Numbers

Find 4 consecutive prime numbers that add up-to 220.



Answer

if the number is prime it must satisfy the condition 6n + 1 or 6n - 1, where n is any integer greater than two.

Since there are 4 prime numbers, on adding the coefficient of the variable n will always be 24.
The number that are close to 220 and  below it that is divisible by 24 are 192 and 216

So, let us choose the numbers as follows
(6n - 1) + (6n + 1) + (6{n + 1} - 1) + (6{n + 1} + 1) = 220

or  24n + 12 = 220
or 24n = 208
what we observe from this is that getting the value of 216 is impossible, so we will instead try to get the value of 192.

to get the value of 192, we must have the left hand side as
24n + 28 = 220

consider these numbers:
(6n - 1) + (6{n + 1} - 1) + (6{n + 2} - 1) +  (6{n + 2} + 1) = 220

or, 24n + 28 = 220
or n = 292/24 = 8

so the numbers are, 47, 53, 59 and 61