Questions tagged [primes]
A puzzle that involves and requires knowledge of prime numbers. Use with [mathematics]
65
questions
13
votes
1
answer
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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 ...
- 1,169
6
votes
4
answers
2k
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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, ...
- 16.9k
10
votes
4
answers
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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 (...
- 10.1k
15
votes
3
answers
1k
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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, ...
- 5,451
10
votes
1
answer
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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 ...
- 16.9k
7
votes
1
answer
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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.
...
- 4,834
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 ...
- 16.9k
5
votes
2
answers
800
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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 ...
- 13.4k
3
votes
2
answers
648
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?
- 16.9k
7
votes
2
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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 ...
- 226
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 ...
- 6,551
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 ...
- 5,632
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
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 ...
- 136
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 ...
- 5,114
5
votes
1
answer
322
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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. ...
- 33.2k
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 ...
- 15.4k
5
votes
2
answers
362
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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.
- 13.4k
17
votes
2
answers
1k
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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 ...
- 8,010
9
votes
1
answer
575
views
Living in prime years
A human was born somewhere in interval of [1;1920] A.D. They lived exactly 100 years. They lived through more years that were prime numbers than any other human (of the same lifespan) who was born in ...
- 468
7
votes
2
answers
648
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 ...
- 30k
13
votes
1
answer
648
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 ...
- 16.9k
11
votes
2
answers
904
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 ...
- 133k
5
votes
2
answers
1k
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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....
- 12k
2
votes
1
answer
524
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 ...
- 16.9k
12
votes
3
answers
1k
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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 ...
- 2,150
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, ...
- 11.6k
2
votes
1
answer
524
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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 ...
- 1,230
4
votes
2
answers
346
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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 ...
- 16.9k
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 ...
- 133k
7
votes
2
answers
601
views
The largest Thursday number
A Thursday number is a number 𝑁 where any three consecutive digits make a prime, and all such primes formed are distinct.
For example, 13739 is a Thursday number because 137, 373, and 739 are all ...
- 10.1k
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 ...
- 133k
8
votes
1
answer
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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 ...
- 133k
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 $[...
- 10.2k
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 ...
- 12k
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 ...
- 111
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}{...
- 2,917
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 ...
- 10.2k
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 ...
- 10.1k
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 ...
- 7,357
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 ...
- 889
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 ...
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 ...
- 2,296
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 ...
- 2,296
6
votes
2
answers
646
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 ...
- 13.4k
6
votes
2
answers
1k
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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
...
- 4,499
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 ...
- 133k
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 ...
- 76k
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 ...
- 4,883
17
votes
3
answers
1k
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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 ...
- 241