163

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Number

$163$ (one hundred and sixty-three) is:

The $38$th prime number

The $9$th prime number after $53$, $71$, $103$, $107$, $109$, $149$, $151$, $157$ which cannot be expressed as either the sum of or the difference between a power of $2$ and a power of $3$

The $33$rd lucky number:

$1$, $3$, $7$, $9$, $13$, $15$, $21$, $\ldots$, $115$, $127$, $129$, $133$, $135$, $141$, $151$, $159$, $163$, $\ldots$

This expression relating $e$ and $\pi$ comes within $10^{-12}$ of an integer:

$e^{\pi \sqrt {163} } \approx 262 \, 537 \, 412 \, 640 \, 768 \, 743 \cdotp 99999 \, 99999 \, 99250 \ldots$

Also see

• Approximate Relations between $\pi$ and $e$: $e^{\pi \sqrt{163} }$

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

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $163$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $163$