593

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Number

$593$ (five hundred and ninety-three) is:

The $108$th prime number

The largest positive integer that cannot be expressed in the form $23 x + 28 y$ for positive integers $x$ and $y$.

The $10$th balanced prime after $5$, $53$, $157$, $173$, $211$, $257$, $263$, $373$, $563$:

$593 = \dfrac {587 + 599} 2$

The $22$nd right-truncatable prime after $2$, $3$, $5$, $7$, $23$, $29$, $31$, $37$, $53$, $59$, $71$, $73$, $79$, $233$, $239$, $293$, $311$, $313$, $317$, $373$, $379$

The $27$th Sophie Germain prime after $2$, $3$, $5$, $11$, $23$, $29$, $41$, $\ldots$, $233$, $239$, $251$, $281$, $293$, $359$, $419$, $431$, $443$, $491$, $509$:

$2 \times 593 + 1 = 1187$, which is prime.

The $41$st long period prime after $7$, $17$, $19$, $23$, $29$, $\ldots$, $491$, $499$, $503$, $509$, $541$, $571$, $577$

Also see

• Largest Number not Expressible as Sum of Multiples of 23 and 28

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Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $593$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $593$