Bombieri–Friedlander–Iwaniec theorem

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In analytic number theory, an advanced branch of mathematics, the Bombieri–Friedlander–Iwaniec theorem^[1] asserts that there are infinitely many prime numbers of the form a² + b⁴. The first few such primes are

2, 5, 17, 37, 41, 97, 101, 137, 181, 197, 241, 257, 277, 281, 337, 401, 457, 577, 617, 641, 661, 677, 757, 769, 821, 857, 881, 977, … (sequence A028916 in OEIS).

The theorem was proved in 1997 by John Friedlander and Henryk Iwaniec, using sieve techniques first developed by Enrico Bombieri.

Iwaniec was awarded the 2001 Ostrowski Prize in part for his contributions to this work.^[2]

[edit] References

1. ^ G. van Golstein Brouwers, D. Bamberg, J. Cairns, "Totally Goldbach numbers and related conjectures". Australian Mathematical Society Gazette. Vol 31(4) (2004), p. 254.
2. ^ "Iwaniec, Sarnak, and Taylor Receive Ostrowski Prize"

[edit] External links

• Iwaniec and Friedlander's paper about the parity-sensitive asymptotic sieve
• "Sieving Prime Numbers From Thin Ore". Barry Cipra, Science magazine. Vol. 279. no. 5347, p. 31.