Bamboozled by Prime Numbers (2024)

Table of Contents
Leave a Reply Post navigation FAQs

Bamboozled by Prime Numbers (1)

Classroom Ideas, Current Event Connection, Main

SCIENCE

One species of bamboo flowers every 120 years. Another flowers every 32 years. Another flowers every 60 years. And now, biologists have suggested a tantalizing hypothesis: bamboo cycles have reached their remarkable lengths through some simple arithmetic. (The Loom, Nat Geo)

Understand how math is the language of science with our introductory encyclopedic entry on quantitative data.

Teachers, scroll down for a quick list of key resources in our Teachers’ Toolkit.

Discussion Ideas

  • Plants are often divided into three categories: annuals, biennials, and perennials. Browse through Carl Zimmer’s easy-to-read, fascinating blog post about bamboo life cycles. Do you think bamboo is an annual, biennial, or perennial?
    • Bamboo is a perennial, meaning it lives for more than two years. Most plants are perennials. Read this article to learn more about how one Nat Geo Explorer is working to make agriculture more sustainable through use of perennials such as switchgrass and sunflowers.
      • Biennials are plants that live for two years. In the first year, a biennial grows leaves, stems, and roots. In the second year, a biennial flowers, producing fruits and seeds. Onions and carrots are biennials.
      • Annuals are plants that complete their life cycle in no more than one year. Wheat and tomatoes are annuals.
  • According to The Loom, scientists “found that the [flowering cycles of bamboo] are tightly clustered around numbers that can be factored into small prime numbers.” What are prime numbers?
    • Take it away, Kevin Barnhart:

    • Prime numbers are positive numbers greater than 1 that cannot be divided evenly by any numbers besides 1 and themselves. (No negative numbers, no 0s, no 1s, no remainders, no decimals!)Take a look at the first 1,000 primes here.
      • Numbers that are not prime are composite: 4, 6, 8, 9, 10 . . . these are composite numbers, because they can be divided evenly by numbers other than 1 and themselves.
    • In this case, “small primes” probably means factors of 2, 3, and 5—the bamboo flowering periods studied can be broken down into factors of 2, 3, and/or 5.
    • Primes are fun:
      • Two is the only even prime, as every other even number can be divided by 2.
      • Five is the only prime number ending in 5, as every other number ending in 5 can be divided by 5.
      • If the numbers of a prime add up to a multiple of 3, that number can be divided by 3 and therefore is not a prime. (Example: 111 (1+1+1=3); 951 (9+5+1=15))
      • There are an infinite number of primes. Infinite! Browse through a few theories proving this, from 300 BCE to 2005.
  • What are some flowering periods that would fit the theory described in The Loom?
    • Think of composite (not prime) numbers: Bamboos that flower every 12 years, every 50 years, every 111 years, even 2,015 years would all fit this theory. Those numbers could all be factored down to small primes—and shorter-lived ancestors.
  • Why would a 120-year life cycle be more beneficial than a 1- or 2-year (annual or biennial) cycle? Read through the blog post and think about food webs in a bamboo forest.
    • According to Carl Zimmer, proving why he’s one of the best science writers around:
      • Rats, birds, pigs, and other animals devour colossal numbers of bamboo seeds. Each gobbled-up seed represents the loss of a potential [bamboo] offspring. If there are enough seed-predators, and they are hungry enough, they can wipe out a bamboo plant’s entire set of seeds.
        “Bamboo plants might fare better . . . if they flowered at the same time. They would overwhelm their enemies with food. Even if they gorged themselves to bursting, they would still leave some seeds untouched. Those surviving seeds would then have enough time to grow into plants that could defend themselves with tough fibers and bitter chemicals.”
  • If bamboo evolved to longer and longer life cycles, could some mutant bamboo go the other way and evolve shorter and shorter life cycles?
    • Not successfully. “If a four-year forest produces a two-year mutant, it will flower half the time in years when it has no protection from predators. The only direction it can go is towards longer cycles.”

TEACHERS’ TOOLKIT

Nat Geo: Bamboo Mathematicians

Nat Geo: What is quantitative data?

Nat Geo: Rat Attack in India Set Off by Bamboo Flowering

Kevin Barnhart: Prime Numbers Rap

The Prime Pages: The First 1,000 Primes

(extra credit!) University of Utah: Euclid’s Theorem (Why are there infinitely many prime numbers?)

  1. Some interesting facts and puzzles about Prime Numbers and Magic Squares, Smith Numbers, and Arithmetic and Palindromic Primes on this blog: http://www.glennwestmore.com.au.

