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In the Prime Out! game, you earn points by building numbers from primes - one step at a time. You will see how prime numbers are like the 'atoms' of arithmetic - the basic building blocks of the numbers we count with every day.

You can play Prime Out! in many different ways: using small or large numbers; by yourself or with a friend; as a leisurely game or a fast-paced timed game! No matter how you choose to play, you will have fun while strengthening your math knowledge and skills. But watch out - if you play often enough, you might just start thinking about numbers in a whole new way!

Prime Out!
a prime factorization game
Player 1
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It's a tie game!
Previous Turn Score 0 points
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Player 2

How to play Prime Out!


Prime Out! is a game built around patterns in prime factorizations. Your objective is to earn points by building the prime factorizations of the numbers on the game board using colored blocks that represent prime numbers. For instance, to build the number 50, you combine one (white) '2' block with two (orange) '5' blocks, because 2 ⋅ 5 ⋅ 5 = 50.

Prime Out! is different than most other math games because it does much more than develop math skills (although it does that, too). Whereas in school, you are usually taught one procedure (using factor trees) to build prime factorizations, when you play Prime Out!, you use many strategies - you actually see the prime factorizations as you build them. In fact, you see more than one of them at a time. This helps you discover patterns and make connections between the prime factorizations of different numbers. Patterns and connections are essential keys that unlock a deeper understanding of mathematical concepts. Playing Prime Out! shows you what makes prime numbers so important - they are the basic building blocks from which all counting numbers are created!

Getting Started

When you begin Prime Out!, you see that you have a few choices to make. You can play on your own or with a friend. You can choose to build smaller numbers when you are first learning, or larger numbers when you are ready for more of a challenge! You may also choose between the 'Regular' version of Prime Out! or the 'Action' version. The Action version is timed - the more quickly you place a block, the more points you earn - but you have to think fast!

Playing a Block

Each player begins with a rack of five colored blocks, with each color standing for a different prime number. Players take turns using the blocks in their racks to build the prime factorizations of the numbers on the game board.

To play a block, just select it from your rack and select a number to play it on. It's as simple as that! You can change your mind as often as you like until you press 'ENTER' to finalize your choice. If the block belongs in the prime factorization of the number, you will receive points and the block will become part of the building. If not, the block will be returned to your rack and you will lose points - so play carefully!

Black blocks are a little different. They do not have numbers printed on them so they are almost like wild cards. Black blocks represent any prime number larger than 19. The correct prime number will appear on the block once you place it (assuming you place it correctly, of course!).

Usually you play one block per turn, but if your "Blocks to be Played" value shows "2" at the beginning of your turn, you may play two blocks. You will play the blocks one at a time and will receive the combined score for the two blocks.

Skipping Your Turn

If there are two players, you may choose to skip your turn if you like. Just hit 'ENTER' before selecting a block and a square. As you will see when we discuss scoring, this might sometimes be a good strategy to keep your opponent from completing a building. However, if you choose to skip your turn when you have a block that can be played, you will lose some points. A message will pop up to remind you of this and ask you to confirm that you really want to skip your turn. Note: If none of your blocks can be played, you will not lose points. However, in this case, your best option is probably to trade your blocks in!

Trading Blocks In

During each game, you are allowed to make as many as three 'trades' (two trades if you choose the range 1-20). When you trade your blocks in, you receive five new blocks in your rack and this ends your turn. A message will pop up asking you to confirm that you want to make the trade.


When your turn begins, your "Blocks to be Played" and "Multiplier" totals for that turn are highlighted. The number of blocks will be either 1 or 2 (usually 1) and your multiplier will be a whole number from 1 through 6. Your score for the turn is the value of the block you played times this multiplier. Black blocks are a little different - they always have a value of 5 points, regardless of the prime number they represent. Examples: If you play a 7 block and your multiplier is 3, you will earn 7 ⋅ 3 = 21 points for that turn. If you play a black block and your multiplier is 2, you will earn 5 ⋅ 2 = 10 points.

If you skip your turn when you could have played a block, or if you play incorrectly, you will lose 20 points.

There is an opportunity for bonus points. If you are the player who completes a building, you will receive an additional 10 points for each block in the building.

The above information about scoring applies to the regular game. There are a few differences in the way the Action game is scored. For more information about this, see the 'Action Game' section below.

The End of the Game

Prime Out! ends when all buildings are complete, or when there are no playable blocks left in either player's rack and all trades have already been taken. The player with the higher score wins. If you are playing by yourself, you can set your own goals!

The Action Game

The Action version of Prime Out! is timed. You will have 30 seconds to play each block. There will be a timing bar to the left of the "ENTER" button showing the percent of time remaining. The faster you play, the more points you get! To be exact, the percent of time you have left will be the percent of the maximum possible number of points you will receive for your turn. For example, if you have 80% of the time left when you complete your turn, you will get approximately 80% of the available points. If you do not play a block within 30 seconds, you will receive no points. However, you should still play a block since there is a penalty for skipping your turn.

Scoring details are a little different for the Action game. To compensate for the lower scores that can result from taking longer to play, multipliers now run from 1-12 instead of 1-6. (Because of this, overall scores in the Action game are often higher!) On the other hand, if you skip a turn when you could have played, or if you misplay a block, the penalty is 40 points instead of 20.

There's one more important difference to keep in mind. When you play the Action game, there will be no messages asking you to confirm that you want to skip a turn or trade your blocks. After all, this would stop the clock! Once you make the choice, there's no going back! This also means that you have to be careful that you've selected a block and a square before you hit the "Enter" button.

A Few Suggestions

If Prime Out! is new to you or if you are playing with high numbers, you may want to start by playing the "Regular" game. As you gain experience and become more familiar with the prime factorizations of the numbers, you can begin working for speed!

Of course, you may choose to use a calculator to help you find factors, especially if Prime Out! is new to you. However, please consider the opportunities and challenges in developing your own mental math strategies. In the long run, if you practice, you can learn to find prime factors in your head much more quickly than you could using a calculator!

There are countless strategies you can use for placing blocks correctly. If you watch closely, you will discover some beautiful patterns in the way the prime factors show up on the board! In fact, this is one of the main points of the game! These patterns - along with your knowledge of multiplication facts, divisibility rules, and estimation skills - will help you place blocks more quickly and accurately.

It also makes a difference when you play your blocks. It is best to place high-valued blocks when you have a high multiplier. This can change your score dramatically! (Because of this, you shouldn't worry if you fall far behind your opponent's score - things can change very quickly in Prime Out!) Also, be sure to watch the other player's rack! Be careful not to give your opponent an unnecessary opportunity to complete a building.

Above all, when you play Prime Out!, be prepared to have fun and learn many new things about prime numbers and prime factorizations. Happy building!

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