1. ## Positive Cube

What is the sum of three smallest prime numbers each of which is two more than a perfect positive cube?

2. Hello, Rimas!

What is the sum of three smallest prime numbers each of which
is two more than a perfect positive cube?
What have you tried?

If you examine the first few cubes, you'll trip over the answer . . .

3. Originally Posted by Rimas
What is the sum of three smallest prime numbers each of which is two more than a perfect positive cube?
Clumsy fingers and being abducted by aliens resulted in my not posting this when I thought I has so here it is again:

24547

RonL

(or I might have already posted it in an alternate reality)

4. Originally Posted by Soroban
Hello, Rimas!

What have you tried?

If you examine the first few cubes, you'll trip over the answer . . .

Thanks i think the answer is 81

5. Hello again, Rimas!

It is very simple . . .

What is the sum of three smallest prime numbers each of which
is two more than a perfect positive cube?

$\begin{array}{cc} \text{cube} & \text{two more} \\
1^3 = 1 & 3 \\ 2^3 = 8 & \not1\!\!\!\!\not0 \\ 3^3 = 27 & 29 \\ 4^3 = 64 & \not6\!\!\!\not6 \\ 5^3 = 125 & 127 \end{array}$

Therefore: . $3 + 29 + 127\;=\;157$

6. Hi:

The positive cubes are (1, 8, 27, 64, 125, 216, ...) 1 + 2 = 3, 27 + 2 = 29, and 2 + 125 = 127. As each is prime, the sum in question is 3 + 29 + 127 = 159.

Regards,

Rich B.