Prime Numbers From 1 to 1000
What are Prime Numbers?
Math students from Class 1 to Class 12 have to deal with prime numbers in different ways at every stage of their education. They need to know a lot about the Prime numbers to do this. This can be improved right from the start. Here, Utopper has given the students a full guide to prime numbers from 1 to 1000 in order to help them learn more.
Prime numbers are one of the most common and basic topics for students to learn about in the branch of mathematics called number theory. Also, the study of numbers is mostly about learning about how prime numbers work. Most mathematicians have learned a few things about prime numbers over the years.One of the most well-known proofs by Euclid shows that there are an infinite number of prime numbers.
The basic idea behind the proof is that if we only had a finite number of primes and a list of all of them, we could multiply them all together and add 1, making a new number that is not divisible by any of the prime numbers on the list. Either that number is a prime number that is not on our list, or it has a prime divisor that is not on our list. In either case, the idea that there could be a finite list of primes, so there must be an infinite number of primes, is wrong.
What do “prime numbers” mean?
There are exactly two factors for every prime number. Prime numbers are those with factors 1 and the number itself. It is known that the prime number is the simplest number. Let’s look at some prime numbers and a list of all the prime numbers from 1 to 1000.
Take the number 11 as an example. You can write it as 11 x 1 or 1 x 11. There is no other method to write the number 11. So the number 11 has two factors : 1 and 11. So, 11 is a prime number. In a similar way, we can say that the numbers 2, 3, 5, 7, 13, 17, etc. can only be written in two ways with a single factor of 1, so they are prime numbers.
Each prime number can be divided only by 1 and by itself. This means that 1 can never be a prime number. Therefore, any prime number must have only two factors and be greater than 1.
What we know about prime numbers
Eratosthenes was the first person to find the prime number (275-194 B.C.). Eratosthenes used a sieve to explain how to separate the prime numbers from the composite numbers in a list of natural numbers.
Using this strategy, students can practise by writing the positive integers from 1 to 1000 and circling the prime numbers, and putting a cross mark on all the composite numbers
How Prime Numbers Are Used
Prime numbers are useful in a number of ways. Here are some ways that students and professionals can use prime numbers in real life:
- For the benefit of students, it is pointed out that the prime factors of large integers are frequently used in modern computer cryptography.
- The world values prime numbers because their peculiar mathematical features make them ideal for modern applications.
- Students can use prime numbers to figure out answers to everyday math problems like division, solving higher-level concepts, and other important things they learn in the subject.
- Number theorists put a lot of weight on the prime numbers because they are the building blocks of all whole numbers.
Prime numbers have certain traits.
There are some things about prime numbers:
- Every number that is greater than 1 can be split into at least two parts by one or more prime numbers.
- Every even positive number above 2 can be written as the sum of two prime numbers.
- Except for 2, all prime numbers other than 2 are odd. So, we can say that the only even prime number is two.
- Two prime numbers are coprime if they are both prime.
Composite Numbers
Composite numbers have at least one factor other than 1 and the number itself. Here are a few examples.
- Let’s say the number is 10. You can write it as 10 x 1, 1 x 10, 2 x 5 and 5 x 2. So 1, 2, 5 and 10 are all parts of 10. Since 10 has more than 2 parts, we can say that it is a composite number.
- Take the number 8, for example. You can write the number 8 as 8 x 1, 1 x 8, 2 x 4, and 4 x 2. So 1, 2, 4, and 8 are all parts of the number 8. So, we can say that the number 8 is made up of two or more parts.
Prime numbers and composite numbers are two different kinds of numbers
Lets Check –
| Prime Number | Composite Numbers |
|---|---|
| There are only two factors for a prime number. | There are more than two factors to a composite number. |
| it can be divided by either 1 or the number itself. | It is divisible by all of its factors. |
| Example – 2, 3, 7, 11, 109 | Example – 4, 8, 10, 15, 85 |
Here is a list of the 1–1000 prime numbers. On the list of prime numbers from 1 to 1000,
There are a total of 168.
| Numbers | Total Prime Numbers | Prime Number from 1 to 1000 |
|---|---|---|
| 1 to 100 | total 25 prime 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 21 prime numbers | 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199 |
| 201-300 | total 16 prime numbers | 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293 |
| 301-400 | total 16 prime numbers | 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397 |
| 401-500 | total 17 prime numbers | 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499 |
| 501-600 | total 14 prime numbers | 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599 |
| 601-700 | total 16 prime numbers | 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691 |
| 701-800 | total 14 prime numbers | 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797 |
| 801-900 | total 15 prime numbers | 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887 |
| 901-1000 | total 14 prime numbers | 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997 |
