Conjectures

(1) 2201 is the only non-palindrome known to have a palindromic cube
(2201^3 = 10662526601)

(2) 3375 (=15*15*15) is the largest known cube which contains all prime digits.


(3) 9 is the only known composite number n such that both

2^n + n^2 and 2^n - n^2 are prime

because 2^9 + 9^2 = 593 and 2^9 - 9^2 = 431

Note : 9 is also the smallest composite number n such that both 2^n + n and 2^n - n

are prime

because 2^9 + 9 = 521 and 2^9 - 9 = 503

How cool is that!