# Tag Archives: prime

## Why Two is My Favorite Number

Many math geeks will pick a favorite number of theirs because of a certain property of said number. Some people choose e, the base of the natural logarithm, some choose π, the ratio between a circles circumference and its diameter, some clever few choose i, the square root of -1, and some people choose a natural number, that is, a positive integer, that has some significance to them, be it 17, 300, 132, or any other number. I choose two (2) as my favorite number and here’s why:

• 2 defines what numbers are even, and what numbers are odd.
• 2 is the first prime number, the smallest prime number and only even prime number. 2 and 3 are the only two consecutive primes.
• The decimal expansion of any simple fraction where the denominator is 2 will always terminate in a 5 or a 0, depending on whether the numerator is even or odd.
• 2 is the base of binary, the number system with the smallest base in which numbers can be written (relatively) easily.
• 2+2=2×2=2^2=2↑↑2=…=4. x↑↑y is called tetration, I’ll go over it later.
• 2 is its own factorial.
• 2 is part of a bunch of other special prime categories, like Fibonacci primes, Lucas primes, factorial primes.
• 2 is a highly composite number, meaning it has more positive whole number factors than any number less than it.
• There are two characters for two in Chinese, 二 and 两.
• 2 is the atomic number of helium, the first noble gas.
• Mersenne primes are found using powers of two.
• The square root of 2 (about 1.414) was the first irrational number to be discovered.
• 2 is the fewest number of dimensions needed for polygons to exist in geometry.
• And finally, a superficial one, my birthday is in February, the second month in the Gregorian calendar.

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## Zero

Zero is a number used to signify nothingness, or an absence of quantity. Zero is also often used, in positional notation systems (such as the widely used Arabic numeral system), to allow for large numbers without symbols to represent orders of magnitude. Zero is the additive identity, which means that zero added to any number will yield that number. Although the Babylonians developed a positional notation system, they lacked a placeholder such as zero. The concept of zero arose independently in China, India, Mesoamerica and the Andes. Zero is not prime because it has an unlimited number of factors (anything times zero is zero), but zero is not composite either (zero cannot be expressed as the product of two primes because zero, which is not prime, must always be a factor). The mathematics of zero put forth by Brahmagupta, excluding one rule, are still in use today. The one rule that is not still in use is the statement that 0/0=0. The operation 0/0 is called an indeterminate form and has no clear mathematical value.

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