103 (number)

Not to be confused with 103 AD or 103 BC.

Natural number

| ← 102  | 103 |  104 →

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← 100 101 102 103 104 105 106 107 108 109 →

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* Integers

← 0 100 200 300 400 500 600 700 800 900 →

Cardinal| one hundred three
Ordinal| 103rd
(one hundred third)
Factorization| prime
Prime| 27th
Greek numeral| ΡΓ´
Roman numeral| CIII, ciii
Binary| 11001112
Ternary| 102113
Senary| 2516
Octal| 1478
Duodecimal| 8712
Hexadecimal| 6716

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

## In mathematics

[edit]

103 is a prime number, and the largest prime factor of  6 ! + 1 = 721 = 7 ⋅ 103 {\displaystyle 6!+1=721=7\cdot 103} .[1] The previous prime is 101. This makes 103 a twin prime.[2] It is the fifth irregular prime,[3] because it divides the numerator of the Bernoulli number B 24 = − 236364091 2730 = − 103 ⋅ 2294797 2730 . {\displaystyle B_{24}=-{\frac {236364091}{2730}}=-{\frac {103\cdot 2294797}{2730}}.}

The equation  64 3 + 94 3 = 103 3 + 1 {\displaystyle 64^{3}+94^{3}=103^{3}+1} 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]

## References

[edit]

1. ^ Sloane, N. J. A. (ed.). "Sequence A002583 (Largest prime factor of n! + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
2. ^ Sloane, N. J. A. (ed.). "Sequence A001097 (Twin primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
3. ^ Sloane, N. J. A. (ed.). "Sequence A000928 (Irregular primes)". The On-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.)". The On-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)". The On-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)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

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1000s

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* 1980
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* 2000
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* 2520
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* 3511
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* 4104
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* 5040
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* 6174
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* 7744
* 7825
* 8000
* 8128
* 8192
* 9000
* 9855
* 9999

* 10,000
* 16,807
* 20,000
* 30,000
* 40,000
* 50,000
* 60,000
* 64,079
* 65,535
* 65,536
* 65,537
* 70,000
* 80,000
* 90,000

* 100,000
* 142,857
* 144,000
* 1,000,000
* 10,000,000
* 43,112,609
* 100,000,000
* 1,000,000,000
* 2,147,483,647
* 4,294,967,295
* 10,000,000,000
* 100,000,000,000

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