Friedlander–Iwaniec theorem
friedlander_iwaniec
Submitter: Bolton Bailey/Project Numina.
Notes: The Friedlander–Iwaniec theorem: there are infinitely many primes of the form `a² + b⁴`.
Source: Friedlander, John, and Henryk Iwaniec. “The Polynomial X² + Y⁴ Captures Its Primes.” Annals of Mathematics, vol. 148, no. 3, 1998, pp. 945–1040. JSTOR, https://doi.org/10.2307/121034.
Informal solution: Friedlander and Iwaniec develop a sieve for primes that, unlike classical sieves, can detect primes in a sequence as thin as `a² + b⁴`. The crux is establishing sum-estimates for a bilinear form involving a Möbius-function-like term and a term for counting representations of a number of the `a² + b⁴` form.
theorem declaration uses `sorry`friedlander_iwaniec : {p : ℕ | p.Prime ∧ ∃ a b, p = a ^ 2 + b ^ 4}.Infinite := ⊢ {p | Nat.Prime p ∧ ∃ a b, p = a ^ 2 + b ^ 4}.Infinite
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