523

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Number

$523$ (five hundred and twenty-three) is:

The $99$th prime number

The $1$st element of the $1$st sequence of $3$ consecutive positive integers whose Euler $\phi$ values are strictly decreasing:

$\map \phi {523} = 522$, $\map \phi {524} = 260$, $\map \phi {525} = 240$

The larger of the $25$th pair of twin primes:

$523 - 521 = 2$

The $34$th left-truncatable prime after $2$, $3$, $5$, $7$, $\ldots$, $197$, $223$, $283$, $313$, $317$, $337$, $347$, $353$, $367$, $373$, $383$, $397$, $443$, $467$

Also see

• First Sequence of Three Consecutive Strictly Decreasing Euler Phi Values

• Previous  ... Next: Left-Truncatable Prime

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

Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $523$