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3 years ago

A large prime number isP = 232582657 - 1

Engineering

1 answer:

sattari [20]3 years ago

3 0

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

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pickupchik [31]

Answer:

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3 years ago

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olya-2409 [2.1K]

Answer:

The answer is " $4.35 \times 10^{-3}\ mm$ and 157.5 MPa".

Explanation:

In point A:

The strength of its products with both the grain dimension is linked to this problem. This formula also for grain diameter of 310 MPA is represented as its low yield point

$y = yo + \frac{k}{\sqrt{x}}$

Here y is MPa is low yield point, x is mm grain size, and k becomes proportionality constant.

Replacing the equation for each condition:

$y = y_o + \frac{k}{\sqrt{(1 \times 10^{-2})}}\\\\\ \ \ \ \ \ \ 230 = yo + 10k\\\\ y = yo + \frac{k}{\sqrt{(6\times 10^{-3})}}\\\\275 = yo + 12.90k$

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To substitute the answer,

$310 = 275 + \frac{(15.5)}{\sqrt{x}}\\\\x = 0.00435 \ mm = 4.35 \times 10^{-3}\ mm$

In point b:

The equation is $\sigma y = \sigma 0 + k y d^{\frac{1}{2}}$

equation is:

$75 = \sigma o+4 ky \\\\175 = \sigma o+12 ky\\\\ky = 12.5 MPa (mm)^{\frac{1}{2}} \\\\ \sigma 0 = 25 MPa\\\\d= 8.9 \times 10^{-3}\\\\d^{- \frac{1}{2}} =10.6 mm^{-\frac{1}{2}}\\$

by putting the above value in the formula we get the $\sigma y$ value that is= 157.5 MPa

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