Statements (26)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
class of prime numbers
|
| gptkbp:defines |
prime numbers that can be written as n^2 + 1 for some integer n
|
| gptkbp:example |
2
101 17 197 257 37 401 5 577 677 |
| https://www.w3.org/2000/01/rdf-schema#label |
Primes of the form n^2 + 1
|
| gptkbp:openProblem |
It is unknown whether there are infinitely many primes of the form n^2 + 1
|
| gptkbp:property |
no known simple formula for generating only primes of this form
for n > 1, n^2 + 1 is always odd n must be even for n^2 + 1 to be even, but only n=1 gives 2 as a prime if n is even and greater than 2, n^2 + 1 is odd and greater than 2 if n is divisible by 3, n^2 + 1 is congruent to 1 mod 3 |
| gptkbp:relatedTo |
Landau's fourth problem
quadratic primes |
| gptkbp:sequence |
OEIS:A002496
|
| gptkbp:studiedBy |
gptkb:Edmund_Landau
|
| gptkbp:studiedIn |
number theory
|
| gptkbp:bfsParent |
gptkb:A002487
|
| gptkbp:bfsLayer |
7
|