Glitch Prime Numbers and Cyclops Numbers

Glitch Prime

A glitch number is a number where all the digits are the same and the middle digit is a different digit. A glitch prime is a number with above property but which is prime.

Following is an example of glitch prime.

99 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 989 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999 999

It has digit 8 in the middle of the long sequence of repeating digit 9.

A glitch number can be written in the form of 10^2M – 10^M – 1. Some of the glitch prime numbers occurs for the following M.

M={1,6,9,154,253,1114,1390}

Cyclops Number

A Cyclops Number is a binary number will all ones except for the middle digit. 101, 11011, 1110111, 111101111, 11111011111 are some of the examples.

It can be given using following formula.

2^2M+1 – 2M – 1

Only prime walu occurs when M = 1 ; Which gives us the value 101. It is 5 in base 10.