127 (number)

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127 is the natural number following 126 and preceding 128.

Cardinal One hundred [and]
twenty-seven
Ordinal 127th
Factorization prime
Roman numeral CXXVII
Binary 1111111
Hexadecimal 7F

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[edit] In mathematics

127 is a Mersenne prime, 27 - 1, and as such, in binary it is a repunit prime, a permutable prime and a palindromic prime. This also means it is the largest integer that can be represented by a signed byte.

As a Mersenne prime, 127 is related to the perfect number 8128. 127 is also an exponent for the Mersenne prime 2127 - 1, making 127 a double Mersenne prime. (2127 - 1 was discovered by Edouard Lucas in 1876, and held the record for the largest known prime for 75 years. It's still the largest prime ever discovered by hand calculations.)

127 is also a cuban prime of the form p = (x3y3) / (xy), x = y + 1. The next prime is 131, with which it comprises a cousin prime. Because the next odd number, 129, is a semiprime, 127 is a Chen prime. 127 is greater than the arithmetic mean of its two neighboring primes, thus it's a strong prime.

It is the sum of the sums of divisors of the first twelve integers.

127 is a centered hexagonal number.

It is the 7th Motzkin number.

It is a nice Friedman number in base 10, since 127 = -1 + 27, as well as binary since 1111111 = (1 + 1)111 - 1 * 1.

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127 is also:

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[edit] References

  • Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 136 - 138