• Login
No Result
View All Result
My Blog
  • Home
  • World
  • Politics
  • Business
  • Science
  • Tech
    Create More Content with This AI Writing Tool — Just $39 for Life

    Create More Content with This AI Writing Tool — Just $39 for Life

    The Pros and Cons of Using AI to Write Your Book

    The Pros and Cons of Using AI to Write Your Book

    ‘Build Your Business From the Perspective Of People’: CureBay’s Founder

    ‘Build Your Business From the Perspective Of People’: CureBay’s Founder

    How Digital Payments Are Disrupting Our Entire Ecosystem

    How Digital Payments Are Disrupting Our Entire Ecosystem

    4 Ways To Use ChatGPT

    4 Ways To Use ChatGPT

    Learn Python from Home with This Info-Packed Bundle with Courses Less Than $3 Each

    Learn Python from Home with This Info-Packed Bundle with Courses Less Than $3 Each

    Trending Tags

    • Sillicon Valley
    • Climate Change
    • Election Results
    • Flat Earth
    • Golden Globes
    • MotoGP 2017
    • Mr. Robot
  • Entertainment
    • All
    • Movie
    • Music
    • Sports
    The ‘Dune’ Miniseries Is a Fascinating Piece of History

    The ‘Dune’ Miniseries Is a Fascinating Piece of History

    Coinbase Offered Them Dream Jobs—and Then Took Them Away

    Coinbase Offered Them Dream Jobs—and Then Took Them Away

    The January 6 Hearings Are Fighting for Your Attention

    The January 6 Hearings Are Fighting for Your Attention

    12 Best Messenger Bags (2022): Crossbody, Slings, Shoulder Bags

    12 Best Messenger Bags (2022): Crossbody, Slings, Shoulder Bags

    Big Tech Has Become a Creature of the Swamp

    Big Tech Has Become a Creature of the Swamp

    Sea to Summit Alto TR1 Review: A Fantastic Ultralight Tent

    Sea to Summit Alto TR1 Review: A Fantastic Ultralight Tent

    Prediction Engines Are Like Karma: You Get What You Stream

    Prediction Engines Are Like Karma: You Get What You Stream

    ‘The Quarry’ Lets You Experience What’s Great About Slasher Films

    ‘The Quarry’ Lets You Experience What’s Great About Slasher Films

    Summer Game Fest’s Biggest Announcement? A ‘Last of Us’ Remake

    Summer Game Fest’s Biggest Announcement? A ‘Last of Us’ Remake

  • Lifestyle
    • All
    • Fashion
    • Health
    • Travel
    nurse

    Everything You Need To Know About Nurse Residency

    Drug detox

    Are you the right candidate for medical detox?

    The Benefit of Using Sunscreen Protection

    Gift Ideas for Celebrating a Loved One’s College Acceptance

    What are the major reasons to form gall bladder stones?

    The ‘Dune’ Miniseries Is a Fascinating Piece of History

    The ‘Dune’ Miniseries Is a Fascinating Piece of History

    Coinbase Offered Them Dream Jobs—and Then Took Them Away

    Coinbase Offered Them Dream Jobs—and Then Took Them Away

    The January 6 Hearings Are Fighting for Your Attention

    The January 6 Hearings Are Fighting for Your Attention

    12 Best Messenger Bags (2022): Crossbody, Slings, Shoulder Bags

    12 Best Messenger Bags (2022): Crossbody, Slings, Shoulder Bags

    Big Tech Has Become a Creature of the Swamp

    Big Tech Has Become a Creature of the Swamp

    Trending Tags

    • Golden Globes
    • Mr. Robot
    • MotoGP 2017
    • Climate Change
    • Flat Earth
  • More
    • Directions
  • Home
  • World
  • Politics
  • Business
  • Science
  • Tech
    Create More Content with This AI Writing Tool — Just $39 for Life

    Create More Content with This AI Writing Tool — Just $39 for Life

    The Pros and Cons of Using AI to Write Your Book

    The Pros and Cons of Using AI to Write Your Book

    ‘Build Your Business From the Perspective Of People’: CureBay’s Founder

    ‘Build Your Business From the Perspective Of People’: CureBay’s Founder

    How Digital Payments Are Disrupting Our Entire Ecosystem

    How Digital Payments Are Disrupting Our Entire Ecosystem

    4 Ways To Use ChatGPT

    4 Ways To Use ChatGPT

    Learn Python from Home with This Info-Packed Bundle with Courses Less Than $3 Each

    Learn Python from Home with This Info-Packed Bundle with Courses Less Than $3 Each

    Trending Tags

    • Sillicon Valley
    • Climate Change
    • Election Results
    • Flat Earth
    • Golden Globes
    • MotoGP 2017
    • Mr. Robot
  • Entertainment
    • All
    • Movie
    • Music
    • Sports
    The ‘Dune’ Miniseries Is a Fascinating Piece of History

    The ‘Dune’ Miniseries Is a Fascinating Piece of History

    Coinbase Offered Them Dream Jobs—and Then Took Them Away

    Coinbase Offered Them Dream Jobs—and Then Took Them Away

    The January 6 Hearings Are Fighting for Your Attention

    The January 6 Hearings Are Fighting for Your Attention

    12 Best Messenger Bags (2022): Crossbody, Slings, Shoulder Bags

    12 Best Messenger Bags (2022): Crossbody, Slings, Shoulder Bags

    Big Tech Has Become a Creature of the Swamp

    Big Tech Has Become a Creature of the Swamp

    Sea to Summit Alto TR1 Review: A Fantastic Ultralight Tent

    Sea to Summit Alto TR1 Review: A Fantastic Ultralight Tent

    Prediction Engines Are Like Karma: You Get What You Stream

    Prediction Engines Are Like Karma: You Get What You Stream

    ‘The Quarry’ Lets You Experience What’s Great About Slasher Films

    ‘The Quarry’ Lets You Experience What’s Great About Slasher Films

    Summer Game Fest’s Biggest Announcement? A ‘Last of Us’ Remake

    Summer Game Fest’s Biggest Announcement? A ‘Last of Us’ Remake

  • Lifestyle
    • All
    • Fashion
    • Health
    • Travel
    nurse

    Everything You Need To Know About Nurse Residency

    Drug detox

    Are you the right candidate for medical detox?

