# Questions tagged [primes]

A puzzle that involves and requires knowledge of prime numbers. Use with [mathematics]

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### Relatively prime numbers

Can you fill in the circles with numbers such that: Each pair of circles connected by one line contains relatively prime numbers Each pair of circles connected by two lines do not contain relatively ...
2k views

### A Prime Ant's Excursion in the Cartesian Plane

An ant resides at the origin of the Cartesian plane. One morning she sets out on a long excursion of its first quadrant and pledges to walk a different prime number of units every day starting with 2, ...
2k views

### A Prime Number equation using all nine digits once

Create an equation with the following conditions All numbers must be one or two digit prime numbers You can only use + and - and = No other math operators You must use all the nine (single) digits (...
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### Primeable numbers

Say a positive integer is primeable if it is prime or some permutation of all its digits (leading 0s allowed in permutations) is a prime. Thus the first few primeable numbers are 2, 3, 5, 7, 11, 13, ...
242 views

### Intermingled primes

This puzzle is part of the Monthly Topic Challenge #14: Think inside the (very small) box!. 6 different, 3 digit primes are stacked here in two layers. You only see the sum of overlapping digits. ...
• 8,010
207 views

### Prime Boggle Game

Two players, Alice and Bob, take turns in identifying and circling prime numbers in this 8 x 8 board of digits. Primes must be read as continuous string of digits, either horizontally (from left to ...
798 views

### Number of 1's needed to write all primes up to P

i) Find, if it exists, a prime P such that the number of 1's used to write all the primes from 2 to P is precisely P. ii) Are there infinitely many such P? If not, find them all. These questions ...
898 views

### Villeta's Soup of Primes

i) Hidden in this 8 x 8 board are the first 31 primes starting with 2 and up to to 127. They occupy adjacent, non-overlapping cells (up to 3), and are read horizontally (from left to right) or ...
646 views

### Covering a room with 34 carpets

There are 34 rectangular integers less than 100 which are the product of two primes. Can a room be covered precisely (no overlaps, etc.) with the 34 rectangles that have as areas these products?
1k views

### My library membership number

My library membership number, which I readily forget, is a 10-digit number, all different digits. However, I do remember it is the largest such number in which any block of four adjacent digits is ...
220 views

### More stepping stones

Start by placing prime numbers 2, 3 and 5 anywhere on an infinite square grid. Now you can place a prime number $p$ subject to the following rules: It must be greater than all the previous numbers ...
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226 views

### Using Prime numbers to get 100 and 1000

Using the digits 1 to 9 exactly once create a set of one or two digit prime numbers. Use those prime numbers and the math operations + - / * and parantheses to get 100. Then use those exact same ...
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237 views

### Planar Investigator

Use logical deduction to place a different digit from 1 to 9 in each circle below so that 8 of the arrows form the primes 23, 31, 41, 53, 59, 79, 89, and 97. (We view an arrow starting at digit A and ...
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322 views

### A prime time traveler

It is the year 2140 and you have just turned 40. After years of research, you have finally invented the time machine! It is a small device that fits in your pocket and allows you to travel in time. ...
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201 views

### Prime sums in a 3x3 grid version 2

Can you place the first 9 natural numbers (1 to 9) in a 3x3 grid such that every row and column sums to a prime? The sums do not need to be distinct. Bonus: can you also make both diagonals sum to a ...
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362 views

### Prime sums in a 3x3 grid

Can you place the first 9 odd primes in a 3x3 grid such that every row, column and both diagonals sum to a prime? The sums do not need to be distinct.
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### Scrabble with prime numbers!

How to Play Overall, gameplay is very similar to typical Scrabble; however, unlike typical Scrabble, you'll be using digits instead of letters (we'll cover your tile bag later). The objective is to ...
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644 views

### Another Rook's Tour of the Chessboard

Place numbers 1 to 64 in the cells of this 8 x 8 board in such a way that consecutive numbers occupy neighboring cells (either vertically or horizontally). Shaded cells must be occupied by prime ...
898 views

### Splitting the Primes

Is it possible to split the 25 primes less than 100 into two disjoint sets such that the sum of the primes in one set equals the product of the primes in the other set? If so, in how many ways can ...
1k views

### A King's Short Walk

Place the numbers 1 to 25 on the cells of this board so that any two consecutive numbers occupy cells that are horizontally, vertically or diagonally adjacent. Prime numbers should occupy shaded cells....
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### Squares and chords in a circle

The whole numbers 1 to 2n are placed in order around a circle. For which n is it possible to draw n non-intersecting chords (one from each number) such that each of them joins two numbers whose sum ...
1k views

### Find an integer where each sum of 5 consecutive digits is prime

Find the largest positive integer with the following properties: every sum of 5 neighboring digits in its decimal representation is a prime number. those prime numbers get smaller and smaller from ...
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327 views

### Magic Square Primes At Most

Take 9 numbers from 1~20 without repetition and fill them in a 3x3 grid so that the sums on each row, each column, and each diagonal are the same. If there are a primes among these 9 numbers at most, ...
• 31
521 views

### Trees from integers [closed]

A set of distinct positive integers is said to be a prime tree of integers if the graph obtained by letting the integers be its vertices, two of which are joined by an edge if (and only if) their sum ...
346 views

### Primes and squares in a grid

i) Place thirteen different three-digit prime numbers in the empty cells of this grid. ii) Now place thirteen different three-digit square numbers in the empty cells of this grid. How many solutions ...
93 views

