Consider all 3-term geometric sequences with first term 1 and with common ratio the square of an integer between 1 and 1000. How many of these 1000 geometric sequences have the property that the sum of the 3 terms is prime?

Question

Consider all 3-term geometric sequences with first term 1 and with common ratio the square of an integer between 1 and 1000. How many of these 1000 geometric sequences have the property that the sum of the 3 terms is prime?

Answer 1

I did this question here

http://www.jiskha.com/display.cgi?id=1367223190

Somebody called "tsong" disagreed, but clearly did not read my solution, since I "proved" that there is only one such case,
when the GS is 1 , 1, 1
that is, when the common ratio is 1
then 1 + 1^2 + 1^4 = 3 , which is a prime number

conclusion: there is only ONE such sequence.