Problem 659. How long is the longest prime diagonal?

Created by Ned Gulley

Solve Later

Stanislaw Ulam once observed that if the counting numbers are arranged in a spiral, the prime numbers contained in it form a surprising pattern. They appear to cluster along diagonals of the spiral matrix.

Given n, return the length of the longest diagonal sequence of primes in spiral(n).

Example:

 Input  n = 7
 Output d = 4

Since isprime(spiral(n)) is

     1     0     0     0     1     0     0
     0     0     0     1     0     0     0
     1     0     1     0     0     0     0
     0     1     0     0     1     1     0
     0     0     1     0     1     0     1
     0     1     0     0     0     1     0
     1     0     0     0     0     0     1

Solve

Solution Stats

Last solution submitted on Aug 23, 2019

Last 200 Solutions

Problem Comments

5 Comments

5 Comments

Show 2 older comments

Jacob on 11 Jun 2012

I agree that the solution is mis-coded. isprime(spiral(4)) gives:
1 0 0 0
0 0 1 1
1 0 1 0
0 0 0 1
which means that d=2 for this case.

Ned Gulley on 11 Jun 2012

Rescoring based on corrected test suite. Sorry about that.

Jonathan Campelli on 11 May 2015

"find the longest diagonal arrangement of primes in spiral(n)" leaves room for misinterpretation.

I would have quickly understood:
"return the length of the longest diagonal sequence of primes in spiral(n)"

David Verrelli on 17 Nov 2017

Like Jonathan Campelli, I still feel the problem statement could be clearer. From the example I eventually figure that reference is being made to the diagonally oriented elements running between elements (1,5) and (4,2) of isprime(spiral(n)). But arguably these are not on a/the "diagonal" of that matrix, per http://mathworld.wolfram.com/Diagonal.html (cf. https://en.wikipedia.org/wiki/Main_diagonal ).

David Verrelli on 17 Nov 2017

Furthermore, there is no mention in the current online MATLAB documentation that "spiral" is actually a function that is already provided with MATLAB — i.e. that the user does not have to write their own function to make the spiral matrix. Apparently, "spiral can be found in the demo folder" [ref: https://stackoverflow.com/questions/29466058/spiral-loop-on-a-matrix-from-a-point].

Solution Comments

Solution 1854983

1 Comment

1 Comment

jianrui fan on 21 Jun 2019

this is really awesome and impressive.I do learn something

Solution 1699697

1 Comment

1 Comment

A C on 27 Dec 2018

n = isprime(spiral(n))

Solution 593819

1 Comment

1 Comment

jianrui fan on 21 Jun 2019

thank you very much

Solution 443569

1 Comment

1 Comment

Ramoflaple on 11 Aug 2015

a good precise algorithm

Solution 117430

1 Comment

1 Comment

Jon on 21 Mar 2014

Best solution that doesn't cheat with a lookup or regexp

Solution 102911

1 Comment

1 Comment

Dirk Engel on 26 Jun 2012

max(diff(find(~zeroOneVector)))-1 returns the longest run of ones in a vector of zeros and ones, but it FAILS IN SEVERAL CASES, e.g.:
- all ones: [1 1 1 1 1] returns empty
- just a single zero: [1 1 0 1 1] returns empty
- all zeros at one end: [1 1 1 0 0] returns 0
- longest run at one end: [1 1 0 1 0] returns the longest run between zeros, here 1

As a workaround for all cases, add zeros to both ends of the vector:
max(diff(find(~[0 zeroOneVector 0])))-1

However, this is not necessary for this solution because the matrix is very sparse.