107 (number)

Summary

107 (one hundred [and] seven) is the natural number following 106 and preceding 108.

← 106 107 108 →
Cardinalone hundred seven
Ordinal107th
(one hundred seventh)
Factorizationprime
Prime28th
Divisors1, 107
Greek numeralΡΖ´
Roman numeralCVII
Binary11010112
Ternary102223
Senary2556
Octal1538
Duodecimal8B12
Hexadecimal6B16

In mathematics edit

107 is the 28th prime number. The next prime is 109, with which it comprises a twin prime, making 107 a Chen prime.[1]

Plugged into the expression  , 107 yields 162259276829213363391578010288127, a Mersenne prime.[2] 107 is itself a safe prime.[3]

It is the fourth Busy beaver number, the maximum number of steps that any Turing machine with 2 symbols and 4 states can make before eventually halting.[4]

It is the number of triangle-free graphs on 7 vertices.[5]

It is the ninth emirp, because reversing its digits gives another prime number (701)

In other fields edit

As "one hundred and seven", it is the smallest positive integer requiring six syllables in English (without the "and" it only has five syllables and seventy-seven is a smaller 5-syllable number).

107 is also:

In sports edit

See also edit

References edit

  1. ^ "Sloane's A109611 : Chen primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
  2. ^ "Sloane's A000043 : Mersenne exponents". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
  3. ^ "Sloane's A005385 : Safe primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
  4. ^ "Sloane's A060843 : Busy Beaver problem: number of steps before halting". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2021-09-24.
  5. ^ Sloane, N. J. A. (ed.). "Sequence A006785 (Number of triangle-free graphs on n vertices)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.