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103 (number)

From Wikipedia, the free encyclopedia
Not to be confused with103 AD or103 BC.
Natural number
← 102103 104 →
Cardinalone hundred three
Ordinal103rd
(one hundred third)
Factorizationprime
Prime27th
Greek numeralΡΓ´
Roman numeralCIII,ciii
Binary11001112
Ternary102113
Senary2516
Octal1478
Duodecimal8712
Hexadecimal6716

103 (one hundred [and] three) is thenatural number following102 and preceding104.

In mathematics

[edit]

103 is a prime number, and the largest prime factor of6!+1=721=7⋅103{\displaystyle 6!+1=721=7\cdot 103}.[1] The previous prime is101. This makes 103 atwin prime.[2] It is the fifthirregular prime,[3] because it divides the numerator of theBernoulli numberB24=−2363640912730=−103⋅22947972730.{\displaystyle B_{24}=-{\frac {236364091}{2730}}=-{\frac {103\cdot 2294797}{2730}}.}

The equation643+943=1033+1{\displaystyle 64^{3}+94^{3}=103^{3}+1} makes 103 part of a "Fermat near miss".[4]

There are 103 different connectedseries-parallel partial orders on exactly six unlabeled elements.[5]

103 is conjectured to be the smallest number for which repeatedly reversing the digits of itsternary representation, and adding the number to its reversal, does not eventually reach a ternarypalindrome.[6]

References

[edit]
  1. ^Sloane, N. J. A. (ed.)."Sequence A002583 (Largest prime factor of n! + 1)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ^Sloane, N. J. A. (ed.)."Sequence A001097 (Twin primes)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^Sloane, N. J. A. (ed.)."Sequence A000928 (Irregular primes)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. ^Sloane, N. J. A. (ed.)."Sequence A050791 (Consider the Diophantine equation x^3 + y^3 = z^3 + 1 (1 < x < y < z) or 'Fermat near misses'. Sequence gives values of z in monotonic increasing order.)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. ^Sloane, N. J. A. (ed.)."Sequence A007453 (Number of unlabeled connected series-parallel posets with n nodes)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  6. ^Sloane, N. J. A. (ed.)."Sequence A066450 (Conjectured value of the minimal number to which repeated application of the "reverse and add!" algorithm in base n does not terminate in a palindrome)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
0 to 199
200 to 399
400 to 999
1000s and 10,000s
1000s
10,000s
100,000s to 10,000,000,000,000s


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