[math-fun] a long series of primes
Hello, I have been working on ways to generate primes with the simplest formula. Here is one : if c = 31622.7 ... then { c^n } is prime for n = 2 to 388 : 387 consecutive primes. { } is the nearest integer. The sequence begins like this : 1000000007 31622776952311 1000000014783746303 31622777186062677745609 1000000022175619536498921059 31622777419814234539614807614633 ... and not listed in the OEIS. Here is the complete list and more precise value of the constant. http://plouffe.fr/NEW/List%20of%20387%20consecutive%20primes.txt I developed a method based on Monte-Carlo and Simulated Annealing https://en.wikipedia.org/wiki/Simulated_annealing The method allows me to find other candidates which would give a longer series of primes. This formulation is the simplest I could imagine. Is there simpler method to generate any number of primes ? Best regards, Simon Plouffe
On Thu, Feb 13, 2020 at 3:01 AM Simon Plouffe <simon.plouffe@gmail.com> wrote:
Is there simpler method to generate any number of primes ?
"Simplicity" depends entirely on the programming language. In Mathematica, the simplest way is Prime[n]. One might think that there are "natural" universal Turing machines, in the sense that unnatural ones can simulate natural ones with short interpreters, but not vice-versa. Somewhat surprisingly, that turns out to be false. -- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com
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