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Three
- Three is the first odd prime number, and the second smallest prime after two.
- Three is the first Fermat prime (22º + 1).
- Three is the first Mersenne prime (22 - 1).
- Three is the second Sophie Germain prime.
- Three is the second Mersenne prime exponent.
- Three is the first lucky prime.
- Three is the first Genocchi prime.
- Three is the second factorial prime (2! + 1).
- Three is the first unique prime due to the properties of its reciprocal.
- Three is the second triangular number.
- Three is the only prime which is one less than a perfect square. Any other number which is one less than a perfect square will be the product of the numbers one more than, and one less than, the square root of said square.
- Three non-collinear points determine a plane and a circle.
- Three is the fourth Fibonacci number and the third that is unique. It is also the second Lucas prime and the second Stern prime.
- Three is the fourth open meandric number.
- Vulgar fractions with 3 in the denominator have a single digit repeating sequences in their decimal expansions, (.000..., .333..., .666..., .999...)
- A natural number is divisible by three if the sum of its digits in base 10 is divisible by 3. For example, the number 21 is divisible by three (3 times 7) and the sum of its digits is 2 + 1 = 3. Because of this, the reverse of any number that is divisible by three (or indeed, any permutation of its digits) is also divisible by three. For instance, 1368 and its reverse 8631 are both divisible by three (and so are 1386, 3168, 3186, 3618, etc..). See also Divisibility rule.
- A triangle is the most durable shape possible, the only "perfect" figure which if all endpoints have hinges will never change its shape unless the sides themselves are bent.
- 3 is the only integer between e and p.
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