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

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Andrew on 15 Mar 2012
Commented: John D'Errico on 29 Apr 2021
Primes(x) and isPrime(x) are not allowed for this question. fprintf should be used. I was thinking of using a while loop with maybe a for and/or if's inside. I am new to MATLAB so any help would be appreciated. Thanks!
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dure zahra on 29 Apr 2021
how to sum them up
John D'Errico on 29 Apr 2021
There are only two prime numbers that are consecutive, that is, 2 and 3. All other primes are NOT consecutive. So the sum of all consecutive primes is 5. It can be no other value. ;-)

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?
Sean de Wolski on 15 Mar 2012
disp([2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229])
Walter Roberson on 15 Mar 2012
The assignment requires that fprintf() be used, so disp() would not be acceptable.

G A on 15 Mar 2012
if a is a prime then length(factor(a)) is equal to 1. You can try while loop.
Walter Roberson on 15 Mar 2012
Please do not give complete code for course assignments!
G A on 15 Mar 2012
Sorry. Edited

Walter Roberson on 15 Mar 2012
If you know a list of primes P, then multiply them all together and add 1. The resulting number will either be prime itself, or will be a composite number that can be factored into at least two primes that are not already on your list. Each time you generate one of these new smaller primes and insert it on to your list, you can take the subset of the list up to that point and start generating from there.

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
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.