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

Question

Andrew 2012-3-15

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评论： John D'Errico 2021-4-29

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 2021-4-29

how to sum them up

John D'Errico 2021-4-29

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. ;-)

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Answer 1

Sean de Wolski 2012-3-15

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在 MATLAB Online 中打开

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?

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Sean de Wolski 2012-3-15

How about really simple?:

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 2012-3-15

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

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Answer 2

G A 2012-3-15

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if a is a prime then length(factor(a)) is equal to 1. You can try while loop.

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Walter Roberson 2012-3-15

Please do not give complete code for course assignments!

G A 2012-3-15

Sorry. Edited

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Answer 3

Walter Roberson 2012-3-15

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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.

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Answer 4

Bud Kelly 2018-3-31

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编辑：Walter Roberson 2018-3-31

在 MATLAB Online 中打开

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

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John D'Errico 2018-3-31

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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