Latest / Kidcast Daily / Ep398: Prime Numbers in nature and technology

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Ep398: Prime Numbers in nature and technology · Kidcast Daily

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  Spin the wheel, let's take a ride.
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  Sports and science bursting from inside a world of wonder.
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  Open wide. Come on kids, let's amplify kid
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  cats. Daily starts your day, Fun and
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  laughter come your way. Sports and Trinia games galore.
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  Welcome to Kick Ass Daily where we bring you news, trivia, fun
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  facts and more made just for curious kids like you.
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  Today we are exploring prime numbers and how they show up in
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  nature and in the devices you use everyday.
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  We will build from the basics to some surprising real world uses
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  and along the way you will get a few quick pauses to think.
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  All right, let's dive right in. First, what is a prime number?
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  A prime number is a whole number greater than one that has
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  exactly 2 factors, one and itself.
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  That means it can be divided evenly only by those two
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  numbers. For example, 357 and 11 are
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  primes. They do not break into equal
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  groups with any other whole number.
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  A number like 12 is not prime because you can divide it by
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  two, 3-4 and six in addition to 1 and 12.
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  Numbers that can be divided evenly by more than two whole
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  numbers are called composite numbers.
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  You can test a small number by trying to divide it by 235 and
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  so on to see if any of those give a whole number result.
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  Here is a yes or no question for you.
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  Is the #1A prime number? No, the number one is not prime
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  because it has only one factor, which is 1.
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  Prime numbers must have exactly two different factors, one and
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  the number itself. This rule helps keep our math
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  system consistent and makes many patterns work properly.
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  Now try a quick trivia question. What is the only even prime
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  number? The answer is 2.
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  All other even numbers can be divided by two, which means they
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  have at least three factors, 1/2 and the number itself that makes
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  them composite. SO2 stands out as the only even
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  prime. Here is another yes or no
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  question. Do mathematicians know for sure
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  that there are infinitely many prime numbers?
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  Yes. More than 2000 years ago, a
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  mathematician named Euclid proved that primes never run
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  out. No matter how far you count, you
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  can always find more primes. This is a big reason why primes
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  are so important. Did you know the smallest few
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  primes are 23571113 and 17? If you list them, the gaps
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  between them change in interesting ways.
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  Sometimes primes come close together, like 17 and 19.
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  Sometimes there is a larger gap, like between 23 and 29.
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  Let's talk about how to spot primes efficiently. 1 classic
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  trick is to check divisibility only up to the square root of a
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  number. If a number has a factor larger
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  than its square root, the matching partner factor is
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  smaller than the square root and you would have already found it.
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  Another classic method is called the Sieve of Eratosthenes.
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  You write down numbers, cross out multiples of two, then
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  multiples of three, then five, and continue.
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  The numbers that are not crossed out are primes.
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  This method works well for finding all primes up to a
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  certain limit. Now let's move into nature.
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  Prime numbers show up in living things in ways that help them
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  survive and grow. Here comes a trivia question
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  that brings in a neat example from the outdoors.
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  Which insect in North America uses a 13 or 17 year life cycle?
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  That are prime numbers? Periodical cicadas.
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  These insects spend most of their lives underground and come
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  out together after 13 or 17 years.
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  Using a prime number of years helps reduce the chance that
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  predators with shorter or regular cycles line up with
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  their emergence as often. Flowers can also show prime
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  counts. Some plants have flowers with
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  three or five petals, which are prime numbers.
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  For example, trilliums often have 3 petals, and wild roses
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  often have 5 petals. Pine cones and pineapples show
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  spiral patterns. The counts of spirals often
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  match numbers from the Fibonacci sequence, like 813 or 21.
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  Sometimes these counts are prime, like 13.
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  These number patterns help pack seeds or scales in a tight,
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  efficient way that fits their growth.
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  Here is a yes or no question introducing a new fact from
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  technology. Do some computer security
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  systems rely on very large prime numbers that are hard to factor?
