Alternating Even-Odd Digit Palindromic Prime

Theorem

Let the notation $\paren {abc}_n$ be interpreted to mean $n$ consecutive repetitions of a string of digits $abc$ concatenated in the decimal representation of an integer.


The integer:

$\paren {10987654321234567890}_{42} 1$

has the following properties:

it is a palindromic prime with $841$ digits
its digits are alternately odd and even.


Proof

It was checked that it is a prime number using the "Alpertron" Integer factorisation calculator on $22$nd March $2022$.

This took approximately $0.4$ seconds.

This number has $20 \times 42 + 1 = 841$ digits.

The remaining properties of this number is obvious by inspection.

$\blacksquare$


Sources

  • 1994: Harvey Dubner: Palindromic Primes with a Palindromic Prime Number of Digits (J. Recr. Math. Vol. 26, no. 4: p. 256)
  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $\left({10987654321234567890}\right)_{42} 1$
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