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10 February, 14:14

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

+2
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  1. 10 February, 17:00
    0
    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
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