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31

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This article is under construction.            

Please do not rely on any information it contains.            


31 is an integer.

Membership in core sequences

Odd numbers ..., 25, 27, 29, 31, 33, 35, 37, ... A005408
Prime numbers ..., 19, 23, 29, 31, 37, 41, 43, ... A000040
Squarefree numbers ..., 26, 29, 30, 31, 33, 34, 35, ... A005117
Numbers of the form 1, 3, 7, 15, 31, 63, 127, 255, 511, ... A000225
Mersenne exponents 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, ... A000043

Note that in addition to being the exponent of a Mersenne prime (2147483647), 31 is itself a Mersenne prime, with its corresponding exponent being 5.

In Pascal's triangle, 31 occurs twice.

Sequences pertaining to 31

Multiples of 31 0, 31, 62, 93, 124, 155, 186, 217, 248, 279, ... A135631
Primes with primitive root 31 2, 7, 17, 29, 47, 53, 59, 61, 67, 71, 73, 89, ... A019357
sequence starting at 27 27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, ... A008884
sequence starting at 84 84, 42, 21, 62, 31, 92, 46, 23, 68, 34, 17, 50, ... A008898

Partitions of 31

There are 6842 partitions of 31.

The Goldbach representations of 31 using distinct primes are: 2 + 29 = 3 + 5 + 23 = 3 + 11 + 17 = 5 + 7 + 19 = 7 + 11 + 13 = 31.

Roots and powers of 31

In the table below, irrational numbers are given truncated to eight decimal places.

5.56776436 A010486 31 2 961
3.14138065 A010602 31 3 29791
2.35961106 A011026 31 4 923521
1.98734075 A011116 31 5 28629151
1.77239404 31 6 887503681
1.63324625 31 7 27512614111
1.53610255 31 8 852891037441
1.46455894 31 9 26439622160671
1.40973073 31 10 819628286980801
A009975

Logarithms and 31st powers

In the OEIS specifically and mathematics in general, refers to the natural logarithm of , whereas all other bases are specified with a subscript.

As above, irrational numbers in the following table are truncated to eight decimal places.

0.20184908 4.95419631 2 31 2147483648
0.29120667 3.43398720 A016654
0.31992323 3.12574985 3 31 617673396283947
0.40369817 2.47709815 4 31 4611686018427387904
0.46867906 2.13365621 5 31 4656612873077392578125
0.52177231 1.91654475 6 31 1326443518324400147398656
0.56666202 1.76472033 7 31 157775382034845806615042743
0.60554725 1.65139877 8 31 9903520314283042199192993792
0.63984646 1.56287492 9 31 381520424476945831628649898809
0.67052815 1.49136169 10 31 10000000000000000000000000000000

Values for number theoretic functions with 31 as an argument

–1
–4
11
32
2
30
1
1
30 This is the Carmichael lambda function.
–1 This is the Liouville lambda function.
31! 8222838654177922817725562880000000
265252859812191058636308480000000

Factorization of some small integers in a quadratic integer ring adjoining the square roots of −31, 31

The commutative quadratic integer ring with unity , with units of the form (), is a unique factorization domain, but it is not norm-Euclidean. is not Euclidean for any function whatsoever, nor is it a UFD at all, having class number 3.

2 Irreducible
3
4 2 2
5 Irreducible
6 2 × 3
7 Irreducible Prime
8 2 3 OR
9 3 2
10 2 × 5 OR
11 Irreducible
12 2 2 × 3
13 Irreducible Prime
14 2 × 7 OR
15 3 × 5
16 2 4
17 Irreducible Prime
18 2 × 3 2
19 Irreducible Prime
20 2 2 × 5 OR OR

Factorization of 31 in some quadratic integer rings

In , 31 is a prime number. But in some quadratic integer rings, it is composite.

TABLE GOES HERE

Representation of 31 in various bases

Base 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Representation 11111 1011 133 111 51 43 37 34 31 29 27 25 23 21 1F 1E 1D 1C 1B

See also

Some integers
0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49
1729