Team Number: 047
School Name: Magdalena High School
Area of Science: Computer Science
Project Title: Twin Prime
Problem Definition:
Primes have been studied by thousands of years by mathematicians around
the world. Euclid Proved that there are infinitely many primes, and
Eratosthenes, another ancient Greek, developed a method of finding all
primes called the Sieve of Eratosthenes.
Twin primes are two consecutive odd numbers that are both prime. It is
believed that there are infinitely many pairs of twin primes, starting
with 3,5 and 5,7. Mathematicians are continually searching for larger and
larger twin primes and study the distance between pairs. We do know that
the sum of the inverses of twin primes is limited, though the sum of the
inverses of primes has been proven to grow without bound. There is a
hypothesis that the sum of the inverses of twin primes is equal to the
number Brun’s Constant, named after
the author of hypothesis.
Mathematicians and computer scientists have found 8494836459690 twin
primes to date, the largest one being 3180323612107001±1 which consists of
32220 digits, and was found by Underbakke, Carmody, and PrimeForm in
2001.
Problem Solution:
The goal of out project is to continue that search by creating a program
that will search for twin primes on multiple processors in a given
interval. The output from this search will be sent to the screen and to
file, and while running our program will increment to the next interval
when a twin primes is found in the current interval. Therefore the
program will search for the next largest known twin primes.
Progress to Date:
At this time, we have developed a program that will find twin primes in a
given interval. We start by finding an array of base primes, which will
consist of the primes up to 65535, found using the Sieve of Eratosthenes.
Then we use this array of base primes to sieve through an array containing
all numbers in the given interval. After finding all multiples of the
base primes in the search interval, the remaining numbers are send to
function called Fermat. In this function, the program uses the Fermat
method of factorization to attempt to find factors, which would eliminate
the possibility of primality. Then all the numbers remaining are prime.
We then search through the primes to find twins. When the twin primes
have been found, they are printed to a screen and will be printed to a
file. We are now beginning to incorporate the GMP library to use with
storing and manipulating large integers and afterwards will integrate MPI
commands in our program so that it can be run on multiple processors.
Expected Resulted:
We expect to find very large twin primes in intervals of huge numbers. We
are attempting to find the largest known pair of twin primes. Our program
will start at a given interval, and move on to the next interval when a
set of twin primes is found in order to search for the next highest pair.
Therefore our program will find the next largest known set of twin
primes.
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