Question
three consecutive primes are summed. when the sum is squared, the result is 72,361. what is the largest of the three primes?
Answers
Reiny
(sum of 3 consecutive primes )^2 = 72361
sum of 3 consecutive primes = 269
269/3 = 89
so the middle prime must be around 89
BUT 89 is a prime
http://primes.utm.edu/lists/small/10000.txt
the one before is 83 and the one after is 97
So the largest of these primes is 97
check:
(83+89+97)^
= 269^2
= 72361 , YEAH!
sum of 3 consecutive primes = 269
269/3 = 89
so the middle prime must be around 89
BUT 89 is a prime
http://primes.utm.edu/lists/small/10000.txt
the one before is 83 and the one after is 97
So the largest of these primes is 97
check:
(83+89+97)^
= 269^2
= 72361 , YEAH!