Quite a few years ago (I can't remember the date but it was obviously some time after I first met Ernie at a New Years Eve party in 2001) I got an unexpected phone call late one afternoon. It was Ernie. He told me that it was his wedding anniversary and he had secretly bought two tickets to see the famous psychic Madame Mu as a surprise for his wife. Unfortunately, his wife was called out of town on unexpected business wouldn't be able to attend. Ernie was in need of company, so if I wanted to see the show with him, I should turn up at the Palais no later than 8.30 pm that evening.
I arrived in time to meet Ernie and we entered the auditorium . The lights dimmed and the curtain rose to show Madame Mu, dressed in a scarlet robe and emerald turban, standing center-stage. The show was very entertaining. A search-light would raster across the audience before stopping on someone who would be invited to speak with Madame Mu. She would ask them to introduce themselves and then, by "communing with the spirit world", she would reveal various facts about them.
About halfway into the show, the spot-light landed on Ernie, who rose and walked down to the stage. He introduced himself as an inventor and amateur mathematician, and Madame Mu announced she would attempt something "a little special" here and would try to "channel the great German mathematician, Carl Fredrich Gauss". The lights dimmed, Madame Mu slumped slightly - seemingly in deep meditation - there was a short pause, then she raised her head again.
"Good evening Ernest", said Mu/Gauss in a strong German accent, "let me entertain you with a little mind reading and lightning calculation". The following conversation then took place:
Mu/Gauss: "If you concatenate the day (1..31), month (1..12), and year of your birth (4 digits), in that order, you will get a number divisible by 7. Correct?".
Ernie: "That is true - but there is a 1 in 7 chance it would be true for any random birthday".
Mu/Gauss: "If you concatenate the year, month, and day of your birth, in that order, you will get a number divisible by 11. Correct?".
Mu/Gauss: "If you concatenate the month, day, and year of your birth, in that order, you will get a number divisible by 13. Correct?".
Ernie: "Correct - and only about 1 in 1000 you could get that right by chance".
Mu/Gauss: "If you add together, those three numbers you just calculated plus your age in whole years, you will get a prime."
Ernie (after a short pause for calculation): "You're right again - the calculation works as you say!"
Mu/Gauss: "And by an amazing coincidence, the same five facts are also true for your father - correct?"
Ernie (after another pause): "Amazing - all true!"
Mu/Gauss: "Thank you Ernest, please return to your seat and enjoy the rest of the show. But as you go, can you confirm your father is currently twice your age in years?"
Ernie: (returning to his seat) "In whole years, yes, that's true."
Later Ernie told me exactly how Mu did her trickery: something to do with internet searches, a hidden radio earpiece, and an accomplice with a "top model clockwork calculator", but that isn't the mystery of this story. As you probably know by now, I'm great at recollecting conversations, but hopeless at remembering numbers. I want to send Ernie a card on his next birthday. I can't remember the date but believe there is sufficient information in this story to calculate not only is date of birth. Can you help me?
PS - As an added note, it may help to know that Ernie's father is alive and well and nothing out of the ordinary in years of age.
ADDENDUM: in case it isn't clear, according to what Ernie told me after the show "those three numbers" refer to the three numbers divisible by 7, 11, and 13 respectively, not the three numbers that make up the date.