A prime number is a whole number greater than 1 that is only divisible by 1 and itself. A composite number is one that has divisors other than 1 and itself. The document then explains that prime numbers follow a pattern of being multiples of 6 plus or minus 1 (6n±1), and provides a two-step process for determining if a number is prime or composite: 1) check if it is a multiple of 6 plus or minus 1, and 2) check if it is divisible by any numbers up to its square root.

1. Prime Number

2. A prime number is a natural number greater than 1 that has
no positive divisors other than 1 and itself.
A natural number greater than 1 that is not a prime number is
called a composite number.
For example, 5 is prime because 1 and 5 are its only positive
integer factors, whereas 6 is composite because it has the
divisors 2 and 3 in addition to 1 and 6.

3. PATTERN IN PRIME NUMBERS

4. After discarding
multiples of 2, 3, 5, 7
Observation:
All primes (above 3)
are multiples of 6
plus 1 or 6 minus 1
(6n ± 1, where n = 1,
2, 3, ...).
This is the necessary
condition to be a
prime number but not
sufficient.

5. How to identify PRIME NUMBER

6. To identify whether a number (more than 3) is prime or not,
we have to check 2 steps.
Step 1: Check whether the number (is “multiples of 6 plus 1
or 6 minus 1”.
If the number is “multiples of 6 plus 1 or 6 minus 1” then go
to step 2 else it is not a prime number.
Step 2: Check whether the number is not divisible by any
number up to the square roots of that number. If the square
root of the number is not a whole number, round up to the
nearest whole number and test up to this number.
If the number satisfy the condition in step 2, then it is a prime
number else not a prime number.

7. Thanks
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