Question

About prime numbers and their properties for

Answer 1

Step-by-step explanation:

• What is Prime number?

A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole numbers that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. Numbers that have more than two factors are called composite numbers. The number 1 is neither prime nor composite.

• Properties:

1. Numbers of prime numbers are uncountable. i.e., the number of primes is infinite.
2. Every Prime number have exactly two factors or divisors.
3. Number of even primes is ONE.
4. G.C.D of co-prime numbers is always ONE as  5 and 7 are the co-primes .G.C.D of 5 and 7 is 1.
5. The largest known prime is 2^43,112,609 - 1.
6. The General formula for generate the primes ::Formula: N = (2^p - 1) with p equal to the primes 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107 etc.
7. If p is a prime, is 2^p - 1 always square free.
8. The Twin Primes Conjecture that there are infinitely many pairs of primes only 2 apart.
9. The term odd prime refers to any prime number greater than 2.
10. All prime numbers above q are of form q = n + m; Where 0 < m < q and m has no prime factor ≤ q.
11. If p is a prime number and a, b are the integers.If p divides ab ,Then p divides a or p divides b.

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