These are some famous conjectures, some of which have yet to be proved or disproved! Exp...

These are some famous conjectures, some of which have yet to be proved or disproved! Explore these conjectures with a partner. Then explain why you think the conjecture is true.

a. Any prime greater than 3 is within 1 unit of a multiple of 6.

b. Every even number can be expressed as the difference of two primes.

c. This conjecture comes from Fermat: Any prime number of the form p=4n+1, can be expressed as the sum of two squares in only one way.

d. This conjecture is called Goldbach’s conjecture after Christian Goldbach (1690–1764): Any even number greater than 2 can be expressed as the sum of two primes. To this day, no one has either found a counterexample or proved this conjecture.

e. Another conjecture made by Goldbach: Any odd number greater than 5 can be expressed as the sum of three prime numbers.

f. Every triangular number can be represented as the sum of a square number and two triangular numbers.