Find the smallest possible sum of six consecutive integers such that none of the integers is prime.
First list primes:
2,3,5,7,11,13,17,19,23,29,31,37,43,47,53... until there is a difference of 8 or more between two consecutive primes. Look for the smallest sum there.
Here is a list of primes up to 199:
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199
Prime numbers less of 200:
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199
You must find where is difference between two prime numbers greater og 6.
First two prime nubers of difference greater og 6 is 89 and 97
So yours six consecutive integers such that none of the integers is prime:
90,91,92,93,94,95
90+91+92+93+94+95=555
To find the smallest possible sum of six consecutive integers such that none of the integers is prime, we need to determine the six consecutive integers that are not prime and sum them up.
We know that prime numbers are numbers that are only divisible by 1 and themselves. Therefore, to identify which numbers are not prime, we need to check if they are divisible by any number other than 1 and themselves.
We can start by selecting the first number. Since we want the smallest possible sum, let's choose the smallest non-prime number, which is 4. The following numbers are consecutive, so we can simply increment the first number to get the remaining values.
So, the six consecutive integers that are not prime would be: 4, 5, 6, 7, 8, 9.
To calculate their sum, we can add them up: 4 + 5 + 6 + 7 + 8 + 9 = 39.
Therefore, the smallest sum of six consecutive integers where none of them is prime is 39.