Alternating Even-Odd Digit Palindromic Prime
Theorem
Let the notation $\left({abc}\right)_n$ be interpreted to mean $n$ consecutive repetitions of a string of digits $abc$ concatenated in the decimal representation of an integer.
The integer:
- $\left({10987654321234567890}\right)_{42} 1$
has the following properties:
- it is a palindromic prime with $841$ digits
- its digits are alternately odd and even.
Proof
By brute force, one supposes.
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Sources
- 1994: Harvey Dubner: Palindromic Primes with a Palindromic Prime Number of Digits (J. Recr. Math. Vol. 26, no. 4: 256)
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $\left({10987654321234567890}\right)_{42} 1$
