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271 (number)

FieldValue
number271
primeyes

271 (two hundred [and] seventy-one) is the natural number after and before .

Properties

271 is a twin prime with 269, a cuban prime (a prime number that is the difference of two consecutive cubes), and a centered hexagonal number. It is the smallest prime number bracketed on both sides by numbers divisible by cubes, and the smallest prime number bracketed by numbers with five primes (counting repetitions) in their factorizations: :270=2\cdot 3^3\cdot 5 and 272=2^4\cdot 17. After 7, 271 is the second-smallest Eisenstein–Mersenne prime, one of the analogues of the Mersenne primes in the Eisenstein integers.

271 is the largest prime factor of the five-digit repunit 11111, and the largest prime number for which the decimal period of its multiplicative inverse is 5: :\frac{1}{271}=0.00369003690036900369\ldots

It is a sexy prime with 277.

References

References

  1. {{cite OEIS. A006512. Greater of twin primes
  2. {{cite OEIS. A002407. Cuban primes
  3. {{cite OEIS. A003215. Hex (or centered hexagonal) numbers
  4. Friedman, Erich. "What's Special About This Number?".
  5. {{cite OEIS. A154598. a(n) is the smallest prime p such that p-1 and p+1 both have n prime factors (with multiplicity)
  6. {{cite OEIS. A066413. Eisenstein-Mersenne primes
  7. {{cite OEIS. A003020. Largest prime factor of the "repunit" number 11...1
  8. {{cite OEIS. A061075. Greatest prime number p(n) with decimal fraction period of length n
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