Problem 60944. Ulam primes first formula

Historical context
The polish-american mathematician Stanislaw Ulam found the formula to give the first 760 prime numbers not given by Euler's formula.
Problem statement
For a given integer m, m >= 1847, list the Ulam prime numbers less or equal to m in a vector up. Also compute their frequency / ratio f compare to all the primes in the same range. If m is not a positive integer greater or equal to 1847, your function should return up = [] and f = 0.
Examples
  • If m = 1847 then up = 1847 and f = 1 since 1847 = P(0) and it is the only prime number m greater or equal and less or equal to 1847;
  • If m = 3000 then up = [1847, 2203, 2393, 2591, 2797] and f = 5/148 since 1847 = P(0), 2203 = P(2), 2393 = P(3), 2591 = P(4), 2797 = P(5), and there are in total 30 prime numbers in the range [1847; 3000] ;
  • If m = 1823 then up = [] and f = 0;
Tip
n is less or equal to 2000 here.
Fobidden functions
  • regexp
  • assignin
  • str2num
See also
Solve

Solution Stats

53.85% Correct | 46.15% Incorrect
Last Solution submitted on Aug 17, 2025

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