    Loading...

    Reply

Leave a Reply

Bamboozled by Prime Numbers (2024)

FAQs

What is the trick for all prime numbers? ›

To find whether a larger number is prime or not, add all the digits in a number, if the sum is divisible by 3 it is not a prime number. Except 2 and 3, all the other prime numbers can be expressed in the general form as 6n + 1 or 6n - 1, where n is the natural number.

Is there a pattern to predict prime numbers? ›

But there's no discernable pattern in the occurrence of the primes. Beyond the obvious — after the numbers 2 and 5, primes can't be even or end in 5 — there seems to be little structure that can help to predict where the next prime will occur.

Is 12345678910987654321 a prime number? ›

This number is a prime.

What is the secret behind prime numbers? ›

Unique Factorization: One of the most important properties of prime numbers is that every natural number greater than 1 can be expressed as a product of prime numbers in a unique way, up to the order of the factors. This is known as the Fundamental Theorem of Arithmetic.

What is the fastest method to find the prime numbers? ›

For relatively small numbers, it is possible to just apply trial division to each successive odd number. Prime sieves are almost always faster. Prime sieving is the fastest known way to deterministically enumerate the primes.

What is the formula for prime number? ›

Each prime number can be written as 6n + 1 or 6n – 1 (with the exception of the products of indivisible numbers, for example 2, 3, 5, 7, 11), where n is a characteristic number an n > 3.

How do you find prime numbers for dummies? ›

A prime number is a number that can only be divided by itself and 1 without remainders. What are the prime numbers from 1 to 100? The prime numbers from 1 to 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97. Why is 1 not a prime number?

What is the best algorithm for finding prime numbers? ›

The most common sequential algorithm for finding primes is the sieve of Eratosthenes, which is specified in Figure 8. The algorithm returns an array in which the ith position is set to true if i is a prime and to false otherwise.

Is there a formula to predict prime numbers? ›

Although it has been known for millennia that there are infinitely many prime numbers, there is no way to predict whether a given number will be prime; only the probability that it will be, given its size.

What is the strategy for prime numbers? ›

To prove whether a number is a prime number, first try dividing it by 2, and see if you get a whole number. If you do, it can't be a prime number. If you don't get a whole number, next try dividing it by prime numbers: 3, 5, 7, 11 (9 is divisible by 3) and so on, always dividing by a prime number (see table below).

What are the rare prime numbers? ›

The first few unique primes are 3, 11, 37, 101, 9091, 9901, 333667, ... (OEIS A040017), which have periods 1, 2, 3, 4, 10, 12, 9, 14, 24, ... (OEIS A051627), respectively.

Why 94 is not a prime number? ›

The number 94 is divisible by 1, 2, 47, 94. For a number to be classified as a prime number, it should have exactly two factors. Since 94 has more than two factors, i.e. 1, 2, 47, 94, it is not a prime number.

What is the best prime number? ›

Well, according to Big Bang Theory's Sheldon Cooper, then 73 is not only the best prime number, but the best number in general. 73 is the 21th prime number, its mirror number is the 12th prime number, who's mirror number 21 is the product of 7*3. Furthermore, 73 is 1001001 in binary, which is a palindrome.

What is the formula for finding prime numbers? ›

There are two methods to find out whether a number is prime number or not. 1st Method: Each prime number can be written as 6n + 1 or 6n – 1 (with the exception of the products of indivisible numbers, for example 2, 3, 5, 7, 11), where n is a characteristic number an n > 3.

How is 11 not a prime number? ›

Yes, 11 is a prime number. The number 11 is divisible only by 1 and the number itself. For a number to be classified as a prime number, it should have exactly two factors. Since 11 has exactly two factors, i.e. 1 and 11, it is a prime number.

Top Articles
Latest Posts
Article information

Author: Zonia Mosciski DO

Last Updated:

Views: 6081

Rating: 4 / 5 (71 voted)

Reviews: 94% of readers found this page helpful

Author information

Name: Zonia Mosciski DO

Birthday: 1996-05-16

Address: Suite 228 919 Deana Ford, Lake Meridithberg, NE 60017-4257

Phone: +2613987384138

Job: Chief Retail Officer

Hobby: Tai chi, Dowsing, Poi, Letterboxing, Watching movies, Video gaming, Singing

Introduction: My name is Zonia Mosciski DO, I am a enchanting, joyous, lovely, successful, hilarious, tender, outstanding person who loves writing and wants to share my knowledge and understanding with you.