All categories

3 years ago

Every Mersenne number is a prime number. True False

Mathematics

1 answer:

Rzqust [24]3 years ago

6 0

Answer:

Every Mersenne number is a prime number is a false statement.

Step-by-step explanation:

Consider the provided information.

Mersenne number are the numbers which is in the form:

$M_n=2^k - 1$

Where k is an integer.

The first Mersenne number are:

1, 3, 7, 15, 31, 63, 127, 255, ...

The prime number are the natural number greater than 1 and they cannot be formed by product of two smaller natural numbers.

First few prime number are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29,..

Now observe that 15 is a mersenne number but it is not a prime number as 15 can be formed by product of 3 and 5.

Thus, Every Mersenne number is a prime number is a false statement.

You might be interested in

The length of a rectangle is 5959 inches greatergreater than twice the width. if the diagonal is 2 inches more than the length,

lorasvet [3.4K]

Length: 2w + 59

width: w

diagonal: (2w + 59) + 2 = 2w + 61

Length² + width² = diagonal²

(2w + 59)² + (w)² = (2w + 61)²

(4w² + 118w + 3481) + w² = 4w² + 122w + 3721

5w² + 118w + 3481 = 4w² + 122w + 3721

w² + 118w + 3481 = 122w + 3721

w² - 4w + 3481 = 3721

w² - 4w - 240 = 0

a = 1, b = -4, c = -240

w = $[-(b) +/- \sqrt{(b)^{2} - 4(a)(c) }]/2(a)$

= $[-(-4) +/- \sqrt{(-4)^{2} - 4(1)(-240) }]/2(1)$

= $[4 +/- \sqrt{(16 + 960) }]/2$

= $[4 +/- \sqrt{(976) }]/2$

= $[2 +/- 4\sqrt{(61) }]/2$

= $1 +/- 2\sqrt{(61) }$

since width cannot be negative, disregard 1 - 2√61

w = 1 + 2√61 ≈ 16.62

Length: 2w + 59 = 2(1 + 2√61) + 59 = 2 + 4√61 + 59 = 61 + 4√61 ≈ 92.24

Answer: width = 16.62 in, length = 92.24 in

7 0

3 years ago

Describe and correct the error in writing the phrase as an expression?

lesantik [10]

Answer:

12 < x

Step-by-step explanation:

In writing 12 less than a number x, the expression, 12 - x is wrong because "less than" is not the same thing as "minus" (-). Rather, the sign, "<" should have been used as follows:

12 < x.

4 0

3 years ago

Factor completely x3 + 8x2 − 3x − 24.

Anna71 [15]

Answer:

Step-by-step explanation:

$x^3+8x^2-3x-24\\\\=(x^2)(x)+(x^2)(8)+(-3)(x)+(-3)(8)\qquad\text{distribute}\\\\=x^2(x+8)-3(x+8)\\\\=(x+8)(x^2-3)\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(x+8)(x^2-(\sqrt3)^2)\\\\=(x+8)(x-\sqrt3)(x+\sqrt3)$