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131 (number)

From Wikipedia, the free encyclopedia
Natural number
← 130131 132 →
Cardinalone hundred thirty-one
Ordinal131st
(one hundred thirty-first)
Factorizationprime
Prime32nd
Divisors1, 131
Greek numeralΡΛΑ´
Roman numeralCXXXI,cxxxi
Binary100000112
Ternary112123
Senary3356
Octal2038
DuodecimalAB12
Hexadecimal8316

131 (one hundred thirty one) is thenatural number following130 and preceding132.

In mathematics

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131 is aSophie Germain prime,[1] anirregular prime,[2] the second 3-digitpalindromic prime, and also apermutable prime with113 and311. It can be expressed as the sum of three consecutive primes, 131 = 41 + 43 + 47. 131 is anEisenstein prime with no imaginary part and real part of the form3n1{\displaystyle 3n-1}. Because the next odd number, 133, is asemiprime, 131 is aChen prime. 131 is anUlam number.[3]

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

131 is the fifth discriminant of imaginaryquadratic 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]

References

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  1. ^"Sloane's A005384 : Sophie Germain primes".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-05-27.
  2. ^"Sloane's A000928 : Irregular primes".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-05-27.
  3. ^"Ulam numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-04-18. Retrieved2016-04-19.
  4. ^Sloane, N. J. A. (ed.)."Sequence A046002 (Discriminants of imaginary quadratic fields with class number 5 (negated))".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2024-08-03.
  5. ^Sloane, N. J. A. (ed.)."Sequence A046005 (Discriminants of imaginary quadratic fields with class number 8 (negated).)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2024-08-03.
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