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# Famous conjectures good

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• 1. Famous conjectures
TOP FIVE
KAREN LOPEZ B.
• 2. 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.
• 3. 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
• 4. 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 9and 16 are 11 and 13
4. LEGENDRE’S CONJECTURE
STATEMENT
Examples
• 5. There are infinitely many primes p such that p+2 is also prime.
3. Conjecture twin prime numbers
STATEMENT
Examples
p = 3 and p+2 = 5
p = 5 and p+2 = 7
p = 11 and p+2 = 13
p = 29 and p+2 = 31
• 6. 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
Examples
STATEMENT
• 7. There aren’t three 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
• 8. « 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