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  Yes. Many secure websites, messaging
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  apps, and digital signatures use methods based on large primes.
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  One well known method is called RSA.
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  It uses two large primes multiplied together to make a
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  composite number. It is easy to multiply the
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  primes, but very hard for a computer to break that big
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  composite back into the exact original primes.
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  If the primes are extremely large, this one way difficulty
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  helps keep information private. Did you know your browser often
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  works with numbers hundreds or even thousands of digits long
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  when it uses strong security? You never see those numbers, but
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  they help your device and the website agree on keys to lock
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  and unlock information safely. Primes also help with other
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  kinds of computer tasks. Some hash tables in programming
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  use prime sizes to spread data more evenly across slots.
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  Certain error correcting codes and digital communications use
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  math built on fields related to primes to detect and fix
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  mistakes caused by noise. Even in timing and music
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  technology, using counts like 5 or 7 can help avoid repeating
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  loops lining up too often, which can reduce unwanted patterns.
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  It's time for a trivia question that introduces a special type
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  of prime. What name is given to prime
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  numbers of the form 2 to the power P -, 1, where the result
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  is prime like 3-7 and 31? They are called Mersenne primes.
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  These primes are useful in research because they make
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  certain tests faster. Did you know the largest known
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  prime number today is a Mersenne prime with more than 41 million
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  digits? It was found by a distributed
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  computing project where many volunteers let their computers
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  help check candidates. You can explore primes at home
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  with simple activities. Try writing numbers from 2 to
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  100 on paper. Cross out multiples of two, then
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  three, then five and seven. Count how many primes remain.
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  You can also try building your own small secret code where you
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  pick two primes, multiply them, and share the product.
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  While this small version is not secure, it shows how the idea of
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  a one way operation works in a simple hands on way.
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  Primes appear in calendars and schedules, too.
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  If two repeating events have prime links, they will line up
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  less often. For example, if one event
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  repeats every five days and another repeats every seven
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  days, they meet only every 35 days, not more often.
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  Choosing numbers that do not share many small factors can
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  help spread out overlaps. Let's add a another neat fact.
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  Did you know that the word prime comes from a Latin word meaning
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  first or chief? In math, primes act like
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  building blocks for whole numbers.
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  Every whole number greater than 1 can be broken down into a
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  product of primes in exactly one way if you ignore the order.
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  This is called the fundamental theorem of arithmetic, and it is
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  a key reason primes matter. Here is a final yes or no
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  question that adds a fresh detail.
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  Can a prime number end with an even digit or with five if it is
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  larger than 5? No.
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  Any number ending in 0, 246, or 8 is even and would be divisible
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  by two. Any number ending in five would
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  be divisible by 5. So primes larger than five never
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  end with an even digit or with five.
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  This quick check helps you rule out nonprimes fast.
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  Before we wrap up, here is one more small tip.
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  When checking if a number is prime, you only need to test
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  division by primes, not by every number.
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  For example, to test 91, try dividing by 7 and 13.
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  Since 7 * 13 is 91, you know it is composite.
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  If none of the primes up to the square root divide your number,
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  then your number is prime. Let's recap what we learned
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  today. A prime number is a whole number
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  greater than one with exactly 2 factors, one and itself.
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  The number one is not prime, and two is the only even prime.
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  There are infinitely many primes in nature.
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  Prime numbers show up in the life cycles of periodical
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  cicadas and in some pedal counts and spiral patterns where primes
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  like 13 can appear. In technology, large primes help
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  keep digital information safe through systems like RSA, and
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  they support tools such as hash tables and error correcting
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  methods. Special families like Mersenne
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  primes lead to record-breaking discoveries, including primes
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  with over 41 million digits. You now have simple strategies
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  to test primes and a better sense of how these special
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  numbers shape patterns in the natural world and power the
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  tools we use everyday. Keep exploring, keep asking
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  questions, and notice the numbers hiding in plain sight
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  all around you. Grab.
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  Your breakfast feelings fine.