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Prime numbers which differ by 6
In
number theory
,
sexy primes
are
prime numbers
that differ from each other by 6. For example, the numbers 5 and 11 are both sexy primes, because both are prime and
11 ? 5 = 6
.
The term "sexy prime" is a
pun
stemming from the
Latin
word for six:
sex
.
If
p
+ 2
or
p
+ 4
(where
p
is the lower prime) is also prime, then the sexy prime is part of a
prime triplet
. In August 2014, the
Polymath
group, seeking the proof of the
twin prime conjecture
, showed that if the
generalized Elliott?Halberstam conjecture
is proven, one can show the existence of infinitely many pairs of consecutive primes that differ by at most 6 and as such they are either
twin
,
cousin
or sexy primes.
[1]
The sexy primes (sequences
OEIS
:
A023201
and
OEIS
:
A046117
in
OEIS
) below 500 are:
- (5,11), (7,13), (11,17), (13,19), (17,23), (23,29), (31,37), (37,43), (41,47), (47,53), (53,59), (61,67), (67,73), (73,79), (83,89), (97,103), (101,107), (103,109), (107,113), (131,137), (151,157), (157,163), (167,173), (173,179), (191,197), (193,199), (223,229), (227,233), (233,239), (251,257), (257,263), (263,269), (271,277), (277,283), (307,313), (311,317), (331,337), (347,353), (353,359), (367,373), (373,379), (383,389), (433,439), (443,449), (457,463), (461,467).
References
[
edit
]
External links
[
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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