It depends on what you mean. Given a list of the first n primes, one can always write a formula which gives the primes, i.e f(1)=2, f(2)=3, f(3)=5, ...f(n)=nth prime. For example, see Lagrange Interpolating Polynomials http://mathworld.wolfram.com/LagrangeInterpolatingPolynomial.html
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