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103 (number)

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Short description: Natural number
← 102 103 104 →
Cardinalone hundred three
Ordinal103rd
(one hundred third)
Factorizationprime
Prime27th
Greek numeralΡΓ´
Roman numeralCIII
Binary11001112
Ternary102113
Quaternary12134
Quinary4035
Senary2516
Octal1478
Duodecimal8712
Hexadecimal6716
Vigesimal5320
Base 362V36

103 (one hundred [and] three) is the natural number following 102 and preceding 104.

In mathematics

103 is a prime number, the largest prime factor of [math]\displaystyle{ 6!+1=721=7\cdot 103 }[/math].[1] The previous prime is 101, making them both twin primes.[2] It is the fifth irregular prime,[3] because it divides the numerator of the Bernoulli number [math]\displaystyle{ B_{24}=-\frac{236364091}{2730}=-\frac{103\cdot 2294797}{2730}. }[/math]

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

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

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

See also

  • 103 (disambiguation)

References

  1. ↑ Sloane, N. J. A., ed. "Sequence A002583 (Largest prime factor of n! + 1)". OEIS Foundation. https://oeis.org/A002583. 
  2. ↑ Sloane, N. J. A., ed. "Sequence A001097 (Twin primes)". OEIS Foundation. https://oeis.org/A001097. 
  3. ↑ Sloane, N. J. A., ed. "Sequence A000928 (Irregular primes)". OEIS Foundation. https://oeis.org/A000928. 
  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.)". OEIS Foundation. https://oeis.org/A050791. 
  5. ↑ Sloane, N. J. A., ed. "Sequence A007453 (Number of unlabeled connected series-parallel posets with n nodes)". OEIS Foundation. https://oeis.org/A007453. 
  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)". OEIS Foundation. https://oeis.org/A066450. 


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