103 (number)

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

In mathematics

103 is a prime number, and the largest prime factor of <math>6!+1=721=7\cdot 103</math>.<ref>Template:Cite OEIS</ref> The previous prime is 101. This makes 103 a twin prime.<ref>Template:Cite OEIS</ref> It is the fifth irregular prime,<ref>Template:Cite OEIS</ref> because it divides the numerator of the Bernoulli number <math display=block>B_{24}=-\frac{236364091}{2730}=-\frac{103\cdot 2294797}{2730}.</math>

The equation <math>64^3+94^3=103^3+1</math> makes 103 part of a "Fermat near miss".<ref>Template:Cite OEIS</ref>

There are 103 different connected series-parallel partial orders on exactly six unlabeled elements.<ref>Template:Cite OEIS</ref>

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.<ref>Template:Cite OEIS</ref>

References

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