Prime Numbers 1 to 50
There are 15 prime numbers from 1 to 50. Any natural number that is greater than 1 and that is divisible only by 1 and itself can be defined as a prime number. In this article, let us see how to find the prime numbers from 1 to 50 and we will list these numbers.
| 1. | How to Find Prime Numbers From 1 to 50? |
| 2. | List of Prime Numbers From 1 to 50 |
| 3. | FAQs on Prime Numbers 1 to 50 |
How to Find Prime Numbers From 1 to 50?
A prime number has exactly two factors and hence it cannot be broken down further into a product of two natural numbers other than 1 and itself. In order to check if any number 'n' is prime or not, we need to follow 3 conditions. The conditions are as follows:
- Condition 1: n must be a positive Integer.
- Condition 2: n should be divisible by 1.
- Condition 3: n should be divisible by n itself.
In order to find the prime numbers from 1 to 50, we can use the Sieve of Eratosthenes algorithm as this algorithm helps us to list all prime numbers quickly, up to a given number. The Sieve of Eratosthenes algorithm is used as shown in the following steps.
Step 1: Make a table of 5 rows and 10 columns starting with 1 and continuing until 50, as shown below.
| 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 |
Step 2: Circle the smallest number which is 2 in the table. Cross all the multiples of 2 until 50. This will eliminate all the even numbers (which are multiples of 2), and are not prime as they have more than 2 factors.The multiples of 2 that are eliminated from the table are as follows: 4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48, and 50. We start with 2 because the number 1 is not a prime number.
Step 3: Repeat Step 2, circle the next smallest number 3 in the list and cross all the multiples of 3. The multiples of 3 that are eliminated from the table are: 9,15,21,27,33,39, and 45.
Step 4: Repeat Step 2, circle the next smallest number 5 in the list, and cross all the multiples of 5. The multiples of 5 that are eliminated from the table are 25 and 35.
Step 5: Repeat Step 2, circle the next smallest number 7 in the list, and cross all the multiples of 7. In this step, 49 is the only remaining multiple of 7 that is eliminated from the table.
Step 6: In each step, we circle the next smallest number as shown below. The numbers that are left finally after eliminating all the multiples are prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47. None of the prime numbers encircled in this step have any more multiples left, that could be eliminated from the table.
This is how all the prime numbers from 1 to 50 are listed as per the Sieve of Eratosthenes algorithm.
List of Prime Numbers From 1 to 50
Let us look at the list of primes from 1 to 50 and the quantity of each under each range in the table given below:
| Range of prime numbers | Quantity | Prime numbers |
|---|---|---|
| Prime numbers from 1 to 10 | 4 | 2, 3, 5, 7 |
| Prime numbers from 11 to 20 | 4 | 11, 13, 17, 19 |
| Prime numbers from 21 to 30 | 2 | 23, 29 |
| Prime numbers from 31 to 40 | 2 | 31, 37 |
| Prime numbers from 41 to 50 | 3 | 41, 43, and 47 |
Hence, there are a total of 15 prime numbers from 1 to 50 as shown below.
Important Notes
Here is a list of a few points that should be remembered while studying prime numbers from 1 to 50:
- Any natural number greater than 1 that is divisible only by 1 and itself, is defined as a prime number
- A prime number has exactly two factors and hence it cannot be broken down further into a product of two natural numbers other than 1 and itself.
- In order to find the prime numbers from 1 to 50, we can use an algorithm called Sieve of Eratosthenes as this algorithm helps us to list the primes numbers quickly, up to a given number.
- There are 15 prime numbers from 1 to 50. They are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47.
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FAQs on Prime Numbers 1 to 50
How many Prime Numbers are there between 1 and 50?
There are a total of 15 prime numbers between 1 to 50. A prime number has exactly two factors and hence it cannot be broken down further into a product of two natural numbers other than 1 and itself.
What are the Prime Numbers from 1 to 50?
The list of prime numbers from 1 to 50 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47.
What is the Probability to Choose One prime Number from 1 to 50?
In order to find the probability of choosing one prime number from 1 to 50, we need to first list the prime numbers from 1 to 50 and then find their total. The list of prime numbers that are less than 50 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47. We can see that there are 15 prime numbers less than or equal to 50. Thus the probability of randomly choosing one prime number from 1 to 50 is 15/50 = 3/10 = 0.3.
What are the Even Prime Numbers from 1 to 50?
The prime numbers from 1 to 50 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47. The only even number that is a prime number between 1 to 50 is 2. Here, 2 is a prime number since it has only two factors 1 and 2.
What is the Sum of Odd Prime Numbers Between 1 to 50?
In order to find the sum of the odd prime numbers from 1 to 50, we need to first list the odd prime numbers from 1 to 50 and then add all of them to find their sum. The list of odd numbers that are prime number from 1 to 50 are 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47. On adding all the odd prime numbers, we get, 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 = 326. So, the sum of all the odd prime numbers from 1 to 50 is 326.
How many Twin prime Numbers are there Between 1 to 50?
There are 6 pairs of twin prime numbers between 1 and 50. They can be listed as follows: (3,5), (5,7), (11,13), (17,19), (29,31), (41,43). Twin prime numbers are the set of those prime numbers that have exactly 1 composite number between them.