103 (number)

← 102 103 104 →
← 100 101 102 103 104 105 106 107 108 109 → List of numbers; 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
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

103 is a prime number, and the largest prime factor of $6!+1=721=7\cdot 103$ .^[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 $B_{24}=-{\frac {236364091}{2730}}=-{\frac {103\cdot 2294797}{2730}}.$

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

In science

103 is the atomic number of lawrencium, a radioactive element named after Ernest Lawrence.

References

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