Prime numbers can only be divided by themselves and one, hence dividing them by another integer does not result in a whole number. As a result, dividing the number by anything other than one or itself yields a non-zero remainder.

**What Is the Total Number of Prime Numbers?**

Eratosthenes, a Greek mathematician from the third century B.C. devised a method for quickly calculating all prime numbers up to a particular quantity. Hence, this method was named the Eratosthenes Sieve.

There are 25 prime numbers in the range of 1 to 100. What is the total number of prime numbers? We’ve known since ancient times that there are an endless number of them. Thus, listing them all is impossible. Because Euclid, the first to demonstrate the existence of an infinite number in the fourth century B.C., did not understand the concept of infinity, he stated that “prime numbers are more than any fixed multitude of them,” implying that if you imagine 100, there are more. If you suspect one million, there are still more.

**How Many Prime Numbers are There Between 1 and 1000**

Let’s try to find **how many prime numbers are there between 1 and 1000**

- Find prime numbers until 100

We’ll make a list of all of the prime numbers in the range of 1 to 100.

Let’s start with number two. Although 2 is a prime number, all multiples of two are composite numbers since they are divisible by two. As a result, we cross off all the multiples of two on the table.

We can cross off multiples of 3 because they will be composite numbers. After all, the next prime number is 3.

After 3, the next prime number is 5; therefore, we eliminate all multiples of 5.

Then there’s the prime number 7 and its multiples, which we cross off the list.

Because the following prime number is 11, all multiples of 11 must be eliminated: 22, 33, 44, 55, 66, 77, 88, and 99. Since we’ve already crossed out all of these numbers, we’ve finished crossing out all of the composite numbers on our table.

This is a list of prime numbers ranging from 1 to 100. You don’t have to memorize them, but remember that lower numbers, such as 2, 3, 5, 7, 11, 13, are preferable.

Prime Numbers 1 to 100 are as follows: 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 (total 25 prime numbers)

**How many prime numbers are there**between 100 and 1,000?

Let’s look at **all the prime numbers** from 100 to 1,000 now.

- 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199 are prime numbers (total 21 prime numbers)
- 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293 are prime numbers (total 16 prime numbers)
- 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397; 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397; 359, 367, 373, 379, 383, 389, 397; 3 (total 16 prime numbers)
- 401, 409, 419, 421, 431, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499 are prime numbers (total 17 prime numbers)
- 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599 are prime numbers (total 14 prime numbers)
- 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691 are prime numbers (total 16 prime numbers)
- 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 799, 7 (total 14 prime numbers)
- Prime Numbers 801⎼900: 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887 (total 15 prime numbers)
- 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997; Prime Numbers 901⎼1000 (total 14 prime numbers)

So, **how many prime numbers are there between 1 and 1000?**

In total, there are 168 prime numbers.

Let’s cross-check the (any two) **prime numbers between 1 and 1000** given above by removing the number’s possible factors.

We can consider the following scenario:

599 = 1 × 599

929 = 1 × 929

The above numbers have only two factors: one and self, with no other conceivable factors, indicating that they are prime numbers. For example, examine the graph below, which displays prime numbers ranging from **1 to 1000**.

**How can we identify Prime Numbers?**

Let’s try to identify** all the prime numbers **after** **finding **how many prime numbers there are between 1 and 1000**,

The prime numbers formula can be used to generate prime numbers or determine whether or not a given integer is prime.

- Formula 1: A prime number greater than three can be expressed as 6n±1

Prime number ≡ ± 1 (mod 6)

Numbers that are multiples of prime numbers are excluded from this approach.

- Formula 2: To obtain prime integers bigger than 40, use the following formula:

n2 + n + 41

**Testing the formula**

**Formula 1:**6n±1 (where n is a natural number greater than three)

Divide 541 by 6 to see if it’s a prime number. One is the remainder. 541 is prime because its representation is 6(90) +1.

**Formula 2:**n2 + n + 41, where n = 0, 1, 2,…., 39

Give values between 0 and 39 to n to obtain a random prime number. Let’s use the number 5 as n.

52 + 5 + 41 = 71 is the result.

The number 71 is considered prime.

**The Rules for Prime Numbers**

A few key points to remember when working with prime numbers and related formulas are listed below.

- Even numbers in the place of any integer in the unit cannot be a prime number.
- The number 2 is the only prime number that is even.
- If the sum of all the digits in a huge integer is divisible by three, it is not a prime number.
- Except for 2 and 3, all other numbers can be written using the formula of prime numbers 6n 1, where n is a natural integer.

**What Is the Importance of Prime Numbers?**

They are the foundation of arithmetic and are important in mathematics and nature.

They are critical in arithmetic because any number is composed of a series of these numbers that combine to produce a unique product.

They’ve been studied since our forefathers etched a set of prime numbers on the Ishango bone over 20,000 years ago (11, 13, 17, and 19). It has been established that the ancient Egyptians collaborated with them over 4,000 years ago. Furthermore, they are well known in nature, and certain species have been able to recognize and utilize them throughout their evolution.

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