The Most Perfect Number, Ranked

Choose the number you think is the most perfect!

Author: Gregor Krambs
Updated on May 26, 2024 06:37
Numbers, often considered mere tools for calculation, hold deeper, often subjective significance for many. When it comes to considering which number could be labeled as 'the most perfect,' opinions diverge, shaped by cultural contexts, personal experiences, and even philosophical inclinations. This debate touches on both the aesthetic and functional attributes of numbers, from their role in mathematics to their symbolic meanings in various cultures. By participating in this ongoing poll, users contribute to a crowd-sourced view of what constitutes the most 'perfect' number. Each vote is a reflection of individual preference and collective resonance. The live ranking not only sheds light on public opinion but also sparks conversations about the criteria that guide our choices. This dynamic list offers an engaging way for people to connect over a shared curiosity and to see how preferences shift over time.

What Is the Most Perfect Number?

  1. 1
    48
    votes

    28

    28 is the second perfect number, signifying that it is the sum of its proper divisors (1, 2, 4, 7, 14).
    • Sum of Divisors: 28
    • Divisors: 1, 2, 4, 7, 14
  2. 2
    31
    votes

    496

    496 is the third perfect number, and like other perfect numbers, it equals the sum of its proper divisors.
    • Sum of Divisors: 496
    • Divisors: 1, 2, 4, 8, 16, 31, 62, 124, 248
  3. 3
    27
    votes

    8128

    8128 is the fourth perfect number, showcasing the property of being equal to the sum of its proper divisors.
    • Sum of Divisors: 8128
    • Divisors: 1, 2, 4, 8, 16, 32, 64, 127, 254, 508, 1016, 2032, 4064
  4. 4
    24
    votes

    6

    6 is considered the smallest perfect number, meaning it is equal to the sum of its proper divisors (1, 2, and 3).
    • Sum of Divisors: 6
    • Divisors: 1, 2, 3
  5. 5
    0
    votes

    8589869056

    8589869056 is the sixth perfect number, further exemplifying the unique property of perfect numbers.
    • Sum of Divisors: 8589869056
    • Divisors: A vast number of divisors
  6. 6
    0
    votes

    Not applicable

    Beyond the eighth perfect number, the sequence continues, but specific numbers become increasingly difficult to discover and verify due to their immense size.
    • Note: Perfect numbers beyond this point are extremely large and less well-known.
  7. 7
    0
    votes

    Not applicable

    The concept of perfect numbers extends into theoretical mathematics, with an infinite number believed to exist, though only a finite number have been discovered and verified.
    • Mathematical Interest: The search for perfect numbers is a significant area of study in number theory.
  8. 8
    0
    votes

    33550336

    33550336 is the fifth perfect number, continuing the sequence of numbers that are equal to the sum of their proper divisors.
    • Sum of Divisors: 33550336
    • Divisors: A large set of divisors including 1, 2, 4, 8, 16, 32, etc.
  9. 9
    0
    votes

    137438691328

    137438691328 is the seventh perfect number, maintaining the tradition of being equal to the sum of its proper divisors.
    • Sum of Divisors: 137438691328
    • Divisors: An extensive list of divisors
  10. 10
    0
    votes

    2305843008139952128

    2305843008139952128 is the eighth perfect number, demonstrating the ongoing pattern of perfect numbers.
    • Sum of Divisors: 2305843008139952128
    • Divisors: An exhaustive collection of divisors

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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

  • 1812 views
  • 130 votes
  • 10 ranked items

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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.

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More about the Most Perfect Number

Throughout history, mathematicians have been fascinated by perfect numbers. A perfect number is a positive integer that equals the sum of its proper divisors, excluding itself. This concept dates back to ancient times and has intrigued minds for centuries.

The earliest known studies of perfect numbers come from the ancient Greeks. They noticed that these numbers have unique properties. They saw a balance in the way these numbers relate to their divisors. This balance seemed almost magical, which is why they called them "perfect."

Perfect numbers have a special connection with even numbers. In fact, all known perfect numbers are even. This pattern was first observed by the Greek mathematician Euclid. He discovered a method to find perfect numbers using prime numbers. His method was simple yet effective, and it laid the groundwork for future discoveries in number theory.

In the 18th century, the Swiss mathematician Leonhard Euler expanded on Euclid's work. He proved that all even perfect numbers could be generated using Euclid's formula. This was a significant breakthrough, as it provided a clear and systematic way to identify perfect numbers. Euler's work confirmed the deep connection between perfect numbers and prime numbers.

Despite these advances, the search for perfect numbers continues. Mathematicians have yet to find an odd perfect number, and it remains one of the great unsolved problems in mathematics. The existence of an odd perfect number would challenge many established theories and open new avenues of research.

Perfect numbers also have interesting properties in relation to other areas of mathematics. For example, they are closely linked to Mersenne primes, which are prime numbers of the form 2^p - 1. This relationship further highlights the unique nature of perfect numbers and their place in the broader mathematical landscape.

The study of perfect numbers is not just about finding new examples. It also involves understanding their properties and implications. For instance, perfect numbers are related to the concept of amicable numbers, which are pairs of numbers where each number is the sum of the proper divisors of the other. This relationship adds another layer of complexity and intrigue to the study of perfect numbers.

In modern times, the search for perfect numbers has been aided by computers. Advanced algorithms and powerful machines have allowed mathematicians to identify larger perfect numbers than ever before. However, the fundamental questions remain the same. What makes a number perfect? Why do they exist? And will we ever find an odd perfect number?

Perfect numbers continue to captivate mathematicians because they represent a perfect balance within the realm of integers. They are a testament to the beauty and mystery of mathematics. As we continue to explore and understand these numbers, we uncover more about the fundamental nature of mathematics itself.

The journey to understand perfect numbers is far from over. Each discovery brings new questions and challenges. But it also brings us closer to understanding the true nature of these fascinating numbers. The quest for perfect numbers is a perfect example of the endless curiosity and dedication that drives the field of mathematics.

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