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Prime numbers are fascinating mathematical entities that have intrigued mathematicians for centuries. The definition of Prime Number states that every natural number bigger than 1, is either a prime itself or can be factorized as a product of primes that is unique up to their order. For instance, the number 5 is prime because there are only two ways to write it as a product, 1 5 and 5 1. But since it is the product of two smaller integers (2 x 2), 4, it is composite. In this article, we will delve into the world of prime numbers, understanding what they are, how to identify them, and their importance in various fields.

## Prime Numbers

Prime numbers play an important role in the number system. These numbers are those that are bigger than 1 which simply have two variables: the number itself and factor 1. This indicates that these natural numbers cannot be divided without leaving a remainder by any number other than 1 and the number itself.

## What is Prime Numbers?

Prime numbers are infinitely abundant and form the building blocks of the entire number system. The term “prime number” (or “prime”) refers to a natural number greater than 1 that is not the sum of two smaller natural numbers.

Natural numbers which are greater than 1 that are divisible only by 1 and themselves. They have no other divisors, making them distinct from composite numbers. For example, 2, 3, 5, 7, and 11 are prime numbers, while 4, 6, 8, and 9 are composite numbers. A composite number is a natural number greater than one that is not prime.

## Prime Numbers 1 to 100

An integer is said to be a prime number if it has exactly two positive divisors or factors. 11 is a prime number because it is divisible by 1 and 11 only. While 9 is not a prime number because it is divisible by 1, 3 and 9, which has more than two factors. There are 25 prime numbers between 1 to 100. In order to understand and perform division and factorization problems, one should know all the prime numbers up to 100. One of the easiest methods to find out prime number is the “Sieve of Eratosthenes”. Students can also gain knowledge about prime number with the help of charts, diagrams, and solved practice papers.

## 1 to 100 Prime Numbers List

The number system has a number of primes. The only two factors in prime numbers, as we are well aware, are 1 and the number itself. Following is a list of prime numbers from 1 to 100.

All Prime Numbers 1 to 100 Chart | |

Prime numbers from 1 and 10 | 2, 3, 5, 7 |

Prime numbers from 10 and 20 | 11, 13, 17, 19 |

Prime numbers between 20 and 30 | 23, 29 |

Prime numbers between 30 and 40 | 31, 37 |

Prime numbers between 40 and 50 | 41, 43, 47 |

Prime numbers between 50 and 60 | 53, 59 |

Prime numbers between 60 and 70 | 61, 67 |

Prime numbers between 70 and 80 | 71, 73, 79 |

Prime numbers between 80 and 90 | 83, 89 |

Prime numbers between 90 and 100 | 97 |

## Prime Numbers from 1 to 200

Prime numbers from 1 to 200 List are given below, which we can learn and crosscheck if there are any other factors for them.

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, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199 |

## All Prime Numbers 1 to 1000

Prime Numbers 1 to 1000 are given in the below table. There are a total of 168 prime numbers between 1 to 1000. They are:

Prime Numbers Chart 1 to 1000 |

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, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997. |

## Prime Numbers Identification

Determining whether a given number is prime or composite can be achieved through various methods. One approach is to divide the number by all smaller numbers up to its square root. If no divisors other than 1 and itself are found, the number is prime. However, this method becomes inefficient for larger numbers. Another popular technique is the Sieve of Eratosthenes, which involves iteratively eliminating multiples of prime numbers to identify prime numbers within a given range.

## Prime Numbers Significance

Prime numbers play a crucial role in numerous fields, including cryptography, number theory, and computer science. They form the foundation of encryption algorithms used to secure sensitive information in modern communication systems. Additionally, prime numbers are fundamental in the study of patterns, distribution, and factorization of numbers. They have practical applications in areas such as prime factorization, which is vital for data encryption and decryption.

## Prime Numbers Uses

Prime numbers, with their unique properties and applications, continue to captivate mathematicians and researchers alike. From their role in cryptography to their significance in number theory, prime numbers serve as an essential cornerstone in various domains. Embracing the beauty and intrigue of prime numbers can deepen our understanding of the fascinating world of mathematics.

## History of Prime Number

Since ancient times, prime numbers have piqued people’s interest, and mathematicians are still looking for prime numbers with magical powers. The prime number theorem, proposed by Euclid, states that there are an unlimited number of prime numbers.

Eratosthenes was a famous scientist who devised a clever method for calculating all prime numbers up to a certain quantity. The Eratosthenes Sieve is the name given to this procedure. We’ll build a list of all numbers from 2 to n if you need to locate prime numbers up to n. All multiples of 2 except 2 will be struck from the list starting with the smallest prime number, p = 2. Assign the next value of p, which is a prime number bigger than 2, in the same way.

## Trick to Find Prime Numbers from 1 to 100 Table

To find prime numbers, we apply a method called “Sieve of Eratosthenes” that can easily filter out prime number from composite numbers. Let us learn the steps of finding prime numbers between 1 to 100.

