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 Pairs of primes (Posted on 2019-07-27)
Imagine a bag containing cards representing all n-digit odd numbers. A random card is drawn and two new numbers are created by preceding the drawn number by each of its even neighbors.

What is the probability that each of those 2 numbers is prime?

Examples:
For n=1 there are 5 cards i.e. 1,3,5,7 and 9. Clearly only numbers 3 and 9 qualifiy since fboth 23 and 43 are primes and so are 89 and 109 & there are no other answers. So for n=1 p=0.4 is the probability we were looking for.
For n=2 I will not provide the answer but will show you one of the qualifying numbers e.g. 69, since both 6869 and 7069 are prime.

Now evaluate the correct probabilities for n=2,3, ...8,9 (or as far as your resources allow) - and you will get a sequence for which you may be credited @ OEIS.

So this time you get a task both challenging and rewarding!
GOOD LUCK...

 No Solution Yet Submitted by Ady TZIDON No Rating

 Subject Author Date An extension Charlie 2019-07-31 10:50:14 re(2): via computer - the start of the soln Steven Lord 2019-07-30 17:00:40 Re how far can one go Ady TZIDON 2019-07-30 02:56:30 A remark re OEIS Ady TZIDON 2019-07-30 02:46:43 a note re further computer searches xdog 2019-07-28 19:07:49 re: via computer - the start of the soln Charlie 2019-07-28 07:58:12 re(2): computer solution through n=6 list continued Charlie 2019-07-27 22:01:14 re: computer solution through n=6 list continued Charlie 2019-07-27 22:00:18 computer solution through n=6 Charlie 2019-07-27 21:57:42 via computer - the start of the soln Steven Lord 2019-07-27 13:16:57

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