103

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Number

$103$ (one hundred and three) is:

The $27$th prime number

The smallest prime number the period of whose decimal expansion is $\dfrac 1 3$ of its maximum length, that is: $34$:

$\dfrac 1 {103} = 0 \cdotp \dot 00970 \, 87378 \, 64077 \, 66990 \, 29126 \, 21359 \, 223 \dot 3$

The $3$rd prime number after $53, 71$ which cannot be expressed as either the sum of or the difference between a power of $2$ and a power of $3$.

The larger of the $9$th pair of twin primes, with $101$

The $21$st happy number after $1$, $7$, $10$, $13$, $19$, $23$, $28$, $31$, $32$, $44$, $49$, $68$, $70$, $79$, $82$, $86$, $91$, $94$, $97$, $100$:

$103 \to 1^2 + 0^2 + 3^2 = 10 \to 1^2 + 0^2 = 1$

The $37$th odd positive integer that cannot be expressed as the sum of exactly $4$ distinct non-zero square numbers all of which are coprime

$1$, $\ldots$, $37$, $41$, $43$, $45$, $47$, $49$, $53$, $55$, $59$, $61$, $67$, $69$, $73$, $77$, $83$, $89$, $97$, $101$, $103$, $\ldots$

Also see

• 103 is Smallest Prime whose Period of Reciprocal is One Third of Maximal

• Previous  ... Next: Primes not Sum of or Difference between Powers of 2 and 3

• Previous  ... Next: Happy Number

• Previous  ... Next: Prime Number
• Previous  ... Next: Twin Primes

• Previous  ... Next: Odd Numbers Not Expressible as Sum of 4 Distinct Non-Zero Coprime Squares

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $103$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $103$