. 27 - 1 = 26. This number is even, and any even number greater than 2 is not prime because it is divisible by 2. Hence, 26 is not a prime number.
2. 29 - 1 = 28. This number is also even and is divisible by 2. Additionally, 28 is divisible by 4 and 7. Therefore, it is not a prime number either.

Neither 26 nor 28 are prime numbers. In mathematics, a prime number is defined as a natural number greater than 1 that is not a product of two smaller natural numbers.

Answer 2

I don't really understand why there is a one, but I can tell you that "29" is prime and "27" is not.