The prime number is the simplest kind of number. Each prime number is divisible by precisely two factors. Prime numbers are those that have just 2 factors, 1 and the number itself.
Read on for prime number instances and the whole list of prime numbers from 1 to 1000
What is a Prime number?
The numbers which have only two factors – 1 and the number itself are known as Prime numbers.
Consider the number 3. It is also possible to write 3 x 1 and 1 x 3. There is no other way to write the number 3 but with a capital letter. As a result, the components of 3 are 1 and 3. Thus, 3 is a prime number. Similarly, we may claim that the numbers 2, 5, 7, 13, 17,… etc. can only be expressed in two ways with a single component equal to 1, and so are prime numbers.
Examples of Prime numbers are 2,3,5,7,11,19, etc.
What Are Composite Numbers?
The non-prime numbers are called composite numbers
- Let us take a number, say 6. It can be written as 6 × 1, 1 × 6, and 2 × 3, So the factors of 6 are 1, 2, 3, and 6. Therefore, we can say that 6 is a composite number as it has only 2 factors.
- Now, let us take a number, say 6, that can be written as 6 × 1, 1 × 6, 2 × 3, and 3 × 2. So, the factors of number 6 are 1, 2, 3, and 6. Therefore, we can say that number 6 is a composite number.
- Let us take a number, say 8. The number 8 can be written as 8 × 1, 1 × 8, 2 × 4, and 4 × 2. So the factors of 8 are 1, 2, 4, as well as 8. Therefore, we can say that the number 8 is a composite number.
History of Prime Numbers
Prime numbers have created a sense of curiosity for humanity since the ancient period. Mathematicians have researched for a long to find prime numbers with mystical properties. Euclid proposed the theorem on prime numbers – infinite numbers of prime numbers are there.
All the prime numbers within 100 are divisible by the smaller numbers. Eratosthenes was one of the most outstanding scientists who created a smart way to determine all the prime numbers up to a given number. This method is known as the Sieve of Eratosthenes. If you want to count the prime numbers up to n, we will generate the list of all numbers from 2 to n. Starting from the smallest prime number p = 2, we will strike off all the multiples of 2, except 2 from the list. On a similar basis, the p has the value of the prime number that is greater than 2.
Properties of Prime Numbers
Important properties of prime numbers are mentioned below:
- There is only one even prime number- 2.
- Any two prime numbers are always coprime to each other.
- A prime number is a whole number that has a value greater than 1.
- Every number can be expressed as the product of prime numbers.
- It has two factors – 1 and the number itself.
How Many Types of Prime Numbers Are There?
Eratosthenes, a Greek mathematician, devised a method for quickly and intelligently calculating the prime numbers up to any given quantity. This is referred to as the Eratosthenes Sieve.
Between 1 and 100, there are 25 prime numbers. What is the total amount of prime numbers? Since ancient times, we have known that there is an unlimited number, so it is impossible to name them all. Due to the fact that Euclid, who demonstrated the existence of an infinite amount in the fourth century B.C., was unfamiliar with the concept of infinity, he stated that “prime numbers are more than any fixed multitude of them,” which means that if you imagine 100 prime numbers, there are more. If you imagine one million, there are still more.
- Twin Primes :
Two consecutive prime numbers having only one number between them are called twin primes. Examples are 5 and 7, 3 and 7, and 11 and 13 are a set of twin primes.
- Co-prime numbers :
A set of numbers that don’t have any other common factor other than 1 are known as co-prime numbers.
When two numbers have only 1 common factor, they are known as co-primes. For example, 4 and 5, 2 and 3, 3 and 7, 4 and 9 are co-primes.
Factors of 7 are 1 and 7. 7 have no common factor other than 1. So, this is a co-prime number.
Properties of co-prime numbers:
- All prime numbers are co-prime to each other.
- All consecutive whole numbers are always co-primed.
- Co-prime numbers need not be prime numbers.
- The Sum of any two co-prime numbers is always co-primed.
List of Prime Numbers from 1 to 1000
| Numbers | Number of Prime Numbers | List of Prime Numbers From 1 to 1000 |
| 1 to 100 | Total of 25 numbers | 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 |
| 101-200 | Total of 21 numbers | 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199 |
| 201-300 | 16 numbers | 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293 |
| 301-400 | 16 numbers | 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397 |
| 401-500 | 17 numbers | 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499 |
| 501-600 | 14 numbers | 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599 |
| 601-700 | 16 numbers | 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691 |
| 701-800 | 14 numbers | 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797 |
| 801-900 | 15 numbers | 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887 |
| 901-1000 | 14 numbers | 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997 |
| Totalnumber of prime numbers that existed from 1 to 1000 is equal to 168 | ||
Difference Between Prime Numbers and Composite Numbers
| Prime Numbers | Composite
Numbers |
| A prime number has only 2 factors. | A composite number generally has more than two factors. |
| It can be divided by 1 and by the number itself. For example, number 3 is divisible by 1 and 3. | It can be divided by all its factors. For example, number 4 is divisible by 2,4 and 1. |
| Examples:
3, 7, 113, 181, 191, etc. |
Examples:
15, 25, 85, 114, 184, etc. |
What do we mean when we say that prime numbers are the key to arithmetic?
They have been researched for almost 20,000 years when our ancestors scribbled a sequence of prime numbers (11, 13, 17, and 19) on the Ishango bone. As if this were a coincidence, the ancient Egyptians collaborated with them 4,000 years ago. Additionally, nature is intimately familiar with them, and some species have uncovered and exploited them throughout their history.
We are referring to various species of cicadas, including the North American Magicicada septendecim. This cicada species started its mating cycle between 13 and 17, not 12, 14, 15, 16, or 18 – precisely 13 or 17. This enables them to escape predators with similar reproductive cycles; for example, consider a predator with a four-year reproductive cycle.
If a cicada’s life cycle is 12 or 14 years, it will encounter a predator far more often than if it is 13 or 17 years. They occur exactly twice every 100 years when they would otherwise coincide in 11 cycles, jeopardising the species’ growth.
Conclusion :
Prime numbers are undoubtedly significant in our everyday lives and in solving routine arithmetic problems and sums. Additionally, it has simplified and facilitated the computation of complex sums. Most importantly, the prime numbers now serve as a foundation for the Number System, one of the branches and the most fundamental discipline of Mathematics; without which, futile efforts to perform simple calculations would have occurred occasionally
