answer:A Mersenne prime is a prime number that can be written in the form 2^n - 1, where n is a positive integer. Since we are looking for the smallest Mersenne prime greater than 3, we can start by testing the next power of 2: 2^3 - 1 = 7 7 is a prime number, so the smallest Mersenne prime greater than 3 is 7.

answer:A Mersenne prime is a prime number that can be written in the form M_n = 2^n - 1, where n is a prime number. To find the smallest Mersenne prime greater than 10,000, we need to find the smallest n such that 2^n - 1 > 10,000 and M_n is prime. We can start by testing prime values of n: n = 11: 2^11 - 1 = 2047 (not prime, divisible by 23) n = 13: 2^13 - 1 = 8191 (prime) Since 8191 is the smallest Mersenne prime greater than 10,000, the answer is 8191.

answer:The smallest Mersenne prime number larger than 2 is 7. Mersenne primes are prime numbers that can be written in the form 2^p - 1, where p is also a prime number. In this case, p = 3, so the Mersenne prime is 2^3 - 1 = 8 - 1 = 7.

answer:A Mersenne prime is a prime number that can be written in the form 2^p - 1, where p is also a prime number. To find the smallest possible value of p, we can start by testing the smallest prime number, which is 2. 2^2 - 1 = 4 - 1 = 3 3 is a prime number, so the smallest possible value of p in the expression 2^p - 1 to make it a Mersenne prime is p = 2.