If I tell you that the sum of three consecutive prime numbers is $173$, how quickly could we find the biggest of these numbers?
[Math] Sum of three consecutive prime numbers is $173$
number theoryprime numbers
number theoryprime numbers
If I tell you that the sum of three consecutive prime numbers is $173$, how quickly could we find the biggest of these numbers?
Best Answer
As quickly as I can add up the first few primes in trios to look them up in the OEIS to get the appropriate result. I searched for
10, 15, 23, 31, 41, which gave me http://oeis.org/A034961 sequence entry for sums of three consecutive primes.Then I clicked on the "list" link and I spotted 173 to the right of 16. This means that the 16th, 17th, 18th primes add up to 173. The 16th prime is 53, so then I verify that 53 + 59 + 61 = 173, which means that the biggest of these numbers is 61.
If there was no OEIS, this could still be done fairly quickly, since 173 is really quite a small number. 173 divided by 3 is approximately 57.7, and since, again, 173 is a small number, the three primes we're looking for should be fairly close to 57.7.
The largest prime below 57.7 is 53, and the smallest prime above is 59, so we can start by trying 47 + 53 + 59 and 53 + 59 + 61; the former falls short, the latter is the answer. If you've got the primes from 2 to 97 and have a calculator, you can probably get the answer by this method in a couple of minutes, if that.