Parallelogram 2 Level 1 14 Sep 2023Prime numbers (and their buddy, one)

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Noun: Parallelogram Pronunciation: /ˌparəˈlɛləɡram/

  1. a portmanteau word combining parallel and telegram. A message sent each week by the Parallel Project to bright young mathematicians.
  • Tackle each Parallelogram in one go. Don’t get distracted.
  • Finish by midnight on Sunday if your whole class is doing parallelograms.
  • Your score & answer sheet will appear immediately after you hit SUBMIT.
  • Don’t worry if you score less than 50%, because it means you will learn something new when you check the solutions.

1. One and prime numbers

(If you have problems watching the video, right click to open it in a new window)

2 marks

1.1 Which important theorem excludes 1 from being considered a prime number?

  • The Fundamental Theorem of Analysis
  • The Fun Theorem of Emental
  • The Fundamental Theorem of Arithmetic
  • (Not answered)
2 marks

1.2 How would 42 be written as a product of primes?

  • 6 × 7
  • 1 × 2 × 21
  • 2 × 3 × 7
  • 2 × 21
  • (Not answered)
2 marks

1.3 In the the video, James followed a pattern to show 1 is a product of zero prime numbers. What is this called?

  • Null Product
  • Empty Product
  • Angsty Product
  • NP Product
  • (Not answered)

2. Primes, squares and cubes

Primes, Square Numbers and Cube Numbers are the gems of the number world!

As a quick reminder:

if you multiply a number by itself you get a square number, 4 × 4 = 16, so 16 is square.

If you multiply by itself again it is now a cube number 4 × 4 × 4 = 64, so 64 is a cube.

2 marks

2.1 How many prime numbers are there between 1 and 20 (including 1 and 20)

  • 7
  • 8
  • 9
  • (Not answered)
2 marks

2.2 How many square numbers are there between 1 and 20 (including 1 and 20)

  • 3
  • 4
  • 20
  • (Not answered)
2 marks

2.3 Are there more prime numbers or square numbers in existence?

  • Prime Numbers
  • Square Numbers
  • There is an infinite amount of both Prime and Square Numbers
  • (Not answered)
2 marks

2.4 Can you find a positive number which is one bigger than a square number, but one less than a cube number? (There is only one out there, but it is less than 50.) Correct Solution: 26

26 is the answer, because it is between 5 × 5 and 3 × 3 × 3.

3. Parallel Circles

Parallel Circles, our weekly online maths sessions with bestselling science author Simon Singh, Countdown champion Junaid Mubeen and a range of guest speakers, start next week.

We have Circles designed for each Level of Parallel, and the best session for you to join is our Level 1 Parallel Circle.

1 mark

3.1 Will you be joining the Parallel Circle next week?

(Note: there is a right answer to this question!)

  • Yes, I'll almost certainly be there!
  • No, I'm much too busy for all that extra maths!
  • (Not answered)

Before you hit the SUBMIT button, here are some quick reminders:

  • You will receive your score immediately, and collect your reward points.
  • You might earn a new badge... if not, then maybe next week.
  • Make sure you go through the solution sheet – it is massively important.
  • A score of less than 50% is ok – it means you can learn lots from your mistakes.
  • The next Parallelogram is next week, at 3pm on Thursday.
  • Finally, if you missed any earlier Parallelograms, make sure you go back and complete them. You can still earn reward points and badges by completing missed Parallelograms.

Cheerio, Simon and Ayliean.