Question

A large prime number isP = 232582657 - 1

Suppose you wish to express P in the binary system used by computers, where the base is 2 instead of 10, and the only possible digits are 0 and 1. The number of binary digits is

Answer 1

Answer:

32582657

Explanation:

If any number is in the form of 2^{n}-1 is known as Mersenne prime. Here, n is a prime number.

For example:

If n is 3 then the corresponding binary number is as follows:

P=2^{3}-1

P=7

Here, the binary representation of P is (111)₂.

The number of binary digits is 3 which are equal to n.

Consider the given expression

P=2^32582657-1

This is also in the form 2^{n}-1

Here the value of n is 32582657.

Hence, the number of binary digits for the given prime number is 32582657