103 (number)
| ||||
|---|---|---|---|---|
| Cardinal | one hundred three | |||
| Ordinal | 103rd (one hundred third) | |||
| Factorization | prime | |||
| Prime | 27th | |||
| Greek numeral | ΡΓ´ | |||
| Roman numeral | CIII | |||
| Binary | 11001112 | |||
| Ternary | 102113 | |||
| Quaternary | 12134 | |||
| Quinary | 4035 | |||
| Senary | 2516 | |||
| Octal | 1478 | |||
| Duodecimal | 8712 | |||
| Hexadecimal | 6716 | |||
| Vigesimal | 5320 | |||
| Base 36 | 2V36 | |||
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
- ↑ Sloane, N. J. A., ed. "Sequence A002583 (Largest prime factor of n! + 1)". OEIS Foundation. https://oeis.org/A002583.
- ↑ Sloane, N. J. A., ed. "Sequence A001097 (Twin primes)". OEIS Foundation. https://oeis.org/A001097.
- ↑ Sloane, N. J. A., ed. "Sequence A000928 (Irregular primes)". OEIS Foundation. https://oeis.org/A000928.
- ↑ 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.
- ↑ Sloane, N. J. A., ed. "Sequence A007453 (Number of unlabeled connected series-parallel posets with n nodes)". OEIS Foundation. https://oeis.org/A007453.
- ↑ 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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