From Wikipedia, the free encyclopedia
In
mathematics
, a
quartan prime
is a
prime number
of the form
x
4
+
y
4
where
x
and
y
are positive
integers
. The
odd
quartan primes are of the form 16
n
+ 1.
For example, 17 is the smallest odd quartan prime: 1
4
+ 2
4
= 1 + 16 = 17.
With the exception of 2 (
x
=
y
= 1), one of
x
and
y
will be odd, and the other will be
even
. If both are odd or even, the resulting integer will be even, and 2 is the only even prime.
The first few quartan primes are
- 2
,
17
,
97
,
257
,
337
,
641
,
881
, … (sequence
A002645
in the
OEIS
).
See also
[
edit
]
References
[
edit
]
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By formula
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By integer sequence
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By property
| |
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Base
-dependent
| |
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Patterns
|
- Twin (
p
,
p
+ 2
)
- Bi-twin chain (
n
± 1, 2
n
± 1, 4
n
± 1, …
)
- Triplet (
p
,
p
+ 2 or
p
+ 4,
p
+ 6
)
- Quadruplet (
p
,
p
+ 2,
p
+ 6,
p
+ 8
)
- k
-tuple
- Cousin (
p
,
p
+ 4
)
- Sexy (
p
,
p
+ 6
)
- Chen
- Sophie Germain/Safe (
p
, 2
p
+ 1
)
- Cunningham (
p
, 2
p
± 1, 4
p
± 3, 8
p
± 7, ...
)
- Arithmetic progression (
p
+
a·n
,
n
= 0, 1, 2, 3, ...
)
- Balanced (
consecutive
p
?
n
,
p
,
p
+
n
)
|
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By size
| |
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Complex numbers
| |
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Composite numbers
| |
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Related topics
| |
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First 60 primes
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