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