MPhil research


u3001114 - Posted on 10 September 2012

Project Description: 

The famous twin-prime conjecture asserts that there are infinitely many prime number pairs of the form {n, n+2}, e.g.
{5, 7}, {11, 13}, {17, 19} etc. So far it is neither proved nor disproved.

This has been generalized to 3-tuple, namely we conjecture that {n, n+2, n+6} can be a prime triple for infinitely many n. e.g {5, 7, 11}, {11, 13, 17} etc. This is also neither proved nor disproved.

To make the problem easier, one relaxes the requirement from being primes to being almost primes. That is, instead of requiring the tuples to be primes, one seeks for showing that they are only composed by a few no. of prime factors.

This makes use of sieve theory in Mathematics.

Research Project Details
Project Duration: 
09/2012 to 10/2012
Project Significance: 
The numerical result will provide information about the prime triple problem.
Remarks: 
The sieve method I use involved summation of a large amount of terms in alternating signs (i.e +/-). HPC certainly helps a lot when doing the computation.