FAMOUS CONJECTURE

S

TOP FIVE

KAREN LOPEZ B.

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.

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.

5. FOUR COLOR THEOREM

STATEMENT Example

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

4. LEGENDRE’S CONJECTURE

STATEMENT

Examples

There are infinitely

many primes p such

that p+2 is also

prime.

p = 3 and p+2 =

5

p = 5 and p+2 =

7

p = 11 and p+2 =

13

p = 29 and p+2 =

31

3. CONJECTURE TWIN PRIME NUMBERS

STATEMENT Examples

Every even integer

greater than 2 can be

expressed as the sum

of two primes.

4 = 2+2

6 = 3+3

8 = 3+5

10 = 3+7 = 5+5

2. GOLDBACH’S CONJECTURE

STATEMENT Examples

No there positive

integers a, b and c, can

satisfy the equation

an + bn = cn for any

integer value of n greater

than two.

For n=2

a=3 b=4 c=5

then

32 + 42 = 52

1. FERMAT’S LAST THEOREM

STATEMENT Example

« 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