As the top detective in Numberland, you believed you had encountered every possible mystery. However, the recent discovery of desiccated corpses of prominent natural numbers—whole numbers greater than zero—has left the city of Digitopolis in turmoil. For the past week, these numbers have been found drained of their essence, leading to a citywide lockdown from sundown to sunrise. Despite these measures, the vampiric feeding frenzy continues unabated, leaving the police helpless and turning to you for assistance.
Putting aside a missing persons case, you delve into the evidence at hand. Most victims have been completely drained, while others exhibit a peculiar thin line of slime separating their digits. This raises the first mystery: what is the significance of these slime-lines, and why are certain digits left untouched?
Upon closer inspection, a pattern begins to emerge. The numbers marked by slime-lines are prime numbers, divisible only by one and themselves. In contrast, the unslimed numbers are not prime. Furthermore, the drained sections of the slimed primes are non-prime. For instance, when the number 71 was slimed, the digit 7 was prime, but 1 was not. Similarly, 461 could have been split into 4 and 61, with 61 being prime, but it was instead divided further into non-prime digits. The number 2099 was split into 20 and 99, both non-prime, and thus both were drained.
This revelation presents a significant problem: there are infinite potential victims, including all non-prime numbers and prime numbers that can be split to reveal at least one non-prime number. However, a few numbers appear immune to this threat. These include the one-digit primes: 2, 3, 5, and 7. Additionally, primes like 23, which can only be split into 2 and 3, both prime, are also immune.
Your missing persons case suddenly becomes relevant. Someone is kidnapping these immune numbers. If you can identify the remaining immune numbers, you might be able to reach them before the kidnapper does. The four one-digit immune numbers—2, 3, 5, and 7—have already been taken. To identify the two-digit immune numbers, you eliminate any numbers ending in 2 or 5, as they are divisible by those numbers. Numbers divisible by 11 and those whose digits sum to a multiple of 3 are also excluded. This leaves a select few, which upon verification, are indeed immune.
With a strong starting point, you search for three-digit immune numbers. Any two consecutive digits must be from the list of two-digit immune numbers, which all end in 3 and 7. This narrows the possibilities to eight options. Further elimination based on divisibility rules leaves only 373, which is prime and therefore immune.
Could a four-digit number be immune? No, as any consecutive three digits would need to be immune, and no immune three-digit number starts with a 7. You rush to the homes of the immune numbers, but arrive too late, except for 373. Just in time, you scare off her would-be kidnapper, a minion rather than the vampire itself. 373 reveals that she and the other immune numbers are part of an ancient prophecy designating them as vampire slayers. Despite their distaste for violence, they gather to confront the vampire.
Trailing the minion to a foreboding castle, you release the kidnapped numbers and confront the vampire. Powerless before the slayers, the vampire is rounded up, the lifeforce is returned to his victims, and he is sent packing. Numberland is safe once more… for now.
Explore your surroundings and find objects or numbers that can represent prime numbers. Write down each prime number you find and explain why it is a prime number. Remember, a prime number is only divisible by 1 and itself.
Using a list of numbers, identify which ones are prime and which are not. Draw a slime-line between the digits of each number and determine if the resulting sections are prime or non-prime. Discuss your findings with a partner.
Write a short story involving a mystery in Numberland. Include prime and non-prime numbers as characters and create clues based on their properties. Share your story with the class and see if they can solve the mystery.
Using the rules from the article, identify two-digit and three-digit immune numbers. Create a chart showing your process of elimination and the final immune numbers. Present your chart to the class.
Create a piece of art using prime numbers. You can draw, paint, or use digital tools to represent prime numbers in a creative way. Explain how you incorporated prime numbers into your artwork and what they represent.
Numbers – Symbols used to represent quantities or values. – There are many different types of numbers, such as whole numbers, fractions, and decimals.
Prime – A whole number greater than 1 that has no positive divisors other than 1 and itself. – The number 7 is a prime number because it can only be divided by 1 and 7.
Digits – The symbols used to write numbers, typically from 0 to 9. – The number 345 has three digits: 3, 4, and 5.
Non-prime – A whole number that has more than two positive divisors. – The number 8 is a non-prime number because it can be divided by 1, 2, 4, and 8.
Immune – Not affected by something; in math, it can refer to numbers that do not change under certain operations. – In a math puzzle, some numbers are immune to being changed when you add zero.
Divisible – A number is divisible by another if you can divide them without leaving a remainder. – The number 20 is divisible by 5 because 20 divided by 5 equals 4 with no remainder.
Pattern – A repeated or predictable sequence of numbers or shapes. – The sequence 2, 4, 6, 8 is a pattern where each number increases by 2.
Mystery – A problem or puzzle that needs to be solved, often involving numbers or equations. – The math mystery involved finding the missing number in the sequence 3, 6, __, 12.
Essence – The fundamental nature or most important quality of something. – The essence of solving equations is to find the value of the unknown variable.
Victims – In math problems, this can refer to numbers that are affected by operations or changes. – In the subtraction problem, the smaller number is often seen as the victim of the operation.
