Questions tagged [primes]

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

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13 votes
1 answer
894 views

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 ...
godlification's user avatar
6 votes
4 answers
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, ...
Bernardo Recamán Santos's user avatar
10 votes
4 answers
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 (...
RogerA's user avatar
  • 5,407
15 votes
3 answers
1k views

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, ...
Bernardo Recamán Santos's user avatar
7 votes
1 answer
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. ...
Retudin's user avatar
  • 8,010
7 votes
1 answer
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 ...
Bernardo Recamán Santos's user avatar
5 votes
2 answers
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 ...
Bernardo Recamán Santos's user avatar
10 votes
1 answer
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 ...
Bernardo Recamán Santos's user avatar
3 votes
2 answers
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?
Bernardo Recamán Santos's user avatar
7 votes
2 answers
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 ...
Bernardo Recamán Santos's user avatar
5 votes
1 answer
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 ...
Dmitry Kamenetsky's user avatar
4 votes
2 answers
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 ...
DrD's user avatar
  • 39.2k
3 votes
2 answers
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 ...
noedne's user avatar
  • 15.4k
5 votes
1 answer
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. ...
Dmitry Kamenetsky's user avatar
3 votes
2 answers
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 ...
Dmitry Kamenetsky's user avatar
5 votes
2 answers
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.
Dmitry Kamenetsky's user avatar
17 votes
2 answers
1k views

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 ...
Hazel へいぜる's user avatar
7 votes
2 answers
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 ...
Bernardo Recamán Santos's user avatar
11 votes
2 answers
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 ...
Bernardo Recamán Santos's user avatar
5 votes
2 answers
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....
Bernardo Recamán Santos's user avatar
2 votes
1 answer
521 views

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 ...
Bernardo Recamán Santos's user avatar
12 votes
3 answers
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 ...
ThomasL's user avatar
  • 11.9k
3 votes
1 answer
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, ...
welly's user avatar
  • 31
2 votes
1 answer
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 ...
Bernardo Recamán Santos's user avatar
4 votes
2 answers
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 ...
Bernardo Recamán Santos's user avatar
3 votes
1 answer
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 ...
DrD's user avatar
  • 39.2k
6 votes
3 answers
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 ...
DrD's user avatar
  • 39.2k
8 votes
1 answer
193 views

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 ...
Bernardo Recamán Santos's user avatar
2 votes
2 answers
219 views

Dividing the first 10 primes into groups whose sum is prime [closed]

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 $[...
Dmitry Kamenetsky's user avatar
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 ...
ThomasL's user avatar
  • 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 ...
Dmitry Kamenetsky's user avatar
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}{...
Favst's user avatar
  • 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 ...
Bernardo Recamán Santos's user avatar
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 ...
Narushiteli's user avatar
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 (...
Dmitry Kamenetsky's user avatar
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. $2^3 \times224299$ $2^2 \times 3^2 \times 19 \times 3557$ $2 \times 5 \times ...
Mamu's user avatar
  • 71
2 votes
1 answer
175 views

My Latest Password

-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 ...
Bernardo Recamán Santos's user avatar
6 votes
3 answers
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 ...
DrD's user avatar
  • 39.2k
1 vote
1 answer
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 ...
Bernardo Recamán Santos's user avatar
13 votes
1 answer
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 ...
Bernardo Recamán Santos's user avatar
6 votes
2 answers
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 ...
Bernardo Recamán Santos's user avatar
3 votes
1 answer
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 ...
Galen's user avatar
  • 2,296
4 votes
1 answer
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 ...
Galen's user avatar
  • 2,296
6 votes
2 answers
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 ...
DrD's user avatar
  • 39.2k
6 votes
1 answer
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 ...
Galen's user avatar
  • 2,296
11 votes
6 answers
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 ...
DrD's user avatar
  • 39.2k
13 votes
2 answers
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 ...
Rupert Morrish's user avatar
17 votes
3 answers
1k views

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 ...
Bernardo Recamán Santos's user avatar
20 votes
1 answer
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 ...
daw's user avatar
  • 3,035
51 votes
5 answers
5k views

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 ...
Bernardo Recamán Santos's user avatar