Titanic Prime consisting of 111 Blocks of each Digit plus Zeroes

Theorem

The integer defined as:

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

where $\paren a_b$ means $b$ instances of $a$ in a string, is a titanic prime.

Proof

It is noted that it has $9 \times 111 + 2284 + 1 = 3284$ digits, making it titanic.

It can be expressed arithmetically as:

$123456789 \times \dfrac {10^{999} - 1} {10^9 - 1} \times 10^{2285} + 1$

It was checked that it is a prime number using the "Alpertron" Integer factorisation calculator on $6$th March $2022$.

This took approximately $50.2$ seconds.

Historical Note

This titanic prime was discovered by Harvey Dubner in December $1985$.

When David Wells reported on this number in his Curious and Interesting Numbers, 2nd ed. of $1997$, he mistakenly expressed the number as:

$\paren 1_{111} \paren 2_{111} \paren 3_{111} \paren 4_{111} \paren 5_{111} \paren 6_{111} \paren 7_{111} \paren 8_{111} \paren 9_{111} \paren 0_{2284} 1$

which it is not.

Sources

• 1985: Harvey Dubner: (unknown) (J. Recr. Math. Vol. 18)
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $\paren 1_{111} \paren 2_{111} \paren 3_{111} \ldots \paren 8_{111} \paren 9_{111} \paren 0_{2284} 1$