Mathematical Calculators

Prime Number Calculator

This calculator will show you whether a number has a prime number or if it is a composite.

Prime Number Calculator

Factors:

Table of contents

What is a Prime number?
There is a difference between a Prime Number and a Composite Number
Is one the prime number?
Is a prime number possible to be negative?
Why 2 is the only even prime number?
What is the difference between a prime Number and a coprime Number?
What is the largest prime number known?
This prime number calculator will tell you if a particular number is prime or composite. If the number is composite, the calculator will also show all factors.
For any integer less than 10,000,000,000,000, or for any whole number greater than 13 digits, test for a prime.

What is a Prime number?

A prime number can be defined as an integer, or the whole number, that is greater than 1 and not divisible either by 1 or itself. Also, a prime number can only have one factor: 1 and itself.
Prime numbers are positive numbers, non-zero numbers, that have exactly two factors -- not more or less.

Examples:

Is 2 a prime number? 2 is a prime number as it only has one factor, 1 and 2.
Is 17 a prime number? Yes, 17 is a prime number, because it only has 2 factors, 1 & 17.
Is 51 a prime number? 51 is not considered a prime because it contains more than two factors. 51 is a compound number. It can be factored using any of these numbers: 1, 3, 17 51.

There is a difference between a Prime Number and a Composite Number

The Sieve of Eratosthenes

In the third century B.C. The third century B.C. saw the discovery of a simple method to find the prime numbers by Eratosthenes, a Greek mathematician.
Follow these steps to find prime numbers between 1 & 100.
Step 1: Create a hundred charts.
Step 2: Leave 1 because it is not a prime number or a composite number.
Step 3: Encircle 2, and then cross out any multiples, as they are not prime.
Step 4: Circle the next uncrossed figure, which is 3, and cross out any multiples. Do not ignore previously crossed numbers, such as 6, 12, 18, etc.
Step 5: Continue to encircle the next number uncrossed and cross out its multiples until all numbers in the table have been crossed or encircled.

Terms Relating to Prime Numbers

Co-Primes: Two numbers are considered coprime if they share only one factor, which is 1. These numbers do not have to be prime. 9 and 10 for example are co-primes.
You will notice that any pair of prime numbers is always co-primes. Because of the two factors they share, their common factor cannot exceed 1. 
Twin-Primes A pair of prime numbers is known as twin primes if only one composite number exists between them. For example, (3, 5), (5, 7), (11, 13), (17, 19), etc.

List of prime numbers between 1 and 100

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
There are 25 prime numbers that range from 1 to 100.

List of prime numbers between 1 and 200

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.
There are 46 prime numbers that range from 1 to 200.

List of prime numbers between 1 and 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.

Here are some facts about prime numbers

2. is the smallest prime number.
2 is the only prime number that is even.
The only prime numbers that are consecutively 2 and 3 are 2.
A whole number, except for 0 or 1, is either a prime number (or a composite number).
All odd numbers do not count as prime numbers. For example, 21, 39, etc.
A prime number cannot exceed 5 ends in a 5.
One of the earliest methods to find prime numbers is the Sieve of Eratosthenes.
Prime numbers become rarer with increasing numbers.
There is no greatest prime number. As of September 2021, the largest prime number is 282,589.933 - 1. This number has 24,862,048 numbers when written in base 10. It may be larger by the time you finish reading this.

Is one the prime number?

One is not a prime or composite number.

Is a prime number possible to be negative?

Prime numbers can't be negative. Prime numbers are part of the natural number set.

Why 2 is the only even prime number?

Any even number greater than 2 is multiplied by 2. Therefore, 2 is the only prime even number.

What is the difference between a prime Number and a coprime Number?

Prime numbers have exactly two factors: 1 and the prime number. The common factor for co-prime numbers is only 1.

What is the largest prime number known?

As of September 2021, the largest prime number is 282,589.933 - 1. This number has 24,862,048 numbers. It could be larger by the time you finish reading this.

Parmis Kazemi
Article author
Parmis Kazemi
Parmis is a content creator who has a passion for writing and creating new things. She is also highly interested in tech and enjoys learning new things.

Prime Number Calculator English
Published: Fri May 27 2022
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