239 (number)

Last updated • 1 min readFrom Wikipedia, The Free Encyclopedia
238 239 240
Cardinal two hundred thirty-nine
Ordinal 239th
(two hundred thirty-ninth)
Factorization prime
Prime yes
Greek numeral ΣΛΘ´
Roman numeral CCXXXIX
Binary 111011112
Ternary 222123
Senary 10356
Octal 3578
Duodecimal 17B12
Hexadecimal EF16

239 (two hundred [and] thirty-nine) is the natural number following 238 and preceding 240.

239 is a prime number. The next is 241, with which it forms a pair of twin primes; hence, it is also a Chen prime. 239 is a Sophie Germain prime and a Newman–Shanks–Williams prime. [1] It is an Eisenstein prime with no imaginary part and real part of the form 3n  1 (with no exponentiation implied). 239 is also a happy number.

239 is the smallest positive integer d such that the imaginary quadratic field Q(d) has class number = 15. [2]

HAKMEM (incidentally AI memo 239 of the MIT AI Lab) included an item on the properties of 239, including these: [3]

Related Research Articles

21 (twenty-one) is the natural number following 20 and preceding 22.

33 (thirty-three) is the natural number following 32 and preceding 34.

23 (twenty-three) is the natural number following 22 and preceding 24.

29 (twenty-nine) is the natural number following 28 and preceding 30. It is a prime number.

71 (seventy-one) is the natural number following 70 and preceding 72.

37 (thirty-seven) is the natural number following 36 and preceding 38.

100 or one hundred is the natural number following 99 and preceding 101.

1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.

300 is the natural number following 299 and preceding 301.

400 is the natural number following 399 and preceding 401.

700 is the natural number following 699 and preceding 701.

600 is the natural number following 599 and preceding 601.

800 is the natural number following 799 and preceding 801.

900 is the natural number following 899 and preceding 901. It is the square of 30 and the sum of Euler's totient function for the first 54 positive integers. In base 10, it is a Harshad number. It is also the first number to be the square of a sphenic number.

311 is the natural number following 310 and preceding 312.

131 is the natural number following 130 and preceding 132.

167 is the natural number following 166 and preceding 168.

251 is the natural number between 250 and 252. It is also a prime number.

30,000 is the natural number that comes after 29,999 and before 30,001.

307 is the natural number following 306 and preceding 308.

References

  1. Sloane, N. J. A. (ed.). "SequenceA088165(NSW primes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-05-28.
  2. "Tables of imaginary quadratic fields with small class number". numbertheory.org.
  3. "Beeler, M., Gosper, R.W., and Schroeppel, R. HAKMEM. MIT AI Memo 239, Feb. 29, 1972. Retyped and converted to html by Henry Baker, April, 1995".
  4. Weisstein, Eric W. "239". mathworld.wolfram.com. Retrieved 2020-08-20.
  5. Sloane, N. J. A. (ed.). "SequenceA157017". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.