## Num3er 1588

Marin Mersenne   (8 September 1588 – 1 September 1648)

The factors of   1588   are:      1    2    4    397    794    1588
The prime factors are:      2 * 2 * 397

1588   is a number of the form   529*n + 1    (n = 3)

1588   is
11000110100   in base 2
2011211   in base 3
120310   in base 4
22323   in base 5
11204   in base 6
4426   in base 7
4426   in base 8
2154   in base 9

1588   is an Apocalyptic Number
1588   is a Deficient Number
1588   is an Odious Number
1588   is an Untouchable Number
1588   has 7 terms in its Zeckendorf representation :
1588   =   987 + 377 + 144 + 55 + 21 + 3 + 1
http://mathworld.wolfram.com/ZeckendorfRepresentation.html
http://en.wikipedia.org/wiki/Zeckendorf’s_theorem

If   n = ±46,   1 + floor((3/4) * n^2)   =   1588

1588   =   3^6   +   3^6   +   2^6   +   2^6   +   1^6   +   1^6

1588   =   12^2   +   38^2

1588   =   2^2   –   4^2   +   40^2
1588   =   – 5^2   +   13^2   +   38^2
1588   =   6^2   +   16^2   +   36^2
1588   =   – 7^2   +   26^2   +   31^2
1588   =   – 9^2   +   15^2   +   38^2
1588   =   – 11^2   +   22^2   +   35^2
1588   =   – 12^2   +   24^2   +   34^2