Almost-primes represented by quadratic polynomials

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Almost prime Pythagorean triples in thin orbits (2010, background): “In this case, the orbit O contains an injection of a‰ne space, and hence standard sieve methods [19] also produce integral points with few prime factors.”
Topologically slice knots of smooth concordance order two (2012, background): “Thus, by Iwaniec’s theorem we have that for an infinite set of positive n, G(n) is either prime or a product of two distinct primes.”