One day, Cheryl and Betty list down possibilities for their birthday dates.
By some strange coincidence, they wrote the same possibilities for their birthday dates.
|Jun 4||Jun 6||Jun 8|
|Jul 4||Jul 5||Jul 6||Jul 8|
|Aug 4||Aug 5||Aug 7||Aug 9|
|Sep 3||Sep 5||Sep 7||Sep 10|
Cheryl then told Betty the day of month of her birthday.
Betty told Cheryl the month of her birthday.
Cheryl: "I know that Betty does not know my birthday."
Betty: "Cheryl does not also know my birthday and my birthday is not on Sep 5."
Cheryl: "You gave me redundant information and my birthday is not on Aug 7."
Betty: "Now I know your birthday and the day of the month of my birthday is a prime number."
Cheryl: "Now I know your birthday."
What is the difference (in days) between Betty's and Cheryl's birthday? (both dates inclusive).