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |

21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |

31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 |

41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 |

51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 |

61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 | 70 |

71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 |

81 | 82 | 83 | 84 | 85 | 86 | 87 | 88 | 89 | 90 |

91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 | 100 |

- Make a table format like shown above.
- Now leave the number 1 as it is because all prime numbers are greater than 1.
- Highlight the number 2 as it is a prime number but leave all the multiples of 2 as it is.
- Next, number 3 and 5 are also prime number; highlight them but leave all of their multiples as it is.
- Lastly, the number 7 is left, keep all the multiple of 7 as it is and finally leftover numbers are prime number as highlighted in the above table.

There are a few tricks to find out prime number. Here are some of them:

- Factorization method: This is the most basic method of finding prime numbers. You can factor a number into its prime factors. If a number has only two factors, 1 and itself, then it is a prime number.
- Sieve of Eratosthenes: This is a more efficient method of finding prime numbers. It works by creating a list of all the numbers from 2 to a given number. Then, you start at the prime number 2 and cross out all the multiples of 2. Then, you move on to the next prime number, 3, and cross out all the multiples of 3 that are not already crossed out. You continue this process until you reach the square root of the given number. Any numbers that are not crossed out are prime numbers.
- Trial division method: This is the simplest method of finding prime numbers. You simply start at 2 and divide the given number by all the numbers from 2 to the square root of the given number. If the given number is divisible by any of these numbers, then it is not a prime number. If it is not divisible by any of these numbers, then it is a prime number.

## How many Prime Numbers between 1 and 100?

There are 25 prime numbers between 1 and 100 are thus 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 73, 79, 83, 89, and 97. Only 1 and the number itself divide each of these numbers. These numbers are hence referred to be prime numbers. These are the first 25 prime numbers, as well.

## Is 1 a Prime Number?

No. We can’t categorise the 1(one) in the prime numbers l1 to 100 List. A number can only be called a prime number if it has two positive elements. Now, the number of positive divisors or factors for 1 is simply one, which is 1. As a result, one is not a prime number.

## What is the Smallest Prime Number?

The smallest prime number is 2. It’s also the only even prime number; all other even numbers, at least 1 and 2, maybe divided by themselves, implying that they’ll have at least three factors.

## What is Primality?

Primality is the attribute of being primary. The Miller–Rabin primality test, which is fast but has a low possibility of error, and the AKS primality test, which always provides the correct result in polynomial time but is too slow to be practical, are two faster algorithms. For a variety of specific forms, such as Mersenne numbers, quick approaches are available. The highest known prime number as of December 2018 is a Mersenne prime with 24,862,048 decimal digits.

As Euclid established circa 300 BC, there exist an endless number of primes. There is no straightforward formula for distinguishing prime numbers from composite numbers. The distribution of primes within natural numbers in the big, on the other hand, can be statistically modelled. The prime number theorem proved towards the end of the nineteenth century, states that the likelihood of a randomly chosen large number being prime is inversely proportional to its number of digits, that is, to its logarithm.

## Properties of Prime Numbers

The following are some of the most essential qualities of prime numbers:

- It is made up of only two factors: 1 and the number itself.
- There is just one prime number that is even, which is 2.
- Any two prime numbers will always be co-prime to one another.
- A prime number is a whole number that is greater than or equal to one.
- The product of prime numbers can be used to express any integer.

## Prime Numbers Things to be Remember

Some Prime Numbers between 1 to 100 key points are given below.

- One and zero are not prime numbers, these are categorized as special or unique numbers.
- 2 is the only even prime number; the rest are odd.
- Divisible by one, and the number itself is a prime number.
- A prime number greater than five and ends with five can be divided by 5, so it cannot be a prime number.

## Prime No Between 1 to 100 Solved Examples

Prime No between 1 to 100 solved examples are given below.

Question 1: Identify the prime numbers from the following list?

17,36,55,79,97

Answer: As per the given list, 17, 79 and 97 are prime numbers. 36 and 55 are composite numbers.

Question 2: Why 25 is not a prime number?

Answer: 1, 5 and 25 are the factors of 25. And since 18 has more than two factors it is not considered a prime number.

Question 3: Find the next four numbers of the following series:

- 67,71, 73…..

- 4, 5, 7…

Answer:

1. It’s a prime number series:

79, 83, 89, and 97 are the next four numbers.

2. In this series each consecutive prime number is added by 2:

2+2=4

3+2=5

5+2=7

So the next four numbers will be 9, 13, 15 and 19.

Question 4: How many prime numbers are between 1 to 100?

Answer: There are 25 prime numbers between 1 to 100.

Question 5: Which of the given ten numbers are prime number; 1,3,10,33,56, 59, 71, 77,89,99 ?

Answer: 3, 59, 71 and 89 are prime numbers as these have only two factors – one and the number itself. We can verify this result from the list of prime numbers between 1 to 100 as shown above.

## Practice Questions based on Prime Number

Here we discussed some Prime Number Between 1 to 100 sample practice questions.

Question 1: Find the average of the last ten prime number?

Question 2: Why is 1 not a prime number?

Question 3: Which is the largest two-digit prime number?

- 97
- 99
- 75
- 84

Question 4: Write the four pairs of prime number less than 20?

Question 5: Is 78 a prime number?