← 126 127 128 →
Cardinalone hundred twenty-seven
Ordinal127th
(one hundred twenty-seventh)
Factorizationprime
Prime31st
Divisors1, 127
Greek numeralΡΚΖ´
Roman numeralCXXVII
Binary11111112
Ternary112013
Octal1778
DuodecimalA712
Hexadecimal7F16

127 (one hundred [and] twenty-seven) is the natural number following 126 and preceding 128. It is also a prime number.

## In mathematics

• As a Mersenne prime, 127 is related to the perfect number 8128. 127 is also an exponent for another Mersenne prime 2127 - 1, which was discovered by Édouard Lucas in 1876, and held the record for the largest known prime for 75 years.
• 2127 - 1 is the largest prime ever discovered by hand calculations, as well as the largest known double Mersenne prime.
• Furthermore, 127 is equal to 27 - 1, and 7 is equal to 23 - 1, and 3 is the smallest Mersenne prime, this makes 7 the smallest double Mersenne prime and 127 the smallest triple Mersenne prime.
• There are a total of 127 prime numbers between 2,000 and 3,000.
• 127 is also a cuban prime of the form ${\displaystyle p=(x^{3}-y^{3})/(x-y)}$, ${\displaystyle x=y+1}$.[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 is a strong prime.[2]
• 127 is a centered hexagonal number.[3]
• It is the 7th Motzkin number.[4]
• 127 is a palindromic prime in nonary and binary.
• 127 is the first Friedman prime in base 10. It is also the first nice Friedman number in base 10, since ${\displaystyle 127=2^{7}-1\,}$, as well as binary since ${\displaystyle 1111111=(1+1)^{111}-1\,}$ .
• 127 is the sum of the sums of the divisors of the first 12 positive integers.[5]
• 127 is the smallest prime that can be written as the sum of the first two or more odd primes: 127 = 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29.[6]
• 127 is the smallest odd number that can't be written in the form p + 2x for p=prime number and x=integer, since 127 - 20 = 126, 127 - 21 = 125, 127 - 22 = 123, 127 - 23 = 119, 127 - 24 = 111, 127 - 25 = 95, and 127 - 26 = 63 are all composite numbers.[7]
• 127 is an isolated prime where neither p-2 nor p+2 are prime.
• 127 is the smallest digitally delicate prime in base 2.[8]
• 127 is the 31st prime number and therefore it is the smallest Mersenne prime with a Mersenne prime index.

127 is also:

## References

1. ^ "Sloane's A002407 : Cuban primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
2. ^ "Sloane's A051634 : Strong primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
3. ^ "Sloane's A003215 : Hex (or centered hexagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
4. ^ "Sloane's A001006 : Motzkin numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
5. ^
6. ^ Sloane, N. J. A. (ed.). "Sequence A071148". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.. Partial sums of sequence of odd primes; a(n) = sum of the first n odd primes.
7. ^
8. ^ Sloane, N. J. A. (ed.). "Sequence A137985". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.. Complementing any single bit in the binary representation of these primes produces a composite number.
9. ^ "Sara". Catholic Encyclopedia. Retrieved September 8, 2015.
10. ^