Facts on prime numbers:

Important facts regarding prime numbers:

1. Negative integers can not be considered as prime numbers.
2. 1 is not a prime. Because no number except 1 divides 1.
3. There exist a positive integer which is both even and prime. (The number 2)
4. The set of all prime numbers does not form a group under usual addition operation because there does not exist any inverse. Under usual addition operation, inverse are the negative numbers.
5. The set of all prime numbers does not form a group under the usual multiplication operation since the fractions are not included in the set.
6. The set of prime numbers is infinite.
7. The properties of the prime number are highly useful in the Public Key Cryptography and The RSA system.
8. The Fundamental Theorem of Arithmetic suggests that prime numbers are the most basic building blocks for the natural numbers.

Statement of The Fundamental Theorem of Arithmetic:

Every natural number n ≥ 2 has a unique factorization

n=p₁^i₁p₂^i₂...p_k^i_k

where the exponents i₁,i₂ ,..,i_k are positive integers and p₁<p₂<...<p_k

are primes.

The theorem can be easily be proved using induction technique. One can find the proof in any standard book on Number theory.

A Game on Prime Numbers:

Consider the following set of prime numbers.

A={ 5, 7, 11, 13, 17, 19, 23}

Put the appropriate elements from the set A to each circle of the below-given figure, such that the summation of elements from each row and each diagonal will be the same prime number.

Answer :

Quizzes on prime numbers:

Which one of the following numbers is not a prime number?

• 2
• -3
• 7
• 13

Answer: -3

1 is a prime number.

• True
• False

Answer: False

Does there exist a number which is both even and prime numbers?

• Yes
• No

Answer: Yes (2 is the only even prime numbers)

The intersection between the set of primes and the set of composite numbers is

• Set of all natural numbers
• Null set
• Set of all integers
• Set of real numbers

Answer: Null set 

The set of all prime numbers is a subset of Natural numbers.

• True
• False

Answer: True

139 is a prime number.

• True
• False

Answer: True