3 is the only integer which is the sum of the preceding positive integers (1 + 2 = 3) and the only number which is the sum of the factorials of the preceding positive integers (). It is also the first odd prime. A quantity taken to the power 3 is said to be cubed.

The sequence 1, 31, 331, 3331, 33331, ... (Sloane's A033175) consisting of n = 0, 1, ... 3s followed by a 1 has its nth term is given by

The result is prime for n = 1, 2, 3, 4, 5, 6, 7, 17, 39, ... (Sloane's A055520); i.e., for 31, 331, 3331, 33331, 333331, 3333331, 33333331, ... (Sloane's A051200), a fact which Gardner (1997) calls "a remarkable pattern that is entirely accidental and leads nowhere."

1, 2, 3x Plus 1 Mapping, Cubed, Period Three Theorem, Ternary, Three-Arc Illusion, Three-Choice Polygon, Three-Choice Walk, Three-Colorable Graph, Three-Colorable Knot, Three Conics Theorem, Three Jug Problem, Three-Valued Logic, Trefoil Knot, Wigner 3j-Symbol, Zero

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