### Number conversion via Prime route

This is a variation of the Word Ladder. Instead this is a number ladder. Convert the number 12345 to the number 54321 in seven or less steps with the following rules A: You can only change any one ...
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249 views

### Is this Prime Sequence the longest?

So you are interested in Prime Numbers and puzzles thereof. You saw the following on PSE and gave it a try and got it long after the correct answer was posted by @hexomino. My Eight Cousins But then ...
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### My Eight Cousins

My eight cousins are all a different prime number of years old, and their average age is a whole number. Recently they all came to visit me and, as they left one by one, I noticed that at all times ...
219 views

Take the first 10 primes. Can you divide them into $g$ disjoint groups, such that the sum of numbers in each group is prime. In particular can you make this work for every value of $g$ in the range $[... • 33.2k 2 votes 2 answers 122 views ### A number built with two-digit primes What is the largest number, which can built as a sequence (from left to right) of different two-digit primes only? For example, 1371731 is valid, 137131 is invalid (containing 13 twice), 139717 is ... • 11.9k 7 votes 4 answers 651 views ### 8x8 square with no adjacent numbers summing to a prime Can you fill a 8x8 grid with numbers from 1 to 8 such that: Every number occurs exactly once in each row and in each column (Latin square). No two adjacent (horizontally or vertically) numbers sum to ... • 33.2k 5 votes 1 answer 274 views ### Solving Kordemsky's Prime Cryptarithm and proving uniqueness This is a cryptarithm from Kordemsky's The Moscow Puzzles, problem 273 to be precise. Each digit is a single-digit prime ($2,3,5,$or$7$). Find a solution and prove that it is unique.$$\begin{array}{... • 153 4 votes 1 answer 204 views ### More primes and squares, in a summation triangle Place a different prime number or perfect square in each of the twenty-one disks that make up the triangle below, so that the number in any disk that lies on two others is precisely the sum of the ... 11 votes 2 answers 850 views ### Time... to be prime? A standard analogue clock face has numbers 1 to 12 around the edge arranged sequentially, which is nice for telling the time, but not especially interesting. It is possible to arrange the numbers in ... • 897 4 votes 2 answers 227 views ### Prime stepping stones Start by placing number$1$anywhere on an infinite square grid. Now place numbers$2, 3, 4, \ldots, K$in order. A number$k$can be placed if the following rules hold: It must be adjacent (... • 33.2k 7 votes 0 answers 300 views ### Even and primes puzzle? These are secret numbers that increase regularly. What are the next two numbers? If you like numbers, it will be fun.$2^3 \times2242992^2 \times 3^2 \times 19 \times 35572 \times 5 \times ...
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-What is your password?- my niece asks me. -It is a four digit number. -I know that. -It is divisible by precisely three primes. -Tell me more. -It has at least one common divisor greater than 1 with ...
362 views

### A Kind of Unique Prime Number

A Prime number with the following properties Less than 7 digits and more than 3 digits ALL digits in the number are Prime numbers-- some repeated. All individual digits in the number add up to a ...
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1 vote
196 views

### On certain triplets of consecutive integers [closed]

While completelely factorizing integers, my student Luciana noticed that the canonical prime factorization of the three consecutive numbers 81=3^4, 82=2x41, and 83=83, use numbers which are all ...
644 views

### Gaby's Puzzle (Primes Around a Circle)

To keep them busy during lockdown, Gaby asked her children to find a way to place the first sixteen primes (2 to 53) around a circle so that either the sum or difference (or both) of any two of them ...
644 views

### Primes in a Line

Place the first 20 primes (2 to 71) in a line so that the sum or difference (or both) of any two primes that find themselves next to each other is always a perfect square. For which other values of N ...
157 views

### Follow the path of relation through the grid #8

There is a relation between rectilinear-adjacent squares such that there is a unique rectilinear path from the top-left corner of the grid down to the bottom-right corner of the grid. Each square can ...
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212 views

### Follow the path of relation through the grid #7

There is a relation between rectilinear-adjacent squares such that there is a unique rectilinear path from the top-left corner of the grid down to the bottom-right corner of the grid. Each square can ...
• 2,296
1k views

### Prime to number conversion

This puzzle relates to Prime to Prime: Get all first 25 Prime Numbers using up to 4 Primes and its sequel Prime to Prime Sequel Using any three of the first 4 prime numbers (2,3,5 and 7) and the ...
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365 views

### Can you cut through the mist?

I've created a mapping between words and complex-valued polynomials, and I've generated examples from word lists that I've I found on another puzzle. You don't need to study every one of these, but I ...
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624 views

### A looped building with Prime rooms lighted

Imagine a building with 200 consecutive connected rooms as shown below. The shape is not important. It could be a circular loop building. You do not know the room numbers but you are told that they ...
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2k views

### It's my sister's birthday

I'd ordered her a cake, but when I got to the bakery to pick it up, the cake decorator had transposed the digits of her age. "She'll thank you for the compliment," I said, "but her age is a prime ...
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### A King's Hamiltonian Tours

a) Place the numbers 1 to 25 in the cells of a 5 x 5 board in such a way that consecutive numbers occur in adjacent cells either vertically, horizontally, or diagonally, and so do cells with numbers 1 ...
573 views

### Prime number snake (2)

This question is inspired by prime number snake. In the following grid, you have to place a number snake of numbers 1 to 100. Consecutive numbers have to go into neighboring cells. Numbers in grey ...
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### Prime Number Snake

Place numbers 1 to 100 in the cells of the 10 x 10 board below in such a way that consecutive numbers occupy neighboring cells (either horizontally or vertically). Shaded cells should contain only ...