Every Day Counts
Carol Prime Days
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These are primes which are also Carol numbers.

Carol numbers are of the form (2n - 1)2 - 2

Carol numbers were first studied by Cletus Emmanuel, who named them after a friend, Carol G. Kirnon.

The sixth Carol prime is 1,046,527 so it's unlikely you'll ever have more than 5 Carol Prime Days. After that they go very big.