1 / 10

PRIME QUADRUPLETS Mathematics Number Theory

By Megan Duke – Muskingum University. PRIME QUADRUPLETS Mathematics Number Theory. Review . Prime – a natural number great than 1 that has no positive divisors other than 1 and itself. Quadruplet – a grouping of 4. What is a prime quadruplet?.

tender
Download Presentation

PRIME QUADRUPLETS Mathematics Number Theory

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. By Megan Duke – Muskingum University PRIME QUADRUPLETS MathematicsNumber Theory

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

  3. What is a prime quadruplet? • 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. Examples • 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. Properties • 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. Properties • 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. Some History • 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. Other Prime groups • 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. Big Picture Question • Are there infinitely many prime quadruplets?

  10. References • http://www.jstor.org/discover/10.2307/3620774?uid=8366280&uid=3739840&uid=2&uid=3&uid=67&uid=62&uid=3739256&uid=8366248&sid=21102911218451 • http://www.javascripter.net/math/primes/quadruplets.htm • http://mathworld.wolfram.com/PrimeQuadruplet.html • http://en.wikipedia.org/wiki/Prime_quadruplet

More Related