The Most Perfect Number, Ranked

Voting rules: Choose the number you think is the most perfect!

Updated on Apr 25, 2024 06:28

In the realm of numbers, finding the most perfect number holds a charm and intrigue passed down through centuries of mathematicians and enthusiasts alike. This curious pursuit not only stimulates the mathematical mind but also serves as a bridge connecting historical theories and contemporary computation. By ranking these unique numbers, we engage in a community-wide narrative that celebrates both the beauty of mathematics and the delight of discovery. Through your votes, each number finds its place in a live and dynamic ranking, reflecting real-time preferences and opinions from around the world. This process allows you to participate in a grand mathematical tradition, contributing to a collective wisdom that values both the logical and the mystical aspects of numbers. So cast your vote, influence the ranking, and see where your favorite numbers stand among the most perfect known to humanity.

What Is the Most Perfect Number?

1

23
votes
6

6 the first perfect number
The number 6 is considered a perfect number in mathematics. It is the smallest number that is equal to the sum of its divisors, excluding itself. It has been studied for centuries and holds a special significance in number theory.

Divisors: 1, 2, 3

Sum of Divisors: 1 + 2 + 3 = 6

Aliquot Sum: 6 - 1 - 2 - 3 = 0

Type: Perfect number

Positive Integer: Yes
2

48
votes
28

28 the second perfect number
28 is a perfect number, meaning that it is the sum of its proper divisors excluding itself. The proper divisors of 28 are 1, 2, 4, 7, and 14, which add up to 28.

Name: 28

Type: Perfect number

Divisors: 1, 2, 4, 7, 14

Sum of divisors: 28

Factors: 1, 2, 4, 7, 14, 28
3

31
votes
496

496 the third perfect number
496 is a perfect number in mathematics, classified as an even, abundant, and semiperfect number. It is the 4th perfect number, which means that it is equal to the sum of its positive divisors excluding itself.

Classification: Even, Abundant, and Semiperfect

Divisors: 1, 2, 4, 8, 31, 62, 124, 248

Sum of Divisors: 496

Prime Factorization: 2^4 * 31

Binary Representation: 111110000
4

26
votes
8128

8128 the fourth perfect number
8128 is a perfect number in mathematics, also known as a narcissistic number. A perfect number is a positive integer that is equal to the sum of its proper divisors, excluding itself. In the case of 8128, its proper divisors are 1, 2, 4, 8, 16, 32, 64, 127, 254, 508, 1016, 2032, 4064, and the sum of these divisors is 8128.

Palindrome: Yes

Digital root: 1

Hexadecimal representation: 1FE0

Number: 8128

Classification: Perfect number
5

13
votes
33,550,336

33,550,336 the fifth perfect number
33,550,336 is a perfect number, which means that it is equal to the sum of its divisors excluding itself. It has been extensively studied in the field of number theory.

Number: 33,550,336

Divisors: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2047, 4094, 8188, 16376, 32752, 65504, 131008, 262016, 524032, 1048064, 2096128, 4192256, 8384512, 16769024, 33538048

Sum of Divisors: 33,550,336

Number of Divisors: 26

Factors: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2047, 4094, 8188, 16376, 32752, 65504, 131008, 262016, 524032, 1048064, 2096128, 4192256, 8384512, 16769024, 33538048
6

9
votes

8,589,869,056

8,589,869,056 the sixth perfect number
7

4
votes
137,438,691,328

137,438,691,328 the seventh perfect number
137,438,691,328 is a number known as a perfect number, specifically a Mersenne prime number. It is also denoted as 2^37 - 1. A perfect number is a positive integer that is equal to the sum of its proper divisors, excluding itself. This particular number holds significance in mathematics and has been a subject of fascination for many mathematicians.

Number Type: Perfect Number

Representation: 2^37 - 1

Total Divisors: 3

Divisor 1: 1

Divisor 2: 137,438,691,327
8

6
votes
2,305,843,008,139,952,128

2,305,843,008,139,952,128 the eighth perfect number
The number 2,305,843,008,139,952,128 is known as a perfect number. It was discovered by Leonhard Euler, a Swiss mathematician.

