| Number | 131 |
|---|---|
| Factorization | prime |
| Prime | 32nd |
| Divisor | 1, 131 |
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 3n - 1. Because the next odd number, 133, is a semiprime, 131 is a Chen prime. 131 is an Ulam number.[3] 131 is also a Honaker prime.
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]
References
- ^ "Sloane's A005384 : Sophie Germain primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
- ^ "Sloane's A000928 : Irregular primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
- ^ "Ulam numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-04-18. Retrieved 2016-04-19.
- ^ Retrieved 2024-08-03.
- ^ Retrieved 2024-08-03.