Download 5 Famous Math Conjectures

FAMOUS
CONJECTURES
TOP FIVE
A conjecture is a proposition that is unproven
but appears correct and has not been
disproven. After demostrating the truth of a
conjecture, this came to be considered a
theorem and as such can be used to build
other formal proofs.
5. FOUR COLOR THEOREM
STATEMENT
Given any separation of a plane into
contiguous regions, called a map, the
regions can be colored using at most four
colors so that no two adjacent regions have
the same color. Two regions are called
adjacent if they share a common boundary
that is not a corner, where corners are the
points shared by three or more regions
Example
4. LEGENDRE’S CONJECTURE
Examples
STATEMENT
There is a prime number
between n2 and (n + 1)2 for
every positive integer n.
 n=1
Between 1 and 4 are 2 and 3
 n=2
Between 4 and 9 are 5 and 7
 n=3
Between 9 and 16 are 11 and 13
3. CONJECTURE TWIN PRIME
NUMBERS
Examples
STATEMENT
There are infinitely many
 p=3
and p+2 = 5
primes p such that p+2 is also
 p=5
and p+2 = 7
prime.
 p = 11
and p+2 = 13
 p = 29
and
p+2 = 31
2 . G O L D BA C H ’ S C O N J E C T U R E
STATEMENT
Examples
Every even integer greater
 4 = 2+2
than 2 can be expressed as
 6 = 3+3
the sum of two primes.
 8 = 3+5
 10 = 3+7 = 5+5
1. FERMAT’S LAST THEOREM
Example
STATEMENT
There are no positive integers a,
For n=2
b and c, can satisfy the equation
a=3
an + bn = c n
for any integer
value of n greater than two.
b=4
then
32 + 42 = 52
c=5
« I have discovered a truly marvelous proof that it is
impossible to separate a cube into two cubes, or a fourth
power into two fourth powers, or in general, any power
higher than the second into two like powers. This
margin is too narrow to contain it. »
Pierre de Fermat[, 1637