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.
Facts
StatementThere are infinitely many prime numbers of the form a squared plus b to the fourth power. 1 Classification
Statement Form Connections
Has Statement Form
In Branch
Source Friedlander-Iwaniec theorem (Wikipedia)
Principal Result Of
Source John Friedlander (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 SourceJohn Friedlander (Wikipedia)
Principal Result Of: John Friedlander, Lead, 1997 resultQuote, Principal Result Of: John Friedlander, Lead, 1997 result
Friedlander proved that infinitely many prime numbers can be obtained as the sum of a square and fourth power
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