What is the smallest two-digit prime that is the sum of three (not necessarily distinct) positive perfect cubes?
Answers
Answer:
I stand corrected. David’s 216 is it. 729 is the next one.
I did this by a very simple and unsophisticated but mercifully short method:
List a bunch of the smallest cubes and see which ones seem like they might be sum of three of the ones before them.
1, 8, 27, 64, 125, 216, 343, 512, 729 aha!
512 + 216 + 1 = 8^3 + 6^3 + 1^1 = 729
729 is a great number. It is also the smallest number after 64 that is both a perfect cube and a perfect square. Coincidence? (64 is also a square which is the sum of two smaller squares.
Answer:
17
Step-by-step explanation:
We begin by listing the smallest positive perfect cubes with two digits or fewer:
1, 8, 27, 64.
And now we sum them. 1+1+1 is too small; 1+1+8=10 which is not prime; but 1+8+8=17, which is indeed a prime. Hence the answer is 17.