# By Megan Duke – Muskingum University.  Prime – a natural number great than 1 that has no positive divisors other than 1 and itself.  Quadruplet – a.

## Presentation on theme: "By Megan Duke – Muskingum University.  Prime – a natural number great than 1 that has no positive divisors other than 1 and itself.  Quadruplet – a."— Presentation transcript:

By Megan Duke – Muskingum University

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

 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

 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, …

 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.

 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.

 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.

 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}

 Are there infinitely many prime quadruplets?