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227 (number)

227 (two hundred [and] twenty-seven) is the natural number between 226 and 228. It is also a prime number.

In mathematics[edit]

227 is the 49th prime number, an index whose value is a square number (7²). It is a twin prime, and the start of a prime triplet (with 229 and 233).^[1]

It is a safe prime, as dividing it by two and rounding down produces the Sophie Germain prime, 113.^[2] It is also:

• aregular prime,^[3]
• aPillai prime,^[4]
• aStern prime,^[5] and
• aRamanujan prime.^[6]

227 and 229 form the first twin prime pair for which neither is a cluster prime.

The 227th harmonic number is the first to exceed 6.^[7]

There are 227 different connected graphs with eight edges,^[8] and 227 independent sets in a 3 × 4grid graph.^[9]

Convergents to π[edit]

227 is the difference between 333 and 106, which are respectively the numerator and denominator in the fourth convergenttopi,^[10][11] correct to four decimal places:

${\displaystyle \pi \approx {\frac {333}{106}}\approx 3.1415{\color {red}0}\ldots }$

Meanwhile, the sum of the first few denominators in convergents to pi (1, 7, 106, 113)^[11] yields 227.^[a]

References[edit]

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