Question

what is a conjecture and give a example

Answer 1

A conjecture is a statement that is considered likely to be true, but has no formal proof. An example would be the Goldbach Conjecture, which says that every even integer greater than 2 can be written as the sum of two primes. For example, 78=19+5978=19+59.

There's also the Twin Prime Conjecture. Notice that there seem to be a lot of pairs of primes that differ by 2, like 17 and 19, 41 and 43, and 59 and 61. The Twin Prime Conjecture says that there are infinitely many such pairs of primes.

Neither of these statements has a formal proof yet, and certainly not for lack of trying. But they really seem like they ought to hold, so we keep searching.
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