Questions tagged [primes]

A puzzle that involves and requires knowledge of prime numbers.

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15
votes
1answer
316 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 ...
44
votes
5answers
4k 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 ...
7
votes
1answer
402 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 ...
13
votes
4answers
1k views

Reconstructing the results of a 6-team soccer tournament

6 teams played in a "round-robin" soccer tournament, in which each team played each other team once. Each game had 3 possible outcomes: team 1 won, draw, or team 2 won. The winning team received 3 ...
13
votes
1answer
268 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 ...
17
votes
3answers
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. ...
4
votes
1answer
228 views

Prime parallel rows for the first 20 numbers

Two positive integers can be joined with a straight segment if their sum is a prime and the segment doesn't intersect any other segments. What is the most number of pairs you can join if you can place ...
2
votes
1answer
102 views

The first 10 prime butterflies

A prime butterfly is a set of three distinct numbers $a,b,c$, such that $a+b$ and $b+c$ are both primes. Can you divide numbers from 1 to 30 into 10 prime butterflies?
5
votes
2answers
284 views

Two equal-sized lists that produce prime sums

Place one or more distinct numbers between 1 and 100 into the lists $𝑃$ and $𝑄$, such that they contain the same number of elements and any number from $𝑃$ added to any number from $𝑄$ gives a ...
15
votes
5answers
963 views

Dividing the first 20 numbers into 3 lists

Place every number from 1 to 20 into one of three lists $P$, $Q$ or $O$, such that any number from $P$ added to any number from $Q$ gives a prime. What is the fewest number of elements that can be in $...
14
votes
1answer
1k views

Prime tree game

Let's play a game. On the first step you place the number 1. On the $n$-th step starting from $n=2$ you place the number $n$ such that: It is adjacent (horizontally or vertically) to one or more ...
4
votes
1answer
157 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!
4
votes
2answers
230 views

Primes from arithmetic and geometric progressions

The five primes, 131, 157, 211, 349, 739, are neither in arithmetic or geometric progression, but are instead the sum of the corresponding terms of two progressions of five terms each, one arithmetic ...
1
vote
1answer
85 views

Neighbouring numbers summing to a prime on a 4x4

Can you place every number from 1 to 16 on a 4x4 grid such that every pair of neighbouring (horizontally and vertically) numbers sum to a prime? Note that the generated primes can be reused. A ...
4
votes
3answers
490 views

Neighbouring numbers summing to a prime on a 3x3

Can you place distinct numbers from 0 to 9 on a 3x3 grid such that every pair of neighbouring (horizontally and vertically) numbers sum to a prime? Can you find multiple solutions? Note that the ...
7
votes
4answers
2k views

Smallest number containing the first 11 primes as sub-strings

113257 contains the first 6 primes as sub-strings when reading them from left to right: 2: 113257 3: 113257 5: 113257 7: 113257 11: 113257 13: 113257 What is the smallest number that contains ...