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Old 2018-03-07, 01:54   #248
Feb 2017

3×5×11 Posts

Originally Posted by gophne View Post
How many contributers consider the distribution of prime numbers to be "random" or "psuedo-random" vs contributers who consider prime numbers to be very orderly distributed in the set of natural numbers?

Poll to be closed on 16/03/2018 (Would appreciate somebody that could summarize the poll results :))

"There are two facts about the distribution of prime numbers. The first is that, [they are] the most arbitrary and ornery objects studied by mathematicians: they grow like weeds among the natural numbers, seeming to obey no other law than that of chance, and nobody can predict where the next one will sprout.

The second fact is even more astonishing, for it states just the opposite: that the prime numbers exhibit stunning regularity, that there are laws governing their behavior, and that they obey these laws with almost military precision."

- Don Zagier, as quoted in Elementary Number Theory: Primes, Congruences, and Secrets -William Stein, January 23, 2017

Poll options;

(1) Random or Psuedo-random
(2) Regular, or
(3) Neither
My poll is not proving to be very popular...only had a prime number of responses to the Poll...1+1 responses so far...including my own respose!

For what it is worth I am more inclined to agree with the latter part of the premises stated by Don Zagier that prime numbers are very "ordered" and the problem of identifying large primes is more a result of the largeness of the numbers concerned w.r.t computational time required to confirm them as prime numbers, even on the most advanced computers available.

The secret would be to discover (or develop?) a formula for primes, which would have the effect of determining primes as high as we could go. My opinion is that since prime numbers are natural numbers missed by the process of sieving by lower natural numbers...the great mathematical minds around should be able to quickly! formulate such formula/algorithm for prime numbers.
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