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A Pinch of History

Eratosthenes: In ancient Greece (modern Libiya), a poet, astronomer and mathematician was born
in 276 BCE. His name was Eratosthenes. He was the first person to calculate the circumference of the
Earth. His calculation was remarkably accurate with an error margin of less than 1%. In Mathematics,
he is said to have discovered the rule of Sieve to find the Primes between two given numbers.
Method of Sieve

Let us see how this method works.
Step 1: Take a square grid paper and write numbers
from 1 to 100 on it. 1 2 3 4 5 6 7 8 9 10

Step 2: Shade the box of 1 as it is a unique number. 11 12 13 14 15 16 17 18 19 20

Step 3: Encircle 2 and cross out all its multiples. 21 22 23 24 25 26 27 28 29 30
Step 4: Encircle the next uncrossed number, i.e., 3 and 31 32 33 34 35 36 37 38 39 40
cross out all its multiples. 41 42 43 44 45 46 47 48 49 50
Step 5: Encircle the next uncrossed number, i.e., 5 and 51 52 53 54 55 56 57 58 59 60
cross out all its multiples.
61 62 63 64 65 66 67 68 69 70
Step 6: Encircle the next uncrossed number, i.e., 7 and
cross out all its multiples. 71 72 73 74 75 76 77 78 79 80

Step 7: Continue this process till all the numbers in 81 82 83 84 85 86 87 88 89 90
the grid except 1 are either encircled or crossed out. 91 92 93 94 95 96 97 98 99 100
All the encircled numbers are prime numbers and all
the crossed-out numbers are composite numbers.

• List the prime numbers: .........................................................................
There are .................... prime numbers between 1 and
100. Knowledge Desk

• List the composite numbers: ............................................ The largest known prime number
............................. so far is of 2,862,048 digits which
There are .................... composite numbers from 1 to 100. was found in the year 2018 using

• Find seven consecutive composite numbers in the grid a computer and it was volunteered
such that there is no prime number between them. by Patrick Laroche.
.........................................................................
Example 6: Write all prime numbers lying between 50 and 90.

Solution: From the Sieve of Eratosthenes, we see the prime numbers lying between 50 and 90 are:
53, 59, 61, 67, 71, 73, 79, 83 and 89.
Example 7: Write five pairs of prime numbers less than
20 whose sum is divisible by 5. Quick Check

Solution: Prime numbers less than 20 are 2, 3, 5, 7, 11, 13, Can you find few more prime pairs
17 and 19. whose sum is a multiple of 5?

147 Prime Time