5 (number)

:This article discusses the number five. For the year 5 AD, see 5. For other uses of 5, see 5 (disambiguation)

In mathematics

Five is the third smallest prime number, after 2 and 3, and before 7. Because it can be written as 2^(2^1)+1, five is classified as a Fermat prime. 5 is the third Sophie Germain prime, the first safe prime, and the third Mersenne prime exponent. Five is the first Wilson prime and the third factorial prime. It is an Eisenstein prime with no imaginary part and real part of the form 3n - 1.

Related Topics:
Prime number - 2 - 3 - 7 - Fermat prime - Sophie Germain prime - Safe prime - Mersenne prime - Wilson prime - Factorial prime - Eisenstein prime

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Five is the only prime number to end in the digit 5, because all other numbers written with a 5 in the ones-place under the decimal system are multiples of five. As a consequence of this, 5 is in base 10 a 1-automorphic number.

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Five is a factor of 10, so vulgar fractions with 5 in the denominator do not yield infinite decimal expansions, unlike most other primes. When written in the decimal system, all multiples of 5 will end in either 5 or 0.

Related Topics:
10 - Vulgar fraction - Denominator - Decimal - 0

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The number 5 is a Fibonacci number, being 2 plus 3. The next Fibonacci number is 8. 5 is also a Pell number.

Related Topics:
Fibonacci number - 2 - 3 - 8 - Pell number

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While polynomial equations of degree 4 and below can be solved with radicals, equations of degree 5 and higher cannot generally be so solved. This is the Abel-Ruffini theorem. This is related to the fact that the symmetric group Sn is a solvable group for n ≤ 4 and not solvable for n ≥ 5.

Related Topics:
Polynomial - 4 - Abel-Ruffini theorem - Symmetric group - Solvable group

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While all graphs with 4 or fewer vertices are planar, there exists a graph with 5 vertices which is not planar: K5, the complete graph with 5 vertices.

Related Topics:
Graphs - Planar - Complete graph

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Five is also the number of Platonic solids.

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A polygon with five sides is a pentagon. Figurate numbers representing pentagons (including five) are called pentagonal numbers. Five is also a square pyramidal number.

Related Topics:
Polygon - Pentagon - Figurate number - Pentagonal number - Square pyramidal number

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Five is the answer to the question asked at the very end of the mathematics quiz show in the movie Little Man Tate. (Our young protagonist blurts out the answer, but the host mishears it as being the answer from the contestant to whom the question is posed, and declares him the winner.)

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In numbering systems

• In binary code five is 101
• In ternary code five is 12
• In quaternary numeral system code five is 11
• In quinary five is 10; in senary code and all codes above (such as decimal, duodecimal and vigesimal) five is 5.
• The Roman numeral for five is V, which comes from a representation of an outstretched hand.
• In the Greek alphabet, ε (epsilon) has numerical value of 5.
• In the Hebrew alphabet, ה (heh) has numerical value of 5.
• In the Cyrillic alphabet, Е has numerical value of 5.
• In the Glagolitic alphabet, (dobro) has numerical value of 5.
• The kanji and Chinese character for five are both 五, and its formal writing in Chinese is 伍 (pinyin wǔ).