express the even number from 100 to 300 as the sum of two prime number
Answers
The even numbers from 100 to 300
First number = a1 = 100
Last number = an = 300
Find the number of terms
an = a1 + (n - 1)d
300 = 100 + (n - 1) 2
300 = 100 + 2n - 2
300 = 98 + 2n
2n = 202
n = 101
Find the sum of the 101 numbers:
Sn = n/2 (a1 + an)
s101 = 101/2 (100 + 300)
s101 = 20200
20200 = 17 + 20183
And both 17 and 20183 are prime numbers
Answer: 17 and 20183
Given:
From 100, 102, 104, ..., 300.
To prove:
The even numbers from 100 to 300 as the sum of two prime numbers.
Solution:
Using arithmetic progression,
To find the number of terms,
an = a1 + (n - 1)d
Where,
an = Last term
a1 = First term
n = Number of terms
d = Difference
Here,
a1 = 100
an = 300
d = 2
300 = 100 + ( n - 1 ) 2
300 = 100 + 2n - 2
300 = 98 + 2n
2n = 202
n = 101
The number of terms in the series = 101
To find the sum,
Sn = n/2 ( a1 + an )
Where Sn = Sum
Sum = 101/2 ( 100 + 300 )
Sum = 20200
20200 can be expressed as 17 + 20183
And both 17 and 20183 are prime numbers
Hence, 17 and 20183