13

13
Basic Information
Cardinal Number	thirteen
Ordinal Number	thirteenth
Roman Numeral	XIII
Greek Numeral	ΙΓ´
Factorization	13
Standard Form	1.3 × 101
Different Representations
Binary Form	11012
Ternary Form	1113
Quaternary Form	314
Quinary Form	235
Senary Form	216
Septenary Form	167
Octal Form	158
Nonary Form	149
Undecimal Form	1211
Duodecimal Form	1112
Tridecimal Form	1013
Quattuordecimal Form	D14
Quindecimal Form	D15
Hexadecimal Form	D16
Septendecimal Form	D17
Octodecimal Form	D18
Novemdecimal Form	D19
Vigesimal Form	D20
Unvigesimal Form	D21
Duovigesimal Form	D22
Trevigesimal Form	D23
Quattuorvigesimal Form	D24
Quinvigesimal Form	D25
Hexavigesimal Form	D26
Septenvigesimal Form	D27
Octovigesimal Form	D28
Novemvigesimal Form	D29
Trigesimal Form	D30
Untrigesimal Form	D31
Duotrigesimal Form	D32
Tretrigesimal Form	D33
Quattuortrigesimal Form	D34
Quintrigesimal Form	D35
Hexatrigesimal Form	D36
Previous	11
Current	13
Next	17

13 is a prime number from 1-100. 13 is prime because it only has 2 factors, 1 and 13. It is said to be an unlucky number, and is skipped in some systems that use numbers, such as elevators. It is the sixth prime number, and the sixth prime number between 1 and 100. The primorial of 13 is 30,030.

Proofs

• — 13 is divisible by 1.

• — 13 is not divisible by 2-12.

• — 13 is divisible by 13.

• Therefore, it has 2 factors and is prime.

As an Exponent of Mersenne Number

2¹³ - 1, which is the number 8,191, is a prime number. It is the 5th Mersenne prime.

​Relationship with other odd numbers

The numbers before

• 7 is the second previous prime number.
  • The difference between 13 and 7 is 6. Therefore, they are sexy primes.
• 9 is the first odd composite number and the second non-trivial square number.
• 11 is the previous prime number.
  • There are no odd numbers between 11 and 13. As a result, they are twin primes.

The numbers after

• The next odd number, 15, is the second composite number. It is divisible by 3 and 5.
• 17 is the next prime number.
  • The difference between 17 and 13 is 4. Therefore, they are cousin primes.
• 19 is the second next prime number.
  • The difference between 19 and 13 is 6. Therefore, they are sexy primes.

Trivia

• The fear of the number 13 is called triskaidekaphobia, which was founded in 1911. It is also a reason for the fear of Friday the 13th, which is often considered an unlucky day.
• 13 and 11 are the only pair of two prime quadruplets. [5, 7, 11, 13] and [11, 13, 17, 19].
• There are only three consecutive prime numbers that end with the same last digit and are separated by 10, they are [3,13,23]. After that, it becomes impossible because every 3rd positive integer is composite since it is a multiple of 3.

Prime Numbers 1-1,000