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prime numbers

Tuesday’s Twister #13 – Prime Numbers

May 19th, 2015 by John Lehet
"There are three kinds of people:  Those that make things happen, those that watch things happen and those that wonder what happened. " - Agent Garbo (Juan Pujol Garcia)

“There are three kinds of people: Those that make things happen, those that watch things happen and those that wonder what happened. ” – Agent Garbo (Juan Pujol Garcia)

Prime numbers are everywhere and they are really easy to understand.  There are just two simple rules to follow:

  • – a prime number is a positive integer greater than 1
  • – a prime number is evenly divisible by only 1 and itself


That’s pretty straight forward.  Many people assume 1 is a prime number, but by definition, it’s not.  It’s important to realize and remember this when dealing with primes.  Also, 2 is the only even prime number, as all other even numbers are divisible by 1, 2 and itself.

Here’s a couple of prime number puzzles to start you off.

 

puzzle 1: What is the smallest 2-digit prime number in which both digits are prime and their sum is prime? 

puzzle 2: What is the largest 2-digit number in which both digits are prime and their sum is prime?

Let’s look at an example number, say 73.  73 is a prime number and it’s digits, 7 and 3 are both  prime.  However, the sum of the digits 7+3 equals 10, which is not prime.  So, 73 will not work for either puzzle 1 or puzzle 2.

Once you solve the first two puzzles, you should have a good handle on prime numbers.  I recommend listing all of the prime numbers less than 100.  To make it a bit more challenging, let’s look at 3-digit numbers.

puzzle 3: List all 3-digit numbers that have prime numbers for all three digits. 

puzzle 4: Of the numbers listed in puzzle 3, list the numbers in which the digits sum to a prime number.

puzzle 5: Of the numbers listed in puzzle 4, which of the numbers are themsleves prime?

Let’s look at an example 3-digit number, say 235.  the digits, 2, 3 and 5, are all prime numbers.  However their sum, 2+3+5, equals 10, which is not a prime number (so it doesn’t work for puzzle 4).

Good luck with the puzzles and have fun.