Titanic Prime consisting of 111 Blocks of each Digit plus Zeroes/Mistake

Source Work

1997: David Wells: Curious and Interesting Numbers (2nd ed.):

The Dictionary

$\paren 1_{111} \paren 2_{111} \paren 3_{111} \ldots \paren 8_{111} \paren 9_{111} \paren 0_{2284} 1$

Mistake

$\paren 1_{111} \paren 2_{111} \paren 3_{111} \ldots \paren 8_{111} \paren 9_{111} \paren 0_{2284} 1 \qquad \qquad$ [$3284$ digits]

The notation indicates that the digits $1$ to $9$ are each repeated $111$ times, followed by $2284$ zeros and a $1$.

The number is prime.

Correction

Sorry, but this is badly wrong.

This prime is reported in Prime Pages as:

$123456789 \times \dfrac {\map {\mathrm R} {999} } {\map {\mathrm R} 9} \times 10^{2285} + 1$

where $\map {\mathrm R} n$ denotes the $n$-digit repunit.

This has been misinterpreted.

The actual number is:

$\paren {123456789}_{111} \paren 0_{2284} 1$

which is not the same thing at all.

We can establish that $123456789 \times \dfrac {\map {\mathrm R} {999} } {\map {\mathrm R} 9} \times 10^{2285} + 1$ is composite, with a factor $397$.

There are primes of the form $\paren 1_{111} \paren 2_{111} \paren 3_{111} \ldots \paren 8_{111} \paren 9_{111} \paren 0_x 1$, where $0 \le x \le 5000$: as follows

$x = 399$

$x = 1667$

$x = 1918$

but this is far off the mark of what Harvey Dubner discovered.

Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $\paren 1_{111} \paren 2_{111} \paren 3_{111} \ldots \paren 8_{111} \paren 9_{111} \paren 0_{2284} 1$