Jump to content

131 (number)

From Wikipedia, the free encyclopedia
← 130 131 132 →
Cardinalone hundred thirty-one
Ordinal131st
(one hundred thirty-first)
Factorizationprime
Prime32nd
Divisors1, 131
Greek numeralΡΛΑ´
Roman numeralCXXXI
Binary100000112
Ternary112123
Senary3356
Octal2038
DuodecimalAB12
Hexadecimal8316

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

In mathematics

[edit]

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]

In the military

[edit]

In transportation

[edit]

In other fields

[edit]

131 is also:

See also

[edit]

References

[edit]
  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.). "Sequence A046002 (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.). "Sequence A046005 (Discriminants of imaginary quadratic fields with class number 8 (negated).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-08-03.