131 (number)

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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
Binary 100000112
Ternary 112123
Senary 3356
Octal 2038
Duodecimal AB12
Hexadecimal 8316

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

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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]

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Related Research Articles

18 (eighteen) is the natural number following 17 and preceding 19.

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

47 (forty-seven) is the natural number following 46 and preceding 48. It is a prime number.

127 is the natural number following 126 and preceding 128. It is also a prime number.

137 is the natural number following 136 and preceding 138.

145 is the natural number following 144 and preceding 146.

311 is the natural number following 310 and preceding 312.

129 is the natural number following 128 and preceding 130.

133 is the natural number following 132 and preceding 134.

167 is the natural number following 166 and preceding 168.

136 is the natural number following 135 and preceding 137.

173 is the natural number following 172 and preceding 174.

141 is the natural number following 140 and preceding 142.

139 is the natural number following 138 and preceding 140.

154 is the natural number following 153 and preceding 155.

159 is a natural number following 158 and preceding 160.

165 is the natural number following 164 and preceding 166.

166 is the natural number following 165 and preceding 167.

182 is the natural number following 181 and preceding 183.

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.