Definition: A perfect number is a positive integer that is equal to the sum of its proper divisors, excluding the number itself.

Divisors: The divisors of 2,305,843,008,139,952,128 are 1, 2, 4, 8, 16, 32, 64, 128, 256, ..., 18,446,744,073,709,551,614.

Proper divisors: The proper divisors of 2,305,843,008,139,952,128 are 1, 2, 4, 8, 16, 32, 64, 128, ..., 5,764,607,520,424,880,624.

Sum of proper divisors: The sum of the proper divisors of 2,305,843,008,139,952,128 is 4,611,686,016,279,904,256.

Perfection: Since the sum of the proper divisors is equal to the number itself, 2,305,843,008,139,952,128 is considered a perfect number.
9

4
votes
2^82,589,933

2^82,589,933 the ninth perfect number (discovered in 2018)
2^82,589,933 is the largest known perfect number, also known as Mersenne prime. It is a prime number that can be represented in the form 2^p - 1, where p is also a prime number. This particular number is obtained when p = 82,589,933.

Significance: Largest known perfect number

Number: 2^82,589,933

Property: Perfect Number

Prime: Yes

Mersenne Prime: Yes
10

5
votes
2^77,232,917-1 (discovered in 2018)

2^77,232,917-1 the largest known prime number and a Mersenne prime, which is also a perfect number
The number 2^77,232,917-1 is the largest known prime number, which was discovered in 2018. It is also referred to as M77232917. This number is significant in the field of prime numbers and mathematical research.

Number type: Prime

Value: 2^77,232,917-1

Discovery year: 2018

Number of digits: 23,249,425

Length in bits: 77,232,917

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Discussion

Ranking factors for perfect number

Divisibility

A perfect number should have proper divisors (excluding itself) that add up to the number itself. For example, 6 is a perfect number because its divisors (1, 2, and 3) add up to 6.
Algebraic form

A perfect number should have a specific algebraic representation. Perfect numbers can be expressed in the form 2^(p-1) * (2^p - 1), where p and 2^p - 1 are both prime numbers.
Rarity

Perfect numbers are rare and unusual. As the numbers get bigger, perfect numbers become less frequent. This rarity makes specific perfect numbers more notable.
Harmony and balance

Perfect numbers have a sense of harmony and balance, as their divisors exhibit a symmetrical relationship. For example, in the case of 28, its divisors (1, 2, 4, 7, 14) seem harmoniously distributed.
Connection to primes

Perfect numbers have a strong connection to prime numbers, as both p and 2^p - 1 need to be prime in the aforementioned algebraic form.
Historical and cultural significance

It's essential to consider how perfect numbers have been discussed, studied, and used throughout history in different cultures. Some cultures attach mystical or religious significance to perfect numbers.
Mathematical properties and relationships

Other fascinating mathematical properties related to perfect numbers, such as their connection to Mersenne primes or how they are related to other number concepts like abundant or deficient numbers, should also be considered.

About this ranking

This is a community-based ranking of the most perfect number. We do our best to provide fair voting, but it is not intended to be exhaustive. So if you notice something or number is missing, feel free to help improve the ranking!

Statistics

1701 views
164 votes
10 ranked items

Voting Rules

A participant may cast an up or down vote for each number once every 24 hours. The rank of each number is then calculated from the weighted sum of all up and down votes.

More information on most perfect number

Background on the Most Perfect Number: The concept of a "perfect number" dates back to ancient Greece, where mathematicians believed that such numbers held mystical significance. In modern mathematics, a perfect number is defined as a positive integer that is equal to the sum of its proper divisors (excluding itself). The first four perfect numbers are 6, 28, 496, and 8128. Each of these numbers has been studied extensively throughout history, with mathematicians searching for patterns and properties that could shed light on the nature of numbers and their relationships to one another. One interesting fact about perfect numbers is that they are quite rare - in fact, only 51 perfect numbers are currently known to exist. However, they continue to captivate the imaginations of mathematicians and enthusiasts alike, and are sure to remain a topic of fascination for years to come.