    The Benefit of Using Sunscreen Protection

    Gift Ideas for Celebrating a Loved One’s College Acceptance

    What are the major reasons to form gall bladder stones?

    The ‘Dune’ Miniseries Is a Fascinating Piece of History

    The ‘Dune’ Miniseries Is a Fascinating Piece of History

    Coinbase Offered Them Dream Jobs—and Then Took Them Away

    Coinbase Offered Them Dream Jobs—and Then Took Them Away

    The January 6 Hearings Are Fighting for Your Attention

    The January 6 Hearings Are Fighting for Your Attention

    12 Best Messenger Bags (2022): Crossbody, Slings, Shoulder Bags

    12 Best Messenger Bags (2022): Crossbody, Slings, Shoulder Bags

    Big Tech Has Become a Creature of the Swamp

    Big Tech Has Become a Creature of the Swamp

    Trending Tags

    • Golden Globes
    • Mr. Robot
    • MotoGP 2017
    • Climate Change
    • Flat Earth
  • More
    • Directions
No Result
View All Result
My Blog
No Result
View All Result
Home National

A Grad Student’s Side Project Proves a Prime Number Conjecture

by lacygibson
June 19, 2022
in National, World
0
A Grad Student’s Side Project Proves a Prime Number Conjecture
0
SHARES
0
VIEWS
Share on FacebookShare on Twitter


as an atom In arithmetic, prime numbers always occupy a special place on the number line. Now, Jared Duker Lichtman, a 26-year-old graduate student at the University of Oxford, has solved a well-known conjecture, establishing another aspect of prime numbers that are special—in a sense, even optimal. “It gives you a larger context to understand in what ways prime numbers are unique and in what way they relate to the larger set of numbers,” he said.

The conjecture involves primitive sets—sequences in which no numbers divide any other numbers. Since every prime number is only divisible by 1 and itself, the set of all prime numbers is an example of a primitive set. The same goes for the set of all numbers with exactly two or three or 100 prime factors.

Primitive sets were introduced in the 1930s by mathematician Paul Erdős. At the time, they were just a tool to make it easier for him to prove a certain number of ancient Greek origins (called perfect numbers). But they quickly became objects of interest—objects Erdős would return to again and again throughout his career.

That’s because, despite their simple definition, primitive sets are truly strange beasts. This oddity can be captured by simply asking how big the original collection can get. Consider the set of all integers up to 1,000. All numbers from 501 to 1,000 — half of the set — form a primitive set, since no number is divisible by any other number. In this way, the original set may contain a large number of number lines. But other primitive sets, such as the sequence of all prime numbers, are very sparse. “It tells you that the original set is really a very broad category that’s hard to grasp directly,” Lichtman said.

To capture the interesting properties of sets, mathematicians study the concept of various sizes.For example, instead of counting how many numbers are in a set, they might do the following: For each number n In the set, substitute it into the expression 1/(n log n), then add all the results. For example, the size of the set {2, 3, 55} becomes 1/(2 log 2) + 1/(3 log 3) + 1/(55 log 55).

Erdős found that for any primitive set, including infinite sets, this sum – “the Erdős sum” – is always finite. Whatever the original set looks like, its sum of Erdős is always less than or equal to some number. So while this sum is “completely alien and vague, at least on the surface,” Lichtman says, it “manages some of the confusion of the original set” in some ways, making it a measuring stick to use correctly.

With this stick in hand, the next natural question to ask is the maximum possible Erdős and how much it could be. Erdős speculated that it would be one of the prime numbers, which turned out to be about 1.64. Through this lens, prime numbers constitute an extreme.

Jared Duker Lichtman called the issue his “faithful partner for the past four years”.

Photograph: Ruoyi Wang/Quanta Magazine

Tags: ConjectureGradmathnumberPrimeProjectProvespuzzleQuantum MagazineSideStudents
lacygibson

lacygibson

Next Post
20 Last-Minute Father’s Day Deals (2022)

30 Last-Minute Father’s Day Deals (2022)

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Recommended

Get a Discount on 10 Refurbished Tech Deals Today

Get a Discount on 10 Refurbished Tech Deals Today

8 months ago
Snap Kills Off Pixy, Its Flying Selfie Drone

Snap Kills Off Pixy, Its Flying Selfie Drone

5 months ago

Popular News

    Connect with us

    • Contact
    • Read Latest News Around The World – Frapios
    Write Us at: [email protected]

    Copyright Reserved © 2022

    No Result
    View All Result
    • Home
    • Politics
    • World
    • Business
    • Science
    • National
    • Entertainment
    • Gaming
    • Movie
    • Music
    • Sports
    • Fashion
    • Lifestyle
    • Travel
    • Tech
    • Health
    • Food

    Copyright Reserved © 2022

    Welcome Back!

    Login to your account below

    Forgotten Password?

    Retrieve your password

    Please enter your username or email address to reset your password.

    Log In