131 (number)

Last updated
← 130 131 132 →
Cardinal one hundred thirty-one
Ordinal 131st
(one hundred thirty-first)
Factorization prime
Prime 32nd
Divisors 1, 131
Greek numeral ΡΛΑ´
Roman numeral CXXXI, cxxxi
Binary 100000112
Ternary 112123
Senary 3356
Octal 2038
Duodecimal AB12
Hexadecimal 8316

131 (one hundred thirty one) is the natural number following 130 and preceding 132.

In mathematics

131 is a Sophie Germain prime, [1] an irregular prime, [2] the second 3-digit palindromic prime, and also a permutable prime with 113 and 311. It can be expressed as the sum of three consecutive primes, 131 = 41 + 43 + 47. 131 is an Eisenstein prime with no imaginary part and real part of the form . Because the next odd number, 133, is a semiprime, 131 is a Chen prime. 131 is an Ulam number. [3]

131 is a full reptend prime in base 10 (and also in base 2). The decimal expansion of 1/131 repeats the digits 007633587786259541984732824427480916030534351145038167938931 297709923664122137404580152671755725190839694656488549618320 6106870229 indefinitely.

131 is the fifth discriminant of imaginary quadratic fields with class number 5, where the 131st prime number 739 is the fifteenth such discriminant. [4] Meanwhile, there are conjectured to be a total of 131 discriminants of class number 8 (only one more discriminant could exist). [5]

Related Research Articles

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

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.

79 (seventy-nine) is the natural number following 78 and preceding 80.

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

53 (fifty-three) is the natural number following 52 and preceding 54. It is the 16th prime number.

113 is the natural number following 112 and preceding 114.

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.

500 is the natural number following 499 and preceding 501.

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.

2000 is a natural number following 1999 and preceding 2001.

7000 is the natural number following 6999 and preceding 7001.

8000 is the natural number following 7999 and preceding 8001.

239 is the natural number following 238 and preceding 240.

311 is the natural number following 310 and preceding 312.

167 is the natural number following 166 and preceding 168.

307 is the natural number following 306 and preceding 308.

References

  1. ↑ "Sloane's A005384 : Sophie Germain primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
  2. ↑ "Sloane's A000928 : Irregular primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
  3. ↑ "Ulam numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-04-18. Retrieved 2016-04-19.
  4. ↑ Sloane, N. J. A. (ed.). "SequenceA046002(Discriminants of imaginary quadratic fields with class number 5 (negated))". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-08-03.
  5. ↑ Sloane, N. J. A. (ed.). "SequenceA046005(Discriminants of imaginary quadratic fields with class number 8 (negated).)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-08-03.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.