View source for 103 (number)

{{Infobox number
| number = 103
| factorization = [[Prime number|prime]]
| prime = 27th
}}
'''103''' ('''one hundred [and] three''') is the [[Natural number|natural number]] following [[102 (number)|102]] and preceding [[104 (number)|104]].

==In mathematics==

103 is a [[Prime number|prime number]], the largest prime factor of <math>6!+1=721=7\cdot 103</math>.<ref>{{cite OEIS|A002583|Largest prime factor of n! + 1}}</ref> The previous prime is [[101 (number)|101]], making them both [[Twin prime|twin prime]]s.<ref>{{cite OEIS|A001097|Twin primes}}</ref> It is the fifth [[Irregular prime|irregular prime]],<ref>{{cite OEIS|A000928|Irregular primes}}</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>{{cite OEIS|A050791|2=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.}}</ref>

There are 103 different connected [[Series-parallel partial order|series-parallel partial order]]s on exactly six unlabeled elements.<ref>{{cite OEIS|A007453|Number of unlabeled connected series-parallel posets with n nodes}}</ref>

103 is conjectured to be the smallest number for which repeatedly reversing the digits of its [[Ternary numeral system|ternary representation]], and adding the number to its reversal, does not eventually reach a ternary palindrome.<ref>{{cite OEIS|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}}</ref>

==See also==
* 103 (disambiguation)

==References==
{{Reflist}}


{{Integers|1}}{{Number-stub}}[[Category:Integers]]

{{Sourceattribution|103 (number)}}