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Math Forum » Discussions » sci.math.* » sci.math

Topic: Is there a polynomial time algorithm for enumerating prime numbers?
Replies: 10   Last Post: Jun 6, 2012 9:53 PM

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Peter Percival

Posts: 1,370
Registered: 10/25/10
Is there a polynomial time algorithm for enumerating prime numbers?
Posted: Jun 5, 2012 5:37 AM
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Let p_n be the n-th prime number (p_1 = 2, etc). Is there a polynomial
P(n), and an algorithm to find p_n in a number of steps* S(n), where S(n)
is bounded by P(n)?

* A step being what? If I were to write a program to implement such an
algorithm, I would take "step" to mean "machine code instruction"; but
there might be a better definition not tied to any particular way of
implementing algorithms.

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