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3 (three; /ˈθriː/) is a number, numeral, and glyph. It is the natural number following 2 and preceding 4.

In mathematics[edit]

Three is approximately π (actually closer to 3.14159) when doing rapid engineering guesses or estimates. The same is true if one wants a rough-and-ready estimate of e, which is actually approximately 2.71828.

Three is the first odd prime number,[1] and the second smallest prime. It is both the first Fermat prime (22n + 1) and the first Mersenne prime (2n − 1), the only number that is both, as well as the first lucky prime. However, it is the second Sophie Germain prime, the second Mersenne prime exponent, the second factorial prime (2! + 1), the second Lucas prime, and the second Stern prime.

Three is the first unique prime due to the properties of its reciprocal.

Three is the aliquot sum of 4.

Three is the third Heegner number.

According to Pythagoras and the Pythagorean school, the number 3, which they called triad, is the noblest of all digits, as it is the only number to equal the sum of all the terms below it, and the only number whose sum with those below equals the product of them and itself.[2]

Three is the second triangular number and it is the only prime triangular number. Three is the only prime which is one less than a perfect square. Any other number which is n2 − 1 for some integer n is not prime, since it is (n − 1)(n + 1). This is true for 3 as well (with n=2), but in this case the smaller factor is 1. If n is greater than 2, both n − 1 and n + 1 are greater than 1 so their product is not prime.

Three non-collinear points determine a plane and a circle.

Three is the fourth Fibonacci number. In the Perrin sequence, however, 3 is both the zeroth and third Perrin numbers.

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...)

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.).