# Questions tagged [primes]

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

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### The Cryptic Constellation

You are a renowned cryptographer who has been contacted by an ancient order known as "The Keepers of the Stars." They guard a secret message passed down through generations, hidden in the ...
1k views

### Today is a prime!

Today, 20240603 already in some parts of the world, is a prime number. Just twenty-one other dates during 2024 are also primes. In what year will there be none?
3k views

### Prime to Prime: Get all first 25 Prime Numbers using up to 4 Primes

The first 25 Prime Numbers are 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97 Using up to 4 prime numbers and the following mathematical operations, get all the 25 primes. + ...
505 views

### Prime to Prime Sequel

This question is inspired by the Prime to Prime puzzle. The first 24 Prime Numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 Using up to 4 prime ...
310 views

### Prime magic star

Can you replace the letters with 10 consecutive primes such that the sum of numbers on each line is equal? I expect this to be solved with a computer. Good luck!
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 ...
993 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 ...
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 (...
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, ...
1k 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 ...
263 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. ...
225 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 ...
1k 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 ...
1k 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?
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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 ...
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### 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 ...
678 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 ...
327 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}{...
208 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 ...
863 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 ...
180 views

-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 ...
366 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 ...
1 vote
198 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 ...