11

11
Basic Information
Cardinal Number	eleven
Ordinal Number	eleventh
Roman Numeral	XI
Greek Numeral	ΙΑ´
Factorization	11
Standard Form	1.1 × 101
Different Representations
Binary Form	10112
Ternary Form	1023
Quaternary Form	234
Quinary Form	215
Senary Form	156
Septenary Form	147
Octal Form	138
Nonary Form	129
Undecimal Form	1011
Duodecimal Form	B12
Tridecimal Form	B13
Quattuordecimal Form	B14
Quindecimal Form	B15
Hexadecimal Form	B16
Septendecimal Form	B17
Octodecimal Form	B18
Novemdecimal Form	B19
Vigesimal Form	B20
Unvigesimal Form	B21
Duovigesimal Form	B22
Trevigesimal Form	B23
Quattuorvigesimal Form	B24
Quinvigesimal Form	B25
Hexavigesimal Form	B26
Septenvigesimal Form	B27
Octovigesimal Form	B28
Novemvigesimal Form	B29
Trigesimal Form	B30
Untrigesimal Form	B31
Duotrigesimal Form	B32
Tretrigesimal Form	B33
Quattuortrigesimal Form	B34
Quintrigesimal Form	B35
Hexatrigesimal Form	B36
Previous	7
Current	11
Next	13

11, or R₂, is the fifth prime number and the first prime with 2 digits. Its only factors are 1 and 11. Moreover, 11 is also the first repunit prime. The primorial of 11 is 2310.

Proofs

• — 11 is divisible by 1.

• — 11 is not divisible by 2-10.

• — 11 is divisible by 11.

• Therefore 11 has exactly 2 integer factors and is prime.

As an Exponent of Mersenne Number

2¹¹ - 1, which is the number 2,047, can be factored into 23 x 89, and is not prime.

Relationship with other odd numbers

The numbers before

• 5 is the second previous prime number.
  • The difference between 11 and 5 is 6. Therefore, they are sexy primes.
• 7 is the previous prime number.
  • The difference between 11 and 7 is 4. Therefore, they are cousin primes.
• The previous odd number, 9, is the second non-trivial square number and is the first odd composite number.

The numbers after

• The next odd number, 13, is a prime number.
  • There are no odd numbers between 11 and 13. As a result, they are twin primes.
• 15, the odd number following 13, is the second odd composite number. It is divisible by 3 and 5.
• 17, the odd number following 15, is a prime number.
  • The difference between 17 and 11 is 6. Therefore, they are sexy primes.

Trivia

• The sum of the digits of 11 returns a prime number. In this case, that sum is 2.
• 11 is the first non-trivial palindrome, a palindrome is a sting of characters that is the same frontwards as backwards
• 11 is the only prime number where the difference between it and two other prime numbers (3 and 19) is 8.
• 11 is part of the only sexy prime quintuplet (5, 11, 17, 23, 29), since all multiples of 5, except for itself, are not prime.
• 11 and 13 are the only pair of two prime quadruplets. [5, 7, 11, 13] and [11, 13, 17, 19].
• The first two-digit prime number, and the first repunit prime number, the next one has 19 ones (R₁₉) and is 1 111 111 111 111 111 111, while the next ones consist of 23 - 11 111 111 111 111 111 111 111 (R₂₃), 317 - 1,(11)*10^316 (R₃₁₇), and 1031 - 1,(11)*10^1030 (R₁₀₃₁) ones.
• The only repunit prime that has an even number of ones. Other repunit prime numbers have an odd number of ones, because those that have an even number of ones, 1111, 111111 etc, are divisible by 11.
• 11 is the first prime number whose position in the set of all primes is greater than two multiplied by the position. 11 is the 5th prime number. (5*2=10), which is less than 11. The same applies to every next prime number, 13 (6*2=12), less than 13. 17 (7*2=14), less than 17. 19 (8 *2=16), less than 19. For example 7, 4th prime number (4*2=8) more than 7. 5 (3*2=6), more than 5. 3 (2*2=4), more than 3. 2 (1*2=2) - the same.
• 11 is the only palindromic prime of even length, since all other palindromic numbers of even length are divisible by 11.
• The divisibility rule for 11 states that if the alternating sum of the digits is divisible by 11, the original number is divisible by 11. For example: 4-9+3-9 = -11, which is divisible by 11, so 4,939 is divisible by 11.

Prime Numbers 1-1,000