SLD
Contributor
OK I was reading up a bit on Taxicab numbers which were created by Srinavasa Ramanujan. They should be called Ramanujan numbers, IMHO. But I was trying to think of other types of unique numbers for no good reason other than my quest for mathematical immortality- which is probably unlikely given that I am nowhere near the level of Ramanujan.
Nevertheless I decided to try and see what happens if you take primes, cube them and add them together. The first such number would be 16, ignoring 1 as a prime. That set doesn’t seem particularly interesting. Then I thought what if we always had to have three such numbers, the first then being 16. Still not interesting. Well, I could be wrong.
Then I decided that they must be three consecutive primes so the first would be 2 cubed plus 3 cubed plus 5 cubed, or 160. I kept going:
160
495
1799
3871
8441
Then I thought I wonder if any of these are primes. Nope. None are. Is that true for all? I plowed onwards:
13969
23939
43415
66347
Finally a prime number!
Therefore I have decided that henceforth, any number that is the sum of three consecutive primes that are each cubed that is also a prime number is a S number.
What’s the next S number?
Nevertheless I decided to try and see what happens if you take primes, cube them and add them together. The first such number would be 16, ignoring 1 as a prime. That set doesn’t seem particularly interesting. Then I thought what if we always had to have three such numbers, the first then being 16. Still not interesting. Well, I could be wrong.
Then I decided that they must be three consecutive primes so the first would be 2 cubed plus 3 cubed plus 5 cubed, or 160. I kept going:
160
495
1799
3871
8441
Then I thought I wonder if any of these are primes. Nope. None are. Is that true for all? I plowed onwards:
13969
23939
43415
66347
Finally a prime number!
Therefore I have decided that henceforth, any number that is the sum of three consecutive primes that are each cubed that is also a prime number is a S number.
What’s the next S number?