Teorema de Friedlander–Iwaniec

Em Teoria analítica dos números, o teorema de Friedlander–Iwaniec[1], chamado por vezes de Teorema de Bombieri-Friedlander-Iwaniec, afirma que existem muitos números primos da forma . Os primeiros números primos desta sequência são:

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, … (sequência A028916 na OEIS)

Este teorema foi provado em 1997 por John Friedlander e Henryk Iwaniec,[2] usando técnicas de teoria dos crivos primeiro desenvolvidas por Enrico Bombieri. Iwaniec recebeu em 2001 o Prêmio Ostrowski em parte, pelas suas contribuições neste trabalho.[3]

Este resultado, contudo, não implica haver um número infinito de primos da forma , ou

2, 5, 17, 37, 101, 197, 257, 401, 577, 677, 1297, 1601, 2917, 3137, 4357, 5477, 7057, 8101, 8837, 12101, 13457, 14401, 15377, … (sequência A002496 na OEIS)

sendo este último um problema não-resolvido.

Referências

  1. ↑ van Golstein Brouwers, G.; Bamberg, D.; Cairns, J. (2004), «Totally Goldbach numbers and related conjectures» (PDF), Australian Mathematical Society Gazette, 31 (4): 251–255 [p. 254] .
  2. ↑ Friedlander, John; Iwaniec, Henryk (1997), «Using a parity-sensitive sieve to count prime values of a polynomial», PNAS, 94 (4): 1054–1058, PMC 19742Acessível livremente, PMID 11038598, doi:10.1073/pnas.94.4.1054 .
  3. ↑ "Iwaniec, Sarnak, and Taylor Receive Ostrowski Prize"

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