Swinnerton-Dyer Polynomial

The th Swinnerton-Dyer polynomial is the monic algebraic number minimal polynomial over the rational numbers whose roots are all sums and differences of the square roots of the first primes, where is a positive integer. It is given by

(1)

Here is the th prime number, and the product is over all independent choices of signs.

The first few Swinnerton-Dyer polynomials are

			(2)
			(3)
			(4)