127 (number)

In mathematics

• As a Mersenne prime, 127 is related to the perfect number 8128. 127 is also the largest known Mersenne prime exponent for a Mersenne number, 2^{127}-1, which is also a Mersenne prime. It was discovered by Édouard Lucas in 1876 and held the record for the largest known prime for 75 years.
  • 2^{127}-1 is the largest prime ever discovered by hand calculations as well as the largest known double Mersenne prime.
  • Furthermore, 127 is equal to 2^{7}-1, and 7 is equal to 2^{3}-1, and 3 is the smallest Mersenne prime, making 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 p=\frac{x^{3}-y^{3}}{x-y}, 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 is a strong prime.
• 127 is a centered hexagonal number.
• It is the seventh Motzkin number.
• 127 is a palindromic prime in nonary and binary.
• 127 is the first Friedman prime in decimal. It is also the first nice Friedman number in decimal, since 127=2^{7}-1 ,, as well as binary since 1111111 = (1 + 1)^{111} - 1 , .
• 127 is the sum of the sums of the divisors of the first twelve positive integers.
• 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.
• 127 is the smallest odd number that cannot be written in the form p+2^{x}, for p is a prime number, and x is an integer, since 127 - 2^0=126, 127 - 2^1=125, 127 - 2^2=123, 127 - 2^3=119, 127 - 2^4=111, 127 - 2^5=95, and 127 - 2^6=63 are all composite numbers.
• 127 is an isolated prime where neither p-2 nor p+2 is prime.
• 127 is the smallest digitally delicate prime in binary.
• 127 is the 31st prime number and therefore it is the smallest Mersenne prime with a Mersenne prime index.
• 127 is the largest number with the property 127 = 1\cdot\textrm{prime}(1) + 2\cdot\textrm{prime}(2) + 7\cdot\textrm{prime}(7), where \textrm{prime}(n) is the nth prime number. There are only two numbers with that property; the other one is 43.
• 127 is equal to \textrm{prime}^{6}(1), where \textrm{prime}(n) is the nth prime number.
• 127 is the number of non-equivalent ways of expressing 10,000 as the sum of two prime numbers.
• 127 is the integer as floor of the imaginary part of the 42th non-trivial zero of the Riemann zeta-function.
• 127 is the smallest prime number that results in a decimal greater than 4 when divided by its prime index. 127 divided by 31 is 4 with a remainder of 3.
• 127 is a Lucky number which is generated by a certain "sieve".
• 127 is the 8th term in the prime number variation of Flavius's sieve.
• 127 is a Fortunate number which is linked to the primorials.

In other fields

• The non-printable "Delete" (DEL) control character in ASCII.
• Linotype (and Intertype) machines used brass matrices with one of 127 possible combinations punched into the top to enable the matrices to return to their proper channel in the magazine.

References

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

References

1. "Sloane's A002407 : Cuban primes". OEIS Foundation.
2. {{cite oeis. A109611. Chen primes: primes p such that p + 2 is either a prime or a semiprime.
3. "Sloane's A051634 : Strong primes". OEIS Foundation.
4. "Sloane's A003215 : Hex (or centered hexagonal) numbers". OEIS Foundation.
5. "Sloane's A001006 : Motzkin numbers". OEIS Foundation.
6. {{Cite OEIS. A024916
7. {{Cite OEIS
8. {{Cite OEIS. A006285. Odd numbers not of form p + 2^x (de Polignac numbers)
9. {{Cite OEIS. A137985. Complementing any single bit in the binary representation of these primes produces a composite number.
10. {{Cite OEIS
11. {{Cite OEIS. A013629. Floor of imaginary parts of nontrivial zeros of Riemann zeta function.
12. {{Cite OEIS. A000959. Lucky numbers
13. {{Cite OEIS. A099243. A variation on Flavius's sieve.
14. {{Cite OEIS