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The fifth counting number.
Five is the third prime number, and the only number that is a member of two different pairs of twin primes: (3, 5) and (5, 7).
It is also a Fermat prime, as it is equal to 2²+1.
It is a member of the first prime triple: 5, 7, 11 and the first prime quadruple: 5, 7, 11, 13.
It is believed but not proved (the odd Goldbach conjecture) that 5 is the largest odd number which cannot be written as the sum of three primes.
It is the fifth Fibonacci number.
It is the number of Platonic solids.
Five is thought to be the only odd untouchable number.
It is the second square pyramidal number: 5=1²+2².
φ(5)=4,     d(5)=2,     σ(5)=6 .