1

Desirae,
Danielle R
Lauren
D.

Divisivility rules
Divisibility
rules in base 2,12 and 60.

Divisibility

Program
to test divisibility using the algorithm

2

JingGu
Rondell
Daisuke

Fermat little theorem.

Proof
of Fermat Little Theorem

Program
to compute the multiplicative order of elements of Z/nZ

3

Lauren D,
Nicole M, Carmelina

Twin primes
Twin prime conjectures.
Brun's theorem.

Proof that the sum of the
reciprocal of the primes diverges.

Program
to find twin primes.
Compare
actual results with guessed or conjectured density

4

Michael
C.
Sabil
Deema

Pseudo primes
Carmichel numbers

Prove that there are
infinitely many pseudo primes with base a.

Programs
to test pseudo primes.
Compare
number of primes and number of pseudoprimes

5

Carson
Monica
Jose

There are infinitely many
primes, density, probability that a given number is prime.

Filip Saidak's
Euclid proof
Other proofs of this
result.

Comparison
between estimated and actual density of
primes.

6

Anand
Sean

The Goldbach conjecture,

Patterns in Goldbach curve. 
count
goldbach pairs, do you see any patterns?

7

Ren,
Cristi,
Alaa,
Xixin

Primality tests (Strong
Probable Primes)

Determine
probability that a number satisfies the prime test.

Write
a program for primality test

8

Ceandra,
Misra,
Alexander
M.

Mersenne primes
Fermat primes
Pepin's Test

Let p and q be odd primes. If p divides Mq, then p = 1 (mod q) and p = +/1 (mod 8).

Generate
mersene and fermat primes.
Pepin's test

9

Nicole
C.
Ashley

Fermat last theorem
Sophie Germain prime.

Proof that Let p = 3 (mod 4) be prime. 2p+1 is also prime if and
only if 2p+1 divides Mp.

find
Sophie Germain primes
Examples of the theorem.

10

Ken
Chantilly
Alexander N

The fundamental theorem
of arithmetic
Amicable numbers

Prove
of the result. Examples in other fields.

find
amicable numbers

11

Davanjit, Konstantin

Euclid algorithm

The probability that two
given numbers are relatively prime.

experiment
with the result you proved.





