By Megan Duke – Muskingum University
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Prime – a natural number great than 1 that
has no positive divisors other than 1 and
itself.
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Quadruplet – a grouping of 4
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a set of four prime numbers in the form
{p, p+2, p+6, p+8}
A representative of the closest possible
grouping of four primes larger than 3
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The smallest prime quadruplet is {5, 7, 11, 13}
followed by {11, 13, 17, 19}
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All prime quadruplets take the form
{30n+11, 30n+13, 30n+17, 30n+19} with the
exception of the first prime quadruplet.
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The first few values of n which give prime
quadruples are n=0, 3, 6, 27, 49, 62, 69, …
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The width of a prime quadruplet is 8.
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Three consecutive odds cannot be a part of a
prime quadruplet since can interval of seven
or less cannot contain more than three odd
numbers unless one of them is a multiple of
three.
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Prime quadruplets that take the form
{30n+11, 30n+13, 30n+17, 30n+19} are called
prime decades.
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The terms in the prime decade all start with
the same number.
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In 1982 a 45-digit prime quadruplet was
discovered by M. A. Penk.
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In 1998, the prime quadruplet with more than
1000 digits was found at the end of an 8 day
search on a computer that used 1400 MHz of
Pentium computer power.
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There are also Prime Quintuplets keeping the
same form {p, p+2, p+6, p+8} as the prime
quadruplets with the addition of p-4 or p+12
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and Prime Sextuplets which is when both p-4
and p+12 are prime with {p, p+2, p+6, p+8}
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Are there infinitely many prime quadruplets?
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http://www.jstor.org/discover/10.2307/3620774
?uid=8366280&uid=3739840&uid=2&uid=3&ui
d=67&uid=62&uid=3739256&uid=8366248&sid
=21102911218451
http://www.javascripter.net/math/primes/qua
druplets.htm
http://mathworld.wolfram.com/PrimeQuadru
plet.html
http://en.wikipedia.org/wiki/Prime_quadruplet