It seems that nobody knows a solution of this Taxicab equation with prime numbers (p, q, r, s, t, u): (1) p^3 + q^3 = r^3 + s^3 = t^3 + u^3 I tried also the equivalent Cabtaxi problem. This new problem should be easier, because allowing both sums and differences. But, I am also unable to get a solution of: (2) p^3 +/- q^3 = r^3 +/- s^3 = t^3 +/- u^3 It is "irritating", because the standard solutions of (2) using prime and non-prime are small and easy to find, the smallest being: 728 = 6^3 + 8^3 = 9^3 - 1^3 = 12^3 - 10^3 Why??? Are (1) and (2) impossible? Any idea? With only (p, q, r, s), the equations have solutions, the smallest being: (3) p^3 + q^3 = r^3 + s^3 6507811154 = 31^3 + 1867^3 = 397^3 + 1861^3 12906787894 = 593^3 + 2333^3 = 1787^3 + 1931^3 (4) p^3 +/- q^3 = r^3 +/- s^3 62540982 = 397^3 - 31^3 = 1867^3 - 1861^3 (based on the first above solution of (3)!) 105161238 = 193^3 + 461^3 = 709^3 - 631^3 Christian.