1,111,111,111,111,111,111

Previous  ... Next

Number

$1 \, 111 \, 111 \, 111 \, 111 \, 111 \, 111$ is:

A prime number

The $2$nd repunit prime

The $13$th unique period prime after $3$, $11$, $37$, $101$, $9091$, $9901$, $333 \, 667$, $909 \, 091$, $99 \, 990 \, 001$, $999 \, 999 \, 000 \, 001$, $9 \, 999 \, 999 \, 900 \, 000 \, 001$, $909 \, 090 \, 909 \, 090 \, 909 \, 091$: its period is $19$:

$\dfrac 1 {1 \, 111 \, 111 \, 111 \, 111 \, 111 \, 111} = 0 \cdotp \dot 00000 \, 00000 \, 00000 \, 000 \dot 9$

The $19$th repunit

The $23$rd permutable prime after $2$, $3$, $5$, $7$, $11$, $13$, $17$, $31$, $37$, $71$, $73$, $79$, $97$, $113$, $131$, $199$, $311$, $337$, $373$, $733$, $919$, $991$

Also see

• Repunit 19 is Unique Period Prime with Period 19

• Previous  ... Next: Repunit Prime
• Previous  ... Next: Permutable Prime
• Previous  ... Next: Repunit
• Previous  ... Next: Unique Period Prime
• Previous  ... Next: Prime Number

Historical Note

The prime nature of $1 \, 111 \, 111 \, 111 \, 111 \, 111 \, 111$ was discovered by a reader of one of Henry Ernest Dudeney's newspaper puzzle columns in $1918$.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $1,111,111,111,111,111,111$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1,111,111,111,111,111,111$