Download presentation

Presentation is loading. Please wait.

Published byHenry Potter Modified over 2 years ago

1
By Megan Duke – Muskingum University

2
Prime – a natural number great than 1 that has no positive divisors other than 1 and itself. Quadruplet – a grouping of 4

3
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

4
The smallest prime quadruplet is {5, 7, 11, 13} followed by {11, 13, 17, 19} All prime quadruplets take the form {30n+11, 30n+13, 30n+17, 30n+19} with the exception of the first prime quadruplet. The first few values of n which give prime quadruples are n=0, 3, 6, 27, 49, 62, 69, …

5
The width of a prime quadruplet is 8. 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.

6
Prime quadruplets that take the form {30n+11, 30n+13, 30n+17, 30n+19} are called prime decades. The terms in the prime decade all start with the same number.

7
In 1982 a 45-digit prime quadruplet was discovered by M. A. Penk. 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.

8
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 and Prime Sextuplets which is when both p-4 and p+12 are prime with {p, p+2, p+6, p+8}

9
Are there infinitely many prime quadruplets?

10
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.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://www.javascripter.net/math/primes/qua druplets.htm http://mathworld.wolfram.com/PrimeQuadru plet.html http://mathworld.wolfram.com/PrimeQuadru plet.html http://en.wikipedia.org/wiki/Prime_quadruplet http://en.wikipedia.org/wiki/Prime_quadruplet

Similar presentations

OK

All About Division. Definition / A nonzero integer t is a divisor of an integer s if there is an integer u such that s = tu. / If t is a divisor of s,

All About Division. Definition / A nonzero integer t is a divisor of an integer s if there is an integer u such that s = tu. / If t is a divisor of s,

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Download ppt on conservation of biodiversity Ppt on content development exercises Ppt on modern indian architecture Download ppt on water a precious resource Ppt on magic words Ppt on computer languages to learn Ppt on single point cutting tool nomenclature Ppt on active directory services Download ppt on mind controlled robotic arms manufacturing Ppt on second law of thermodynamics for kids