Number 13 in Math

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Number 13 in Math.   Number 13      (More Math. pages)

 

A prime number whose digits are the first 2 odd numbers.

 

An absolute prime number (or permutable prime number): both numbers 13 and 31 are prime or in fact, absolute prime.

 

A Mersenne exponent: 213–1 = 8191 is the 5th Mersenne prime number.

 

The 2nd Wilson prime number. The only known Wilson prime numbers (up to value 5×108) are: 5, 13 and 563.

 

Reversible numbers and their squares: 132 = 169 and 312 = 961 = 312.

 

162,409 = 169×961 = 4032 = 13×13×31×31.

 

The 7th Fibonacci number.

 

510,510 is the product of first 7 prime numbers, of 2 consecutive numbers and of 4 consecutive Fibonacci numbers: 510,510 = 2×3×5×7×11×13×17 = 714×715 = 13×21×34×55.

 

The 13th prime number is 41, sum of all prime numbers not greater than 13:

41 = 2+3+5+7+11+13.

 

Sum of all prime numbers from 3 to 13 is the product of 2 numbers 3 and 13: 39 = 3´13 = 3+5+7+11+13.

 

1353 = 3×11×41 is sum of 41 consecutive numbers from 13 to 53: 13+14+15+…+51+52+53 = 1353.

 

The sum s(n) = 14n+2+24n+2+34n+2+44n+2+54n+2+64n+2 is always divisible by 13 for any positive integer.

 

Squares of 2 consecutive numbers that use the same digits: 132 = 169 and 142 = 196. Others: 1572 & 1582 and 9132 & 9142.

 

Three square numbers using the same digits: 132 = 169, 142 = 196 and 312 = 961.

 

The number of books comprising Euclid’s work: Elements, a foundation for planar (Euclidean) geometry.

 

The number of only Archimedean solids: cuboctahedron, great rhombicosidodecahedron, great rhombicuboctahedron, icosidodecahedron, small rhombicosidodecahedron, small rhombicuboctahedron, snub cube, snub dodecahedron, truncated cube, truncated dodecahedron, truncated icosahedron (soccer ball), truncated octahedron and truncated tetrahedron.

 

1/13 = 0.076923076923… or 0.076923. Multiples of 076923 by 3, 4, 9, 10 and 12 yield 5 other rotations of the digits of the number itself: 230769, 307692, 692307, 769230 and 923076, respectively. Its multiple by 13 is 999,999.

 

The product of the first 8 consecutive prime numbers, divided by 10:  2×3×5×7×11×13×17×19/10 = 969,969 is a palindromic number.

 

13×93 = 1,209 = 31×39

26×93 = 2,418 = 62×39

13×62 =    806 = 31×26.

 

8×8+13 = 77      

88×8+13 = 717

888×8+13 = 7117

8888×8+13 = 71117

88,888×8+13 = 711,117

888,888×8+13 = 7,111,117

8,888,888×8+13 = 71,111,117

88,888,888×8+13 = 711,111,117

888,888,888×8+13 = 7,111,111,117

8,888,888,888×8+13 = 71,111,111,117

 

A supersingular prime numbers factors of the order of the Monster group M:

246×320×59×76×112×133×17×19×23×29×31×41×47×59×71 =

= 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000.

 

The first Markov numbers are 1, 2, 5, 13, 29, 34, 89, 169, 194, 233…