Mathematics Atlas

How Proof Is Made
Sign In
Text size
100%
Theme
Theorem

Friedlander-Iwaniec Theorem

Number Theory

The Friedlander-Iwaniec theorem is a result in analytic number theory stating that there are infinitely many prime numbers expressible in the form a squared plus b to the fourth power, for integers a and b. The first several such primes are 2, 5, 17, 37, 41, 97, 101, 137, 181 and 197. The difficulty of the result lies in the sparseness of numbers of this form: the count of integers of this form below a bound X grows only on the order of X to the three-quarters power, far slower than the integers overall. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/

Facts
Statement
There are infinitely many prime numbers of the form a squared plus b to the fourth power. 1
Proof Year
1997 1
Classification
Statement Form
Existence Theorem 1
Connections

Has Statement Form

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

In Branch

Source Friedlander-Iwaniec theorem (Wikipedia)
Sources
1. Friedlander-Iwaniec theorem (Wikipedia)
  • Introduction
    there are infinitely many prime numbers of the form
  • History
    The theorem was proved in 1997 by John Friedlander and Henryk Iwaniec
  • In Branch: Analytic Number Theory, Lead sentence
View the Source
Comments (0)
No comments yet. Be the first to share a thought.
Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.