Prime Numbers


Prime Number
A natural number different from 1 that does not have any divisor other than 1 and .

Composite number
A natural number that is neither 1 nor a prime number.
A composite number can be decomposed as a unique product of prime numbers.

The powers of the prime factors of are:

(satisfying )

Twin prime numbers (unsolved)
There are infinite combinations such as

of prime numbers that differ by 2.

Goldbach's conjecture (unsolved)
Every even number greater than 2 can be expressed as a sum of 2 prime numbers.

Distribution of prime numbers
Definition
number of prime numbers that do not exceed
Properties
If is sufficiently large,then

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