# How can I write a program that can display the first 50 consecutive prime numbers starting with 2?

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##### 3 Comments

John D'Errico
on 29 Apr 2021

### Accepted Answer

Sean de Wolski
on 15 Mar 2012

for ii = 1:inf

nguess = ii;

mat = tril(bsxfun(@times,2:nguess,(2:nguess).'));

pn = setdiff(2:nguess,mat(logical(mat)));

if numel(pn)>50

pn = pn(1:50);

break

end

end

Maybe?

##### 4 Comments

Walter Roberson
on 15 Mar 2012

The assignment requires that fprintf() be used, so disp() would not be acceptable.

### More Answers (3)

Walter Roberson
on 15 Mar 2012

##### 0 Comments

Bud Kelly
on 31 Mar 2018

Edited: Walter Roberson
on 31 Mar 2018

Here's a small and very tight bit of code that will generate prime numbers up to any searchlimit you wish. It's fast too. On my Macbook Pro it lists primes up to 10,000 in only 0.112 seconds. Fast enough? Here's the code:

searchlimit = 100; % here you can set any searchlimit you wish

primes = 2; % initialize list starting with 2

for i = 1 : searchlimit % begin for loop

if mod(2+i, primes) ~= 0 % go through i's by 2

primes = [primes; 2+i]; % if prime add to primes list

end

end % end for loop

primes % print list of primes in single column (note: no semicolon!)

toc; % end timer and display elapsed time in seconds

% for your reference, the prime numbers less than 100 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

##### 1 Comment

John D'Errico
on 31 Mar 2018

I would not call it tight. Dynamic growth of an array, which is a huge problem here. See how incredibly slowly this code runs to find all primes less than 1e6. (6 minutes or so on my old mac. It even forced my CPU fan to kick on.) This code checks all the even numbers greater than 2. It performs far more modulus tests than is necessary.

Just use a sieve. Way faster. A simple implementation of a basic sieve required 0.080629 seconds on my old Mac to generate all 78498 primes less than 1e6.

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