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No one suspected that Ax + By = Cz (note unique exponents) might also be impossible with co-prime bases until a remarkable discovery in 1993 by a Dallas, Texas number theory enthusiast by the name of Andrew Beal. Beal was working on FLT when he began to look at similar equations with independent exponents. He constructed several algorithms to generate solution sets but the very nature of the algorithms he was able to construct required a common factor in the bases. He began to suspect that co-prime bases might be impossible and set out to test his hypothesis by computer....

Status Name Nationality Thrust** Propellants Notes Out-of-production F-1 USA 1.7 million Liquid Oxygen - Kerosene 5 used in each Apollo Saturn Stage 1. Flown between 1967 to 1973. Development stopped RD-270 USSR 1.5 million Nitrogen Tetroxide – UDMH Tested, but never flown. Largest single-chamber engine designed by USSR. Development stopped M-1 USA 1.2 million Liquid Oxygen – Liquid Hydrogen Designed as replacement for F-1. Program canceled in 1966. In production   BA-810 USA 810,000 Hydrogen Peroxide - Kerosene Stage 2 engine of BA-2 launch vehicle. First test 1Q 2000; first flight 2002. In production   RS-68 USA 745,000 Liquid...