Are there infinite perfect numbers?

It is not known whether there are infinitely many perfect numbers, nor whether there are infinitely many Mersenne primes

Mersenne primes

In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form M_n = 2ⁿ − 1 for some integer n. They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century. If n is a composite number then so is 2ⁿ − 1.

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Mersenne prime - Wikipedia

. As a side note, there are names for non-perfect numbers: if the sum of a number's proper factors are less than the number, it's a deficient number.

How many perfect numbers are there?

There are around 51 known perfect numbers. There are only 2 perfect numbers from 1 to 100 which are 6 and 28. The latest perfect number was discovered in 2018 which has 49,724,095 digits.

What is the largest perfect number found?

At the moment the largest known Mersenne prime is 2 82 589 933 − 1 2^{82 589 933} - 1 282 589 933−1 (which is also the largest known prime) and the corresponding largest known perfect number is 2 82 589 932 ( 2 82 589 933 − 1 ) 2^{82 589 932} (2^{82 589 933} - 1) 282 589 932(282 589 933−1).

Why is 28 a perfect number?

We see that 28 is still perfect by this definition: Its proper divisors are 1, 2, 4, 7 and 14, its improper divisor is 28, and the sum of all its divisors, 1 + 2 + 4 + 7 + 14 + 28, is 56, which is 2 × 28.

Why is 496 a perfect number?

The number 496 is a perfect number, because its proper divisors add up to give 496. The divisors of 496 are as follows: 1, 2, 4, 8, 16, 31, 62, 124, 248, 496.

Perfect Number

Why is 33550336 a perfect number?

Our purpose here is discovery. A Perfect Number is a natural number such that its value is equal to the sum of its proper divisors[1]. The first seven Perfect Numbers are: 6, 28, 496, 8128, 33550336, 8589869056, 137438691328.

Is 4096 a perfect number?

Yes, 4096 is the perfect cube since its cube root is a whole number, i.e. 16.

Why is 1089 a magic number?

1089 is widely used in magic tricks because it can be "produced" from any two three-digit numbers. This allows it to be used as the basis for a Magician's Choice.

Why is the number 1729 special?

1729, the Hardy-Ramanujan Number, is the smallest number which can be expressed as the sum of two different cubes in two different ways. 1729 is the sum of the cubes of 10 and 9 - cube of 10 is 1000 and cube of 9 is 729; adding the two numbers results in 1729.

What is a mystery number in math?

A number N is said to be a mystery number if the number can be expressed by the sum of two numbers. Note that these two numbers must be reverse of each other. It lies between 22 to 198, i.e. 22<=N<=198.

Is Googolplexian the largest number?

The Science Part

A Googolplexian is a number with 10¹⁰⁰ zeroes. Whilst larger numbers can be imagined, the Googolplexian is the largest number that could be found in the dictionary.

Why is googolplex the biggest number?

A googol is 10 to the 100th power, which is 1 followed by 100 zeros. While this is an unimaginably large number, there's still an infinite quantity of larger numbers. One such number is googolplex, which is 10 to the power of a googol, or 1 followed by a googol of zeros.

What is the perfect number of the universe?

The number 42 is especially significant to fans of science fiction novelist Douglas Adams' “The Hitchhiker's Guide to the Galaxy,” because that number is the answer given by a supercomputer to “the Ultimate Question of Life, the Universe, and Everything.”

Why is 73 a perfect number?

"The Alien Parasite Hypothesis," the number 73 is actually pretty special. "73 is the 21st prime number," Sheldon explains. "Its mirror, 37, is the 12th and its mirror, 21, is the product of multiplying 7 and 3 ... and in binary 73 is a palindrome, 1001001, which backwards is 1001001."

Is 0 is a perfect number?

Since zero satisfies all the definitions of squares, it is considered as a perfect square.

Are there any odd perfect numbers?

While the general form of even perfect numbers is well-known, the existence or non-existence of odd perfect numbers is still an open problem.

Why is 6174 a magic number?

6174 is known as Kaprekar's constant after the Indian mathematician D. R. Kaprekar. This number is renowned for the following rule: Take any four-digit number, using at least two different digits (leading zeros are allowed).

Is 4104 a Ramanujan number?

1. Numbers like 1729, 4104, 13832, are known as Hardy – Ramanujan Numbers. They can be expressed as sum of two cubes in two different ways.

Is 728 a Ramanujan number?

Ramanujan's 1-way solution

Some of these numbers include : {2, 9, 16, 28, 35, 54, 65, 72, 91, 126, 128, 133, 152, 189, 217, 224, 243, 250, 280, 341, 344, 351, 370, 407, 432, 468, 513, 520, 539, 559, 576, 637, 686, 728, 730, 737, ...}

What is 33x33 33 33x33 33 33 divided by 0?

So, when we are dividing 33×33+33-33 by 0 then the answer will be infinity. Hence, the value of 33×33+33-33 is infinity.

Why is anything divided by 0 infinity?

As much as we would like to have an answer for "what's 1 divided by 0?" it's sadly impossible to have an answer. The reason, in short, is that whatever we may answer, we will then have to agree that that answer times 0 equals to 1, and that cannot be ​true, because anything times 0 is 0.

Is 42 a Harshad number?

Harshad numbers in base 10 form the sequence: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42, 45, 48, 50, 54, 60, 63, 70, 72, 80, 81, 84, 90, 100, 102, 108, 110, 111, 112, 114, 117, 120, 126, 132, 133, 135, 140, 144, 150, 152, 153, 156, 162, 171, 180, 190, 192, 195, 198, 200, ...

Is 9x3 a perfect cube?

Through order of operations, this simplifies to 9⋅3, which we know is equal to 27. So, 27 is a perfect cube!

Is 13824 a perfect square?

After grouping the prime factors in triplets, it's seen that no factor is left without grouping. After grouping the prime factors in triplets, its seen that no factor is left without grouping. Thus, 13824 is a perfect cube and its cube root is 2 × 2 × 2 × 3 = 24.

Why is 224 not a perfect square?

To make 224 a perfect square we have to make the power of 2 and 7 even number in the prime factorization of 224. And the prime factorization of 224: 2⁵ × 7.