Question
Ogechi is trying to demonstrate that 7 is a Mersenne prime. Which of the following expressions should she use? (1 point) \( 2(3)+1 \) \( 2^{3}-1 \) \( 2(3)-1 \) 7 is not a Mersenne prime.
Ask by Ayala Crawford. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Ogechi should use \( 2^{3} -1 \) to demonstrate that 7 is a Mersenne prime.
Solution
To demonstrate that 7 is a Mersenne prime, Ogechi should use the expression:
\[ 2^{3} - 1 \]
This is because a Mersenne prime is defined as a prime number of the form \( 2^n - 1 \). In this case, \( 2^3 - 1 = 7 \), which is indeed a prime number.
**Answer:** \( 2^{3} -1 \)
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To show that 7 is a Mersenne prime, Ogechi should use the expression \( 2^{3}-1 \). This evaluates to \( 2^3 = 8 \), and when subtracting 1, we get 8 - 1 = 7. Since 7 is prime and can be expressed in this form, it confirms that 7 is indeed a Mersenne prime! To have a bit of fun with Mersenne primes, did you know that they have a special connection to perfect numbers? In fact, every even perfect number can be derived from a Mersenne prime! The relationship was famously proven by the mathematician Euclid way back in ancient times, showing just how intertwined these concepts are in the world